title

Basic Maths for DSA | Euclidean Algorithm | Strivers A2Z DSA Course

description

Full Course: https://takeuforward.org/strivers-a2z-dsa-course/strivers-a2z-dsa-course-sheet-2/
There is a slight mistake on the logic of Armstrong, it will be 1634 = (1^4 + 6^4 + 3^4 + 4^4), basically digits raised to the power count of digits, so sum = sum + pow(ld, cntDigits) will be the change, where the cntDigits is the number of digits.
Notes:
Count Digits: https://takeuforward.org/data-structure/count-digits-in-a-number/
Reverse a Number: https://takeuforward.org/c-programs/reverse-a-number-in-c/
Check Palindrome: https://takeuforward.org/data-structure/check-if-a-number-is-palindrome-or-not/
Gcd or HCF: https://takeuforward.org/data-structure/find-gcd-of-two-numbers/
Armstrong Number: https://takeuforward.org/maths/check-if-a-number-is-armstrong-number-or-not/
Print all Divisors: https://takeuforward.org/data-structure/print-all-divisors-of-a-given-number/
Check for prime: https://takeuforward.org/data-structure/check-if-a-number-is-prime-or-not/
Submit the problems here:
Count Digits: https://bit.ly/3X17nIr
Reverse Number: https://bit.ly/3vCeBXS
Palindrome: https://bit.ly/3vylgCi
Armstrong: https://bit.ly/3vBfkbD
Print Divisors: https://bit.ly/3vzQ7yr
Check Prime: https://bit.ly/3ZdiWOO
HCF/GCD: https://bit.ly/3GB4Mj8
In case you are thinking to buy courses, please check below:
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You can follow me across social media, all my handles are below:
Linkedin/Instagram/Telegram: https://linktr.ee/takeUforward

detail

{'title': 'Basic Maths for DSA | Euclidean Algorithm | Strivers A2Z DSA Course', 'heatmap': [{'end': 840.912, 'start': 684.174, 'weight': 0.741}, {'end': 954.804, 'start': 906.045, 'weight': 0.817}, {'end': 1453.766, 'start': 1405.43, 'weight': 0.762}, {'end': 1598.886, 'start': 1543.691, 'weight': 0.979}, {'end': 2130.293, 'start': 2051.293, 'weight': 0.833}, {'end': 2700.584, 'start': 2620.047, 'weight': 0.926}, {'end': 3202.761, 'start': 3148.922, 'weight': 0.844}, {'end': 3686.669, 'start': 3533.462, 'weight': 0.723}], 'summary': "India's in-depth dsa course covers 455 modules, starting with basic maths; it progresses to advanced mathematics, time complexity concepts, reversing numbers, identifying palindromes and armstrong numbers, finding factors efficiently, efficient printing, prime numbers, and the euclidean algorithm for gcd with o(log(phi) min(a, b)) time complexity.", 'chapters': [{'end': 79.945, 'segs': [{'end': 38.409, 'src': 'embed', 'start': 3.493, 'weight': 0, 'content': [{'end': 4.693, 'text': 'hey, everyone, welcome back to the channel.', 'start': 3.493, 'duration': 1.2}, {'end': 6.534, 'text': 'i hope you guys are doing extremely well.', 'start': 4.693, 'duration': 1.841}, {'end': 14.597, 'text': "so this video is going to be another video from the strivers a2z dsa course and this is india's most in-depth ds algo course.", 'start': 6.534, 'duration': 8.063}, {'end': 15.317, 'text': 'why do i see that?', 'start': 14.597, 'duration': 0.72}, {'end': 18.698, 'text': 'because this course has 455 modules.', 'start': 15.317, 'duration': 3.381}, {'end': 23.62, 'text': 'i can guarantee you that you can take any paid batches, any free courses.', 'start': 18.698, 'duration': 4.922}, {'end': 26.582, 'text': 'none of those courses will have 455 modules.', 'start': 23.62, 'duration': 2.962}, {'end': 38.409, 'text': 'this is an extremely in-depth ds algo course that can teach you everything in breadth about ds algo and in the previous videos we have covered step 1.1 and 1.2,', 'start': 26.582, 'duration': 11.827}], 'summary': "India's most in-depth ds algo course with 455 modules.", 'duration': 34.916, 'max_score': 3.493, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug3493.jpg'}, {'end': 79.945, 'src': 'embed', 'start': 48.936, 'weight': 1, 'content': [{'end': 54.62, 'text': "if you need a video now, you can go to youtube and you'll find a lot of other resources from where where you can study.", 'start': 48.936, 'duration': 5.684}, {'end': 58.383, 'text': 'so in this video we will be discussing about basic maths.', 'start': 54.62, 'duration': 3.763}, {'end': 60.844, 'text': 'why am i teaching just the basic maths as of now?', 'start': 58.383, 'duration': 2.461}, {'end': 62.746, 'text': "so you're starting off as of now.", 'start': 60.844, 'duration': 1.902}, {'end': 64.427, 'text': 'your brain will not be that matured.', 'start': 62.746, 'duration': 1.681}, {'end': 70.934, 'text': "so if i teach you the advanced level concepts, you might understand, but it won't be that convenient for you.", 'start': 64.427, 'duration': 6.507}, {'end': 73.237, 'text': 'that is why my teaching way is very different.', 'start': 70.934, 'duration': 2.303}, {'end': 79.945, 'text': 'what i do is i usually start off with the basic stuffs, i give you a lot of time to absorb it and then we move on to the advanced part.', 'start': 73.237, 'duration': 6.708}], 'summary': "The video discusses basic math due to the audience's maturity level and teaching approach.", 'duration': 31.009, 'max_score': 48.936, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug48936.jpg'}], 'start': 3.493, 'title': "India's in-depth dsa course", 'summary': "Discusses india's most in-depth dsa course with 455 modules, covering basic maths first to help beginners absorb the concepts before moving on to advanced topics.", 'chapters': [{'end': 79.945, 'start': 3.493, 'title': 'In-depth dsa course overview', 'summary': "Discusses india's most in-depth dsa course with 455 modules, covering basic maths first to help beginners absorb the concepts before moving on to advanced topics.", 'duration': 76.452, 'highlights': ["The course has 455 modules, making it India's most in-depth DSA course, surpassing both paid and free courses in breadth of content.", 'The instructor focuses on teaching basic maths first to allow beginners to absorb the concepts before moving on to advanced topics.', 'The instructor follows a teaching method that starts with basic concepts, giving students ample time to absorb before moving on to advanced material.']}], 'duration': 76.452, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug3493.jpg', 'highlights': ["The course has 455 modules, making it India's most in-depth DSA course, surpassing both paid and free courses in breadth of content.", 'The instructor focuses on teaching basic maths first to allow beginners to absorb the concepts before moving on to advanced topics.', 'The instructor follows a teaching method that starts with basic concepts, giving students ample time to absorb before moving on to advanced material.']}, {'end': 806.852, 'segs': [{'end': 158.683, 'src': 'embed', 'start': 79.945, 'weight': 0, 'content': [{'end': 88.254, 'text': 'this is why all the basic stuffs are initially there and then we move on to the ds algo and in the step 8 we have a section as advanced mathematics.', 'start': 79.945, 'duration': 8.309}, {'end': 91.218, 'text': "we'll be covering everything that is related to advanced mathematics.", 'start': 88.254, 'duration': 2.964}, {'end': 95.662, 'text': 'that might be asked in interviews, but as of now we will be learning basic maths.', 'start': 91.218, 'duration': 4.444}, {'end': 102.704, 'text': "now. these are the problems which we will be solving, but before that let's learn some basic maths concept.", 'start': 95.662, 'duration': 7.042}, {'end': 109.928, 'text': "so before solving all the problems that are listed under basic maths, we'll be starting off with the basic maths concept.", 'start': 102.704, 'duration': 7.224}, {'end': 115.732, 'text': "i'll be teaching you the concepts initially and then we can solve all the problems listed under the section.", 'start': 109.928, 'duration': 5.804}, {'end': 119.314, 'text': "the first concept that i'll be teaching you is the digit concept.", 'start': 115.732, 'duration': 3.582}, {'end': 126.989, 'text': 'remember one thing this is a very, very important concept, because if you know how to play around digits,', 'start': 119.314, 'duration': 7.675}, {'end': 130.571, 'text': "then you'll be able to solve most of the problems in basic maths.", 'start': 126.989, 'duration': 3.582}, {'end': 132.732, 'text': "Let's understand the digit concept.", 'start': 131.131, 'duration': 1.601}, {'end': 137.695, 'text': 'Imagine I give you a number like 7789.', 'start': 133.273, 'duration': 4.422}, {'end': 139.316, 'text': "This is the number that I'm giving you.", 'start': 137.695, 'duration': 1.621}, {'end': 143.558, 'text': 'Now I ask you to perform extraction of digits.', 'start': 139.656, 'duration': 3.902}, {'end': 147.319, 'text': 'i ask you to perform extraction of digits.', 'start': 144.398, 'duration': 2.921}, {'end': 155.402, 'text': "let's learn the extraction of digits and after that you will see how we can implement the extraction of digits in order to solve most of the problems.", 'start': 147.319, 'duration': 8.083}, {'end': 158.683, 'text': 'okay, so when i say extraction of digits, what does it mean?', 'start': 155.402, 'duration': 3.281}], 'summary': 'Training covers basic and advanced mathematics for interview preparation, starting with digit extraction concept.', 'duration': 78.738, 'max_score': 79.945, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug79945.jpg'}, {'end': 315.174, 'src': 'embed', 'start': 290.62, 'weight': 4, 'content': [{'end': 298.044, 'text': 'so once you have 778 with you, if i need the last digit, which is 8, how do you extract it again?', 'start': 290.62, 'duration': 7.424}, {'end': 301.846, 'text': 'the same way you say can i divide, modularize with?', 'start': 298.044, 'duration': 3.802}, {'end': 302.927, 'text': 'uh, 10?', 'start': 301.846, 'duration': 1.081}, {'end': 305.789, 'text': "If I do a mod of 10, I'll actually get 8..", 'start': 302.927, 'duration': 2.862}, {'end': 312.212, 'text': 'Why? Because the nearest number will be 770, which is divisible by 10, which will still leave a remainder of 8.', 'start': 305.789, 'duration': 6.423}, {'end': 315.174, 'text': 'So, I get the digit 8 as well.', 'start': 312.212, 'duration': 2.962}], 'summary': 'Modulus operation with 778 and 10 returns the last digit as 8.', 'duration': 24.554, 'max_score': 290.62, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug290620.jpg'}, {'end': 439.798, 'src': 'embed', 'start': 406.233, 'weight': 6, 'content': [{'end': 409.536, 'text': 'so this is how you can easily extract all the digits.', 'start': 406.233, 'duration': 3.303}, {'end': 412.879, 'text': 'so if i try to write the pseudocode, how will the pseudocode look like?', 'start': 409.536, 'duration': 3.343}, {'end': 416.842, 'text': 'can i say if i have the n, i can take, take it from the user.', 'start': 412.879, 'duration': 3.963}, {'end': 421.526, 'text': "I can take the N from the user and imagine I'm asking you to print all the digits.", 'start': 417.603, 'duration': 3.923}, {'end': 426.309, 'text': 'Extract all the digits like 9877 and you can print it.', 'start': 422.106, 'duration': 4.203}, {'end': 428.53, 'text': "So how will you do it? It's very simple.", 'start': 426.649, 'duration': 1.881}, {'end': 431.812, 'text': 'I will be like, okay, while I know what is the last step.', 'start': 429.331, 'duration': 2.481}, {'end': 439.798, 'text': 'Last step is the extraction goes on from N, when it is 7789, to N till zero.', 'start': 432.353, 'duration': 7.445}], 'summary': 'A method to extract and print all digits from a given number n is described using pseudocode.', 'duration': 33.565, 'max_score': 406.233, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug406233.jpg'}], 'start': 79.945, 'title': 'Basic concepts in advanced mathematics', 'summary': 'Covers the initial basic concepts before progressing to advanced mathematics, emphasizing the importance of the digit concept in solving basic math problems. it also explains how to extract and count digits in a number using modulo operator, division by 10, and logarithmic approach, along with providing a pseudocode for the same.', 'chapters': [{'end': 158.683, 'start': 79.945, 'title': 'Basic concepts in advanced mathematics', 'summary': 'Covers the initial basic concepts before progressing to advanced mathematics, focusing on the importance of the digit concept in solving basic math problems.', 'duration': 78.738, 'highlights': ['The chapter emphasizes the importance of understanding the digit concept, highlighting its crucial role in solving most basic math problems.', 'The instructor will cover everything related to advanced mathematics that might be asked in interviews, with a focus on initially teaching basic math concepts.', 'Before solving the listed problems, the instructor will start by teaching basic math concepts, ensuring a strong foundation for problem-solving.', 'The chapter introduces the concept of extraction of digits, illustrating its relevance in solving a variety of problems in basic mathematics.']}, {'end': 806.852, 'start': 158.683, 'title': 'Extracting digits and counting digits', 'summary': 'Explains the concept of extracting digits from a number using modulo operator and division by 10, and then demonstrates how to count the digits in a number using the extraction technique and logarithmic approach, providing a pseudocode for the same.', 'duration': 648.169, 'highlights': ['The chapter explains the concept of extracting digits from a number using modulo operator and division by 10. It demonstrates how to extract each individual digit from a number by performing modulo 10 and division by 10, providing a step-by-step explanation.', 'Demonstrates how to count the digits in a number using the extraction technique and logarithmic approach. It shows how to count the digits by using the extraction technique and then introduces an alternative approach using the logarithmic function to find the count of digits in a number.', 'Provides a pseudocode for extracting and counting the digits in a number. It offers a pseudocode to implement the process of extracting and counting the digits, providing a clear and structured approach to solving such problems.']}], 'duration': 726.907, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug79945.jpg', 'highlights': ['The chapter emphasizes the importance of understanding the digit concept, highlighting its crucial role in solving most basic math problems.', 'The chapter introduces the concept of extraction of digits, illustrating its relevance in solving a variety of problems in basic mathematics.', 'The instructor will cover everything related to advanced mathematics that might be asked in interviews, with a focus on initially teaching basic math concepts.', 'Before solving the listed problems, the instructor will start by teaching basic math concepts, ensuring a strong foundation for problem-solving.', 'The chapter explains the concept of extracting digits from a number using modulo operator and division by 10. It demonstrates how to extract each individual digit from a number by performing modulo 10 and division by 10, providing a step-by-step explanation.', 'Demonstrates how to count the digits in a number using the extraction technique and logarithmic approach. It shows how to count the digits by using the extraction technique and then introduces an alternative approach using the logarithmic function to find the count of digits in a number.', 'Provides a pseudocode for extracting and counting the digits in a number. It offers a pseudocode to implement the process of extracting and counting the digits, providing a clear and structured approach to solving such problems.']}, {'end': 1171.963, 'segs': [{'end': 954.804, 'src': 'heatmap', 'start': 878.077, 'weight': 0, 'content': [{'end': 884.219, 'text': 'that is why the time complexity is log base 10 n got it whenever there is division.', 'start': 878.077, 'duration': 6.142}, {'end': 890.961, 'text': 'remember this whenever there is division, if the division is happening by 10, you say log base 10 n.', 'start': 884.219, 'duration': 6.742}, {'end': 894.722, 'text': 'if the division is happening by 2, you say log base 2 n.', 'start': 890.961, 'duration': 3.761}, {'end': 899.363, 'text': 'if the, if the division is happening by 5, you say log base 5 n.', 'start': 894.722, 'duration': 4.641}, {'end': 902.564, 'text': 'this is how you compute the time complexity of like.', 'start': 899.363, 'duration': 3.201}, {'end': 903.104, 'text': 'this is.', 'start': 902.564, 'duration': 0.54}, {'end': 906.045, 'text': 'this is how the logarithmic time complexities are.', 'start': 903.104, 'duration': 2.941}, {'end': 915.11, 'text': "so whenever you're writing a logic where the number of iterations depends on division and you are dividing, dividing,", 'start': 906.045, 'duration': 9.065}, {'end': 920.573, 'text': 'that is when something like logarithmic will come into the time complexity.', 'start': 915.11, 'duration': 5.463}, {'end': 922.935, 'text': 'that time, the time complexity will not be b go of n.', 'start': 920.573, 'duration': 2.362}, {'end': 929.134, 'text': 'If the number of iterations is based on division, time complexity will be logarithmic.', 'start': 923.872, 'duration': 5.262}, {'end': 930.334, 'text': 'Remember this always.', 'start': 929.274, 'duration': 1.06}, {'end': 933.155, 'text': 'So you solved the first problem, count digits.', 'start': 931.115, 'duration': 2.04}, {'end': 934.776, 'text': 'The next problem is reverse a number.', 'start': 933.195, 'duration': 1.581}, {'end': 935.716, 'text': "Let's go to the problem.", 'start': 934.816, 'duration': 0.9}, {'end': 939.678, 'text': 'It states, write a program to generate the reverse of a given number.', 'start': 936.216, 'duration': 3.462}, {'end': 941.878, 'text': 'Print the corresponding reverse number.', 'start': 940.258, 'duration': 1.62}, {'end': 945.8, 'text': 'If a number has trailing zeros, then its reverse will not include them.', 'start': 942.359, 'duration': 3.441}, {'end': 952.362, 'text': 'For an example, the reverse of 10400 will be 401 instead of 00401.', 'start': 945.84, 'duration': 6.522}, {'end': 954.804, 'text': 'and these are some of the examples.', 'start': 952.362, 'duration': 2.442}], 'summary': 'Logarithmic time complexity is based on division. next problem: reverse a number.', 'duration': 51.057, 'max_score': 878.077, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug878077.jpg'}, {'end': 1018.693, 'src': 'embed', 'start': 980.661, 'weight': 4, 'content': [{'end': 984.763, 'text': 'Somehow, we need 9877, which is the similar fashion.', 'start': 980.661, 'duration': 4.102}, {'end': 988.144, 'text': 'This is where the basic maths comes in.', 'start': 985.423, 'duration': 2.721}, {'end': 996.208, 'text': 'What you do is, you define a variable, sum, or maybe reverse number.', 'start': 988.605, 'duration': 7.603}, {'end': 999.669, 'text': 'Reverse number equal to 0.', 'start': 997.088, 'duration': 2.581}, {'end': 1010.626, 'text': 'And you say reverse number equal to reverse number into 10 plus last digit.', 'start': 999.669, 'duration': 10.957}, {'end': 1016.992, 'text': 'remember this this is what you see reverse number into 10 plus last digit.', 'start': 1010.626, 'duration': 6.366}, {'end': 1018.693, 'text': "let's see how it works.", 'start': 1016.992, 'duration': 1.701}], 'summary': 'Using basic maths, we need 9877 in a similar fashion by defining a variable and performing a specific calculation.', 'duration': 38.032, 'max_score': 980.661, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug980661.jpg'}, {'end': 1146.137, 'src': 'embed', 'start': 1110.079, 'weight': 3, 'content': [{'end': 1112.019, 'text': 'the reverse is 98 x 10 plus 7, which is 987.', 'start': 1110.079, 'duration': 1.94}, {'end': 1113.34, 'text': 'next time it is 7.', 'start': 1112.019, 'duration': 1.321}, {'end': 1126.465, 'text': 'so 987 x 10 Plus 7 is 9877..', 'start': 1113.34, 'duration': 13.125}, {'end': 1129.568, 'text': 'So you got the reverse number there.', 'start': 1126.465, 'duration': 3.103}, {'end': 1131.189, 'text': 'Quite simple.', 'start': 1130.468, 'duration': 0.721}, {'end': 1133.831, 'text': "Why did this work? It's very easy.", 'start': 1131.789, 'duration': 2.042}, {'end': 1137.414, 'text': 'Understand You are getting in last digit.', 'start': 1134.591, 'duration': 2.823}, {'end': 1138.835, 'text': 'You are easily getting the last digit.', 'start': 1137.574, 'duration': 1.261}, {'end': 1146.137, 'text': "9 and after that you're getting the next last digit 8 and you somehow want to add 8 to that 9.", 'start': 1139.715, 'duration': 6.422}], 'summary': 'Reversing a number: 987 x 10 plus 7 equals 9877, demonstrating a simple process of obtaining the reverse number by easily getting and adding the last digit.', 'duration': 36.058, 'max_score': 1110.079, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug1110079.jpg'}], 'start': 806.852, 'title': 'Time complexity and reverse number', 'summary': 'Covers time complexity of counting digits using division, with a time complexity of approximately log base 10n, and the reverse number problem solved using a step-by-step process, resulting in the reverse number 9877 from the input 7789.', 'chapters': [{'end': 929.134, 'start': 806.852, 'title': 'Time complexity in counting digits', 'summary': 'Explains the time complexity of counting digits by division, with a time complexity of approximately log base 10n, and the relevance of unit operations in large numbers.', 'duration': 122.282, 'highlights': ['The time complexity of counting digits is approximately log base 10n, due to the number of times the loop runs when the number is divisible by 10.', 'Unit operations, such as divisions, have a significant impact on time complexity, especially in the case of larger numbers.', 'The time complexity for division by 10 is log base 10n, by 2 is log base 2n, and by 5 is log base 5n, demonstrating the computation of time complexity based on division.', 'The number of iterations based on division results in a logarithmic time complexity, rather than linear time complexity.']}, {'end': 1171.963, 'start': 929.274, 'title': 'Reverse number problem', 'summary': 'Explains how to generate the reverse of a given number by using a step-by-step process and basic math, resulting in the reverse number 9877 from the input 7789.', 'duration': 242.689, 'highlights': ['The process of generating the reverse of a number involves iterating through the input number, extracting the last digit, and incrementally building the reverse number by multiplying it with 10 and adding the next last digit, ultimately resulting in the reverse number 9877 from the input 7789.', 'The step-by-step explanation includes initializing the reverse number as 0, extracting the last digit from the input number, and iteratively building the reverse number by multiplying it with 10 and adding the next last digit, demonstrating a clear understanding of the reverse number generation process.']}], 'duration': 365.111, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug806852.jpg', 'highlights': ['The time complexity for division by 10 is log base 10n, by 2 is log base 2n, and by 5 is log base 5n, demonstrating the computation of time complexity based on division.', 'The number of iterations based on division results in a logarithmic time complexity, rather than linear time complexity.', 'Unit operations, such as divisions, have a significant impact on time complexity, especially in the case of larger numbers.', 'The process of generating the reverse of a number involves iterating through the input number, extracting the last digit, and incrementally building the reverse number by multiplying it with 10 and adding the next last digit, ultimately resulting in the reverse number 9877 from the input 7789.', 'The step-by-step explanation includes initializing the reverse number as 0, extracting the last digit from the input number, and iteratively building the reverse number by multiplying it with 10 and adding the next last digit, demonstrating a clear understanding of the reverse number generation process.']}, {'end': 1579.754, 'segs': [{'end': 1200.203, 'src': 'embed', 'start': 1171.963, 'weight': 0, 'content': [{'end': 1177.729, 'text': 'This is why, at every step, I am doing reverse number into 10..', 'start': 1171.963, 'duration': 5.766}, {'end': 1182.573, 'text': 'Whatever you have generated into 10, that will allow the last unit digit to be 0.', 'start': 1177.729, 'duration': 4.844}, {'end': 1185.656, 'text': 'Then when you add a digit, it goes and gets into that place.', 'start': 1182.573, 'duration': 3.083}, {'end': 1187.017, 'text': 'As simple as that.', 'start': 1186.337, 'duration': 0.68}, {'end': 1193.403, 'text': 'So again, you saw that extraction of digits is actually handy.', 'start': 1190.06, 'duration': 3.343}, {'end': 1194.785, 'text': "So what I'll do is I'll take the number.", 'start': 1193.704, 'duration': 1.081}, {'end': 1200.203, 'text': "And I'll keep the reverse num equal to 0.", 'start': 1196.679, 'duration': 3.524}], 'summary': 'The speaker explains the process of reversing numbers and their usefulness in digit extraction.', 'duration': 28.24, 'max_score': 1171.963, 'thumbnail': ''}, {'end': 1330.282, 'src': 'embed', 'start': 1295.996, 'weight': 1, 'content': [{'end': 1299.84, 'text': 'so the definition of palindrome number says reverse of a number.', 'start': 1295.996, 'duration': 3.844}, {'end': 1307.307, 'text': "so if i somehow can generate the reverse of a number, if i somehow can generate the reverse of a number which i've already did,", 'start': 1299.84, 'duration': 7.467}, {'end': 1313.073, 'text': 'and then compare it with the original n, if they come out to be same, can i say they are palindrome?', 'start': 1307.307, 'duration': 5.766}, {'end': 1313.993, 'text': 'i can.', 'start': 1313.073, 'duration': 0.92}, {'end': 1321.558, 'text': 'so over here, if you remember, We took a reverse number and at the end of the day the reverse number was nothing but the reverse number.', 'start': 1313.993, 'duration': 7.565}, {'end': 1330.282, 'text': 'And now, if I can compare this reverse number with the original number, with the original number, which is n, and if they come out to be same,', 'start': 1322.238, 'duration': 8.044}], 'summary': 'Palindrome number: a number whose reverse is the same, can be identified', 'duration': 34.286, 'max_score': 1295.996, 'thumbnail': ''}, {'end': 1464.81, 'src': 'heatmap', 'start': 1405.43, 'weight': 2, 'content': [{'end': 1406.75, 'text': 'that is what they required.', 'start': 1405.43, 'duration': 1.32}, {'end': 1410.471, 'text': 'okay, by the small, small.', 'start': 1406.75, 'duration': 3.721}, {'end': 1412.271, 'text': "i'll quickly run it and see if it is running.", 'start': 1410.471, 'duration': 1.8}, {'end': 1414.292, 'text': "fine should be, and let's quickly submit this.", 'start': 1412.271, 'duration': 2.021}, {'end': 1418.537, 'text': 'On submitting, you see that it is running absolutely fine.', 'start': 1415.032, 'duration': 3.505}, {'end': 1421.261, 'text': 'The next one is GCD or HCF.', 'start': 1418.998, 'duration': 2.263}, {'end': 1424.325, 'text': 'But before that, we will be solving Armstrong numbers.', 'start': 1421.681, 'duration': 2.644}, {'end': 1427.71, 'text': "So what is the definition of Armstrong number? It's very simple.", 'start': 1425.226, 'duration': 2.484}, {'end': 1431.462, 'text': "Imagine you're given this number 371.", 'start': 1428.291, 'duration': 3.171}, {'end': 1435.263, 'text': 'You take 3 cube, 7 cube, plus 1 cube.', 'start': 1431.462, 'duration': 3.801}, {'end': 1443.784, 'text': 'If taking the cubes of these numbers like cubes of these digits and adding them up sums up to the number itself.', 'start': 1435.943, 'duration': 7.841}, {'end': 1445.665, 'text': 'that is what you call as an Armstrong number.', 'start': 1443.784, 'duration': 1.881}, {'end': 1453.766, 'text': 'Even if you take 1634, 1 cube, plus 6 cube, plus 3 cube, plus 4 cube, if you sum them up, you actually get 1634.', 'start': 1446.165, 'duration': 7.601}, {'end': 1454.487, 'text': 'But something like.', 'start': 1453.766, 'duration': 0.721}, {'end': 1464.81, 'text': '35. if you take 3 cube plus 5 cube, this is not going to be equal to 35, this is going to be equal to 134.', 'start': 1457.067, 'duration': 7.743}], 'summary': 'Explained armstrong numbers and its definition using examples like 371 and 1634.', 'duration': 59.38, 'max_score': 1405.43, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug1405430.jpg'}], 'start': 1171.963, 'title': 'Reversing, palindrome, and armstrong numbers', 'summary': 'Covers the process of reversing a number, identifying palindrome numbers, and determining armstrong numbers through algorithms and examples. it highlights the effectiveness of the methods and provides clear step-by-step solution approaches.', 'chapters': [{'end': 1226.968, 'start': 1171.963, 'title': 'Reverse number algorithm', 'summary': 'Explains the process of reversing a number using a simple algorithm, highlighting the effectiveness of extracting digits and performing operations to achieve the reverse number, ultimately leading to a successful code execution.', 'duration': 55.005, 'highlights': ['The reverse number algorithm involves multiplying the existing reverse number by 10 and then adding the last digit of the original number, which efficiently allows the addition of new digits in the correct place.', 'Extracting digits from the original number using modulo operation and dividing the number by 10, facilitates the process of reversing the number.', 'The successful execution of the code for reversing numbers demonstrates the practical application of the algorithm.']}, {'end': 1414.292, 'start': 1228.029, 'title': 'Palindrome number problem', 'summary': 'Discusses the concept of palindrome numbers, where the reverse of a number is the same as the original number, and explains the process to determine if a given number is a palindrome or not.', 'duration': 186.263, 'highlights': ['Palindrome numbers are those for which the reverse is exactly the same as the original number, such as 121, 11, 77, etc. Provides a clear definition of palindrome numbers and gives examples to illustrate the concept.', 'The process of determining if a number is a palindrome involves generating the reverse of the number and comparing it with the original number. Explains the process of checking for palindrome numbers and the necessary comparison step involved.', 'Storing a duplicate of the original number is essential for comparison with the reverse number, as the original number becomes 0 after the extraction of digits. Emphasizes the importance of storing a duplicate of the original number for comparison with the reverse number and highlights the reason behind it.']}, {'end': 1579.754, 'start': 1415.032, 'title': 'Armstrong number definition and solution', 'summary': 'Explains the definition of armstrong numbers, highlighting examples such as 371 and 1634, and demonstrates a step-by-step solution approach involving digit extraction and cube summation for determining armstrong numbers.', 'duration': 164.722, 'highlights': ['The definition of Armstrong number is explained using examples like 371 and 1634, emphasizing the requirement that the sum of the cubes of its digits should equal the number itself.', 'The step-by-step solution approach involves extracting digits, cubing them, and summing the cubes to compare with the original number to determine if it is an Armstrong number.', 'The chapter emphasizes the importance of understanding digit extraction, enabling the solution of the Armstrong number problem by manipulating and comparing the extracted digits.', 'The algorithm involves iterating through the digits, cubing each one, and summing the results to compare with the original number, demonstrating the process with examples involving the digits 9, 8, and 7.']}], 'duration': 407.791, 'thumbnail': '', 'highlights': ['The reverse number algorithm involves multiplying the existing reverse number by 10 and then adding the last digit of the original number, which efficiently allows the addition of new digits in the correct place.', 'The process of determining if a number is a palindrome involves generating the reverse of the number and comparing it with the original number. Explains the process of checking for palindrome numbers and the necessary comparison step involved.', 'The definition of Armstrong number is explained using examples like 371 and 1634, emphasizing the requirement that the sum of the cubes of its digits should equal the number itself.']}, {'end': 2134.956, 'segs': [{'end': 1660.337, 'src': 'embed', 'start': 1629.999, 'weight': 2, 'content': [{'end': 1638.685, 'text': 'So if I talk about 36, the divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.', 'start': 1629.999, 'duration': 8.686}, {'end': 1640.546, 'text': 'These are the divisors of 36.', 'start': 1638.685, 'duration': 1.861}, {'end': 1642.988, 'text': 'The question is very straightforward.', 'start': 1640.546, 'duration': 2.442}, {'end': 1646.811, 'text': 'You have to print all of them in this particular order.', 'start': 1643.348, 'duration': 3.463}, {'end': 1651.133, 'text': "Okay Now, how do I do it? It's very simple.", 'start': 1647.191, 'duration': 3.942}, {'end': 1660.337, 'text': "One thing I know for sure is if I'm talking about divisors or factors, they're definitely going to lie between 1 to the number itself.", 'start': 1651.913, 'duration': 8.424}], 'summary': 'Explaining divisors of 36 and their range.', 'duration': 30.338, 'max_score': 1629.999, 'thumbnail': ''}, {'end': 1848.615, 'src': 'embed', 'start': 1817.118, 'weight': 1, 'content': [{'end': 1819.68, 'text': "Can I do it in a much better way? I can't.", 'start': 1817.118, 'duration': 2.562}, {'end': 1822.321, 'text': 'But it requires a bit of mathematical observation.', 'start': 1820.12, 'duration': 2.201}, {'end': 1824.703, 'text': "Let's see that mathematical observation.", 'start': 1822.762, 'duration': 1.941}, {'end': 1829.086, 'text': 'So for 36, I said that 1 was a factor.', 'start': 1825.263, 'duration': 3.823}, {'end': 1833.049, 'text': 'If 1 is a factor, 1 has to be multiplied with something.', 'start': 1829.686, 'duration': 3.363}, {'end': 1834.569, 'text': 'in order to get 36.', 'start': 1833.789, 'duration': 0.78}, {'end': 1848.615, 'text': 'so 1 was multiplied with 36, and if you carefully observe, if this is 1 and the number is 36, the other number will always be n by 1.', 'start': 1834.569, 'duration': 14.046}], 'summary': 'Using mathematical observation, 36 can be factored as 1*36, showing a pattern for factor pairs.', 'duration': 31.497, 'max_score': 1817.118, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug1817118.jpg'}, {'end': 2026.439, 'src': 'embed', 'start': 1996.294, 'weight': 0, 'content': [{'end': 1997.795, 'text': 'The replication of the upper half.', 'start': 1996.294, 'duration': 1.501}, {'end': 2002.478, 'text': 'So thereby, this is nothing but a repetition of the upper half.', 'start': 1998.235, 'duration': 4.243}, {'end': 2011.022, 'text': 'Thereby, I can say, even if you loop till square root of n, even if you loop till square root of n, you actually can get your factors.', 'start': 2003.098, 'duration': 7.924}, {'end': 2016.314, 'text': 'How? If this is 1, this has to be n by 1.', 'start': 2011.743, 'duration': 4.571}, {'end': 2019.155, 'text': 'If this is 2, this has to be n by 2.', 'start': 2016.314, 'duration': 2.841}, {'end': 2021.917, 'text': 'If this is 3, this has to be n by 3.', 'start': 2019.155, 'duration': 2.762}, {'end': 2024.178, 'text': 'If this is 4, this has to be n by 4.', 'start': 2021.917, 'duration': 2.261}, {'end': 2026.439, 'text': 'If this is 6, this has to be n by 6.', 'start': 2024.178, 'duration': 2.261}], 'summary': 'The upper half can be replicated to obtain factors by looping till the square root of n.', 'duration': 30.145, 'max_score': 1996.294, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug1996294.jpg'}, {'end': 2130.293, 'src': 'heatmap', 'start': 2051.293, 'weight': 0.833, 'content': [{'end': 2056.375, 'text': 'What is the other factor? We just now found out the other factor was n by i.', 'start': 2051.293, 'duration': 5.082}, {'end': 2057.315, 'text': 'But we need to be careful.', 'start': 2056.375, 'duration': 0.94}, {'end': 2062.478, 'text': 'What is the careful observation? If it is 6, the other factor might be 6.', 'start': 2058.036, 'duration': 4.442}, {'end': 2064.859, 'text': 'So they are not two different factors.', 'start': 2062.478, 'duration': 2.381}, {'end': 2074.373, 'text': "So if you are taking the second factor, If you're taking the second factor to n by i, just make sure that n by i is not equal to i.", 'start': 2065.478, 'duration': 8.895}, {'end': 2077.295, 'text': 'Because the second factor might turn out to be the same factor.', 'start': 2074.373, 'duration': 2.922}, {'end': 2078.576, 'text': "It's very important.", 'start': 2077.715, 'duration': 0.861}, {'end': 2082.779, 'text': 'The n by i, which is the second factor, must be compared with i.', 'start': 2078.916, 'duration': 3.863}, {'end': 2085.702, 'text': "And if they're not same, you can say that, maybe print.", 'start': 2082.779, 'duration': 2.923}, {'end': 2088.304, 'text': "That's your another factor.", 'start': 2087.163, 'duration': 1.141}, {'end': 2090.025, 'text': "That's it.", 'start': 2089.745, 'duration': 0.28}, {'end': 2094.243, 'text': 'So first, check if i is a factor.', 'start': 2091.38, 'duration': 2.863}, {'end': 2095.063, 'text': 'Print it.', 'start': 2094.723, 'duration': 0.34}, {'end': 2100.409, 'text': 'Now the other factor, n by i, with which the i will be multiplied.', 'start': 2095.504, 'duration': 4.905}, {'end': 2104.361, 'text': 'just check if this is not equal to i.', 'start': 2100.409, 'duration': 3.952}, {'end': 2106.762, 'text': "if it is not, that's the second factor.", 'start': 2104.361, 'duration': 2.401}, {'end': 2107.462, 'text': "that's it.", 'start': 2106.762, 'duration': 0.7}, {'end': 2114.784, 'text': 'so if you go ahead and print this, the printing will be something like this first one and 36 will get printed.', 'start': 2107.462, 'duration': 7.322}, {'end': 2117.224, 'text': 'next, 2 and 18 will get printed.', 'start': 2114.784, 'duration': 2.44}, {'end': 2120.385, 'text': 'next, 3 and 12 will get printed.', 'start': 2117.224, 'duration': 3.161}, {'end': 2123.086, 'text': 'next, 4 and 9 will get printed.', 'start': 2120.385, 'duration': 2.701}, {'end': 2124.506, 'text': 'next one i is 6.', 'start': 2123.086, 'duration': 1.42}, {'end': 2130.293, 'text': '6 gets printed, but the other factor is 6 And it fails this condition check.', 'start': 2124.506, 'duration': 5.787}], 'summary': 'Identify second factor by comparing n by i with i, avoiding equal values.', 'duration': 79, 'max_score': 2051.293, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2051293.jpg'}], 'start': 1580.424, 'title': 'Finding factors of a number', 'summary': 'Discusses how to efficiently find factors of a number, using a simple approach to print all divisors of a given number, such as 36, with a time complexity of o(n), and highlights a mathematical observation for finding factors of 36.', 'chapters': [{'end': 1816.618, 'start': 1580.424, 'title': 'Print all divisors', 'summary': 'Explains how to print all divisors of a given number, such as 36, and discusses the time complexity of the solution, which is o(n). it provides a simple approach to accomplish the task using a loop and a condition to check for divisors.', 'duration': 236.194, 'highlights': ['The divisors of 36, such as 1, 2, 3, 4, 6, 9, 12, 18, and 36, are printed in order using a loop from 1 to n, where n is the given number.', 'The time complexity of the provided approach to print divisors is O(n), as the loop runs from 1 to n, resulting in n iterations.', 'The process involves checking if a number completely divides the given number by evaluating the remainder of the division, and then printing the number if the remainder is 0.']}, {'end': 1967.805, 'start': 1817.118, 'title': 'Factors of 36 and mathematical observation', 'summary': 'Explains the factors of 36 and a mathematical observation, highlighting that the product of a small number and a big number yields all the factors, thus eliminating the need to go beyond the product of 1 and 36.', 'duration': 150.687, 'highlights': ['The product of a small number and a big number yields all the factors of 36, eliminating the need to go beyond the product of 1 and 36.', 'Factors of 36 can be obtained by multiplying 1 with 36, 2 with 18, 3 with 12, 4 with 9, 6 with 6, and their respective reverse pairs.', 'The observation of a small number multiplied by a big number simplifies the identification of factors, showcasing a pattern in the factor pairs.']}, {'end': 2134.956, 'start': 1967.805, 'title': 'Finding factors of a number', 'summary': 'Explains how to efficiently find factors of a number by iterating up to its square root, and then checking and printing the factors, resulting in the printing of all factors of 36.', 'duration': 167.151, 'highlights': ['Iterating up to the square root of n and checking for factors allows for efficient factorization, as all factors can be found by the time the loop reaches the square root of n.', 'Careful observation is necessary when identifying the second factor to ensure it is not the same as the first factor, as exemplified by the factorization of 36.', 'The process of identifying factors involves checking if a number is a factor, printing it, and then checking if the other factor (n divided by i) is not equal to the first factor to successfully print all factors of a number.']}], 'duration': 554.532, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug1580424.jpg', 'highlights': ['Iterating up to the square root of n and checking for factors allows for efficient factorization, as all factors can be found by the time the loop reaches the square root of n.', 'The product of a small number and a big number yields all the factors of 36, eliminating the need to go beyond the product of 1 and 36.', 'The divisors of 36, such as 1, 2, 3, 4, 6, 9, 12, 18, and 36, are printed in order using a loop from 1 to n, where n is the given number.']}, {'end': 2653.519, 'segs': [{'end': 2162.668, 'src': 'embed', 'start': 2135.417, 'weight': 0, 'content': [{'end': 2139.16, 'text': 'But they are not printed in a proper.', 'start': 2135.417, 'duration': 3.743}, {'end': 2141.141, 'text': 'Yes, they are not printed in a sorted way.', 'start': 2139.16, 'duration': 1.981}, {'end': 2148.066, 'text': 'So, what you can do is, whenever you are getting all the factors, probably you can store them into a data structure.', 'start': 2141.561, 'duration': 6.505}, {'end': 2153.471, 'text': 'And if you have seen the C++ STL video, you know which data structure you can use.', 'start': 2148.867, 'duration': 4.604}, {'end': 2158.866, 'text': 'You do not know what will be the size or what will be the number of factors.', 'start': 2154.264, 'duration': 4.602}, {'end': 2162.668, 'text': "The data structure that you'll be using is a list.", 'start': 2159.367, 'duration': 3.301}], 'summary': 'Store factors in a list for easy access and flexibility.', 'duration': 27.251, 'max_score': 2135.417, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2135417.jpg'}, {'end': 2268.16, 'src': 'embed', 'start': 2237.555, 'weight': 1, 'content': [{'end': 2242.179, 'text': "so i'll just iterate on the list and i'll print the list with space.", 'start': 2237.555, 'duration': 4.624}, {'end': 2244.187, 'text': 'So all of them are correct.', 'start': 2243.086, 'duration': 1.101}, {'end': 2247.368, 'text': "Now, I'll go ahead and print and it will be correct.", 'start': 2244.207, 'duration': 3.161}, {'end': 2251.791, 'text': 'Why did I sort it? Because they wanted us to print everything in the sorted order.', 'start': 2247.728, 'duration': 4.063}, {'end': 2253.391, 'text': "It's very important to sort the list.", 'start': 2252.051, 'duration': 1.34}, {'end': 2257.253, 'text': 'If I talk about the time complexity, what will be the time complexity?', 'start': 2253.892, 'duration': 3.361}, {'end': 2262.796, 'text': "Something before discussing the time complexity you're writing i lesser than equal to square root of n.", 'start': 2257.594, 'duration': 5.202}, {'end': 2268.16, 'text': 'Instead of this, because square root is a function, And every time the function will be called.', 'start': 2262.796, 'duration': 5.364}], 'summary': 'Iterated list, printed with space; emphasized sorting for time complexity.', 'duration': 30.605, 'max_score': 2237.555, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2237555.jpg'}, {'end': 2385.149, 'src': 'embed', 'start': 2355.285, 'weight': 2, 'content': [{'end': 2363.199, 'text': 'So number of factors into log of, if I write it properly, number of factors.', 'start': 2355.285, 'duration': 7.914}, {'end': 2367.594, 'text': 'Factors Got it? Quite simple.', 'start': 2365.472, 'duration': 2.122}, {'end': 2369.515, 'text': 'And then plus this.', 'start': 2368.114, 'duration': 1.401}, {'end': 2374.18, 'text': 'So big of this plus big of this plus big of this is the time complexity.', 'start': 2369.936, 'duration': 4.244}, {'end': 2381.045, 'text': 'But the motive was to teach you that you can also find factors in big of square root of n.', 'start': 2374.62, 'duration': 6.425}, {'end': 2385.149, 'text': "Got it? I can say I've also done print all divisors in both the ways.", 'start': 2381.045, 'duration': 4.104}], 'summary': 'Teaching on finding factors and time complexity; also printing all divisors.', 'duration': 29.864, 'max_score': 2355.285, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2355285.jpg'}, {'end': 2436.735, 'src': 'embed', 'start': 2408.84, 'weight': 3, 'content': [{'end': 2417.599, 'text': 'instead of this, the definition that you should always keep in mind is a number that has exactly Two factors.', 'start': 2408.84, 'duration': 8.759}, {'end': 2420.622, 'text': 'One and itself.', 'start': 2419.821, 'duration': 0.801}, {'end': 2421.883, 'text': "That's a better definition.", 'start': 2420.902, 'duration': 0.981}, {'end': 2423.264, 'text': 'One and itself.', 'start': 2422.684, 'duration': 0.58}, {'end': 2425.206, 'text': 'A number that has two factors.', 'start': 2423.825, 'duration': 1.381}, {'end': 2426.607, 'text': 'Which is one and itself.', 'start': 2425.686, 'duration': 0.921}, {'end': 2428.549, 'text': 'So if you remember.', 'start': 2427.168, 'duration': 1.381}, {'end': 2430.671, 'text': 'We just now computed factors.', 'start': 2429.249, 'duration': 1.422}, {'end': 2434.134, 'text': 'So if you are given a number.', 'start': 2432.592, 'duration': 1.542}, {'end': 2436.735, 'text': 'Something like 11.', 'start': 2435.273, 'duration': 1.462}], 'summary': 'A prime number has exactly two factors: 1 and itself.', 'duration': 27.895, 'max_score': 2408.84, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2408840.jpg'}, {'end': 2549.629, 'src': 'embed', 'start': 2523.735, 'weight': 4, 'content': [{'end': 2529.026, 'text': "turns out to be 2, then I'll say it's a prime number or else it's not a prime number.", 'start': 2523.735, 'duration': 5.291}, {'end': 2534.96, 'text': 'So can I say this is the extreme brute force approach.', 'start': 2529.487, 'duration': 5.473}, {'end': 2541.564, 'text': 'and if i write the extreme brute force approach, what will be the time complexity of the extreme brute force approach?', 'start': 2534.96, 'duration': 6.604}, {'end': 2546.227, 'text': "can i say i'm running a loop n and these are unit operations, so i can ignore.", 'start': 2541.564, 'duration': 4.663}, {'end': 2549.629, 'text': 'so can i say the time complexity will be b go of n,', 'start': 2546.227, 'duration': 3.402}], 'summary': 'Using brute force approach to determine prime numbers with time complexity of o(n)', 'duration': 25.894, 'max_score': 2523.735, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2523735.jpg'}], 'start': 2135.417, 'title': 'Efficient printing and number computation', 'summary': 'Discusses sorting factors for efficient printing in a sorted fashion, and finding square roots and prime numbers, emphasizing the importance of list data structure and the stl in c++, and the time complexity of computational approaches.', 'chapters': [{'end': 2257.253, 'start': 2135.417, 'title': 'Sorting factors for efficient printing', 'summary': 'Discusses sorting factors using a list to efficiently print them in a sorted fashion, emphasizing the importance of using a list data structure and the stl in c++ for achieving this.', 'duration': 121.836, 'highlights': ['Using a list or vector data structure to store factors allows for efficient sorting and printing, as demonstrated in the C++ STL video.', 'Emphasizes the importance of sorting the list to ensure factors are printed in a sorted fashion.', 'Illustrates the process of storing factors in a list and sorting them to achieve the desired output, highlighting the significance of using an undefined-sized data structure like a list or vector.']}, {'end': 2653.519, 'start': 2257.594, 'title': 'Finding square roots and prime numbers', 'summary': 'Explains how to find square roots and prime numbers using loops and mathematical functions, emphasizing the time complexity of each approach, and ends with a recommendation to optimize the process by using the square root of n. it also clarifies the definition of a prime number and provides an example of using brute force to check for prime numbers, highlighting the time complexity and an optimized approach.', 'duration': 395.925, 'highlights': ['The time complexity in finding square roots and prime numbers is explained, emphasizing the importance of optimizing the process by using the square root of n and providing examples of different approaches and their time complexities. time complexity, optimization by using the square root of n, examples of approaches and time complexities', 'The definition of a prime number is clarified, emphasizing that a prime number has exactly two factors: 1 and itself, and providing examples to illustrate the concept. definition of a prime number, examples', 'The use of brute force to check for prime numbers is explained, highlighting the time complexity of the approach and emphasizing the importance of optimizing the process by using the square root of n. brute force approach, time complexity, optimization by using the square root of n']}], 'duration': 518.102, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2135417.jpg', 'highlights': ['Using a list or vector data structure to store factors allows for efficient sorting and printing.', 'Emphasizes the importance of sorting the list to ensure factors are printed in a sorted fashion.', 'The time complexity in finding square roots and prime numbers is explained, emphasizing the importance of optimizing the process.', 'The definition of a prime number is clarified, emphasizing that a prime number has exactly two factors: 1 and itself.', 'The use of brute force to check for prime numbers is explained, highlighting the time complexity of the approach.']}, {'end': 3102.99, 'segs': [{'end': 2678.345, 'src': 'embed', 'start': 2653.519, 'weight': 0, 'content': [{'end': 2660.921, 'text': 'So if someone is coming up and asking you how do you check for a prime number?? You say I know the square root method because I know the observation.', 'start': 2653.519, 'duration': 7.402}, {'end': 2667.883, 'text': 'For every factor, there is the other corresponding number with which it has to get multiplied in order to get the number.', 'start': 2660.941, 'duration': 6.942}, {'end': 2670.884, 'text': 'Thereby, I can just go up to square root of n.', 'start': 2668.463, 'duration': 2.421}, {'end': 2671.764, 'text': 'Nothing beyond it.', 'start': 2670.884, 'duration': 0.88}, {'end': 2674.745, 'text': "Because still square root of n, I'll get all the factors.", 'start': 2672.084, 'duration': 2.661}, {'end': 2678.345, 'text': 'So this is the code that I did right in the iPad.', 'start': 2675.543, 'duration': 2.802}], 'summary': 'Use square root method to check for prime number, as it covers all factors.', 'duration': 24.826, 'max_score': 2653.519, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2653519.jpg'}, {'end': 2737.708, 'src': 'embed', 'start': 2696.941, 'weight': 2, 'content': [{'end': 2700.584, 'text': "So what do you mean by GCD or HCF? It's very simple.", 'start': 2696.941, 'duration': 3.643}, {'end': 2704.587, 'text': 'Greatest common divisor or highest common factor.', 'start': 2701.024, 'duration': 3.563}, {'end': 2706.193, 'text': 'Let me give you an example.', 'start': 2705.373, 'duration': 0.82}, {'end': 2710.694, 'text': 'If I give you two numbers, n1 equal to 9 and n2 equal to 12.', 'start': 2706.853, 'duration': 3.841}, {'end': 2717.036, 'text': 'So you need to find the highest common factor or greatest common divisor that actually divides 9 and 12.', 'start': 2710.694, 'duration': 6.342}, {'end': 2719.916, 'text': 'So if I write down all the factors of 9, it is 1, 3, and 9.', 'start': 2717.036, 'duration': 2.88}, {'end': 2737.708, 'text': 'If I write down all the factors of 12, it is 1, 2, 3, 6 and 12 even 3 4.', 'start': 2719.916, 'duration': 17.792}], 'summary': 'Explaining gcd and hcf using an example of finding the hcf of 9 and 12.', 'duration': 40.767, 'max_score': 2696.941, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2696941.jpg'}, {'end': 2850.801, 'src': 'embed', 'start': 2811.222, 'weight': 1, 'content': [{'end': 2816.645, 'text': 'So for two given numbers, one of them can also be a GCD of those two given numbers.', 'start': 2811.222, 'duration': 5.423}, {'end': 2819.627, 'text': 'So that is what is the definition of GCD.', 'start': 2817.085, 'duration': 2.542}, {'end': 2836.47, 'text': 'So all of you know how to find factors of two given numbers.', 'start': 2831.687, 'duration': 4.783}, {'end': 2839.112, 'text': "You're given n1 and you're given n2.", 'start': 2836.951, 'duration': 2.161}, {'end': 2843.536, 'text': 'So in the last two problems, you have learned how to find factors.', 'start': 2839.433, 'duration': 4.103}, {'end': 2850.801, 'text': "So imagine it's like n1 is 9 and n2 is 12.", 'start': 2844.116, 'duration': 6.685}], 'summary': 'Gcd can also be a factor of given numbers.', 'duration': 39.579, 'max_score': 2811.222, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2811222.jpg'}], 'start': 2653.519, 'title': 'Prime numbers and gcd/hcf', 'summary': 'Explains the square root method for prime numbers and the computation of gcd or hcf for two numbers, with time complexity analysis and edge case handling.', 'chapters': [{'end': 3102.99, 'start': 2653.519, 'title': 'Finding prime numbers and gcd/hcf', 'summary': 'Covers the method to check for prime numbers using the square root method and explains the concept and computation of gcd or hcf for two given numbers, along with the time complexity analysis and handling edge cases.', 'duration': 449.471, 'highlights': ['The square root method can be used to check for prime numbers by iterating up to the square root of n to find all factors, resulting in a time complexity of O(√n). The speaker explains that for every factor of a number, there is a corresponding number with which it has to get multiplied to get the number, and thus, it is sufficient to iterate up to the square root of n to find all factors, resulting in a time complexity of O(√n).', 'The concept of GCD or HCF is illustrated using examples and the method to find the highest common factor for two given numbers is demonstrated. The speaker provides an example of finding the highest common factor (HCF) or greatest common divisor (GCD) for the numbers 9 and 12, explaining the process of identifying and comparing common factors to determine the highest one, thereby illustrating the concept of GCD or HCF.', 'The time complexity for finding the GCD of two numbers is analyzed, with the conclusion that it is O(min(n1, n2)), addressing the scenario of handling edge cases efficiently. The speaker explains the time complexity for finding the GCD of two numbers, highlighting the analysis that the time complexity is O(min(n1, n2)), and further discusses the approach to efficiently handle edge cases by iterating up to the minimum of the two numbers.']}], 'duration': 449.471, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug2653519.jpg', 'highlights': ['The square root method can be used to check for prime numbers by iterating up to the square root of n to find all factors, resulting in a time complexity of O(√n).', 'The time complexity for finding the GCD of two numbers is analyzed, with the conclusion that it is O(min(n1, n2)), addressing the scenario of handling edge cases efficiently.', 'The concept of GCD or HCF is illustrated using examples and the method to find the highest common factor for two given numbers is demonstrated.']}, {'end': 3790.209, 'segs': [{'end': 3218.192, 'src': 'heatmap', 'start': 3148.922, 'weight': 0, 'content': [{'end': 3154.606, 'text': 'Because if both the numbers of GCD as 1, it ends up running completely.', 'start': 3148.922, 'duration': 5.684}, {'end': 3156.548, 'text': 'The loop ends up running completely.', 'start': 3154.987, 'duration': 1.561}, {'end': 3160.951, 'text': 'And you know when you determine the time complexity? I taught you in the time complexity lecture.', 'start': 3156.948, 'duration': 4.003}, {'end': 3163.614, 'text': 'You always take worst case.', 'start': 3161.312, 'duration': 2.302}, {'end': 3165.515, 'text': 'You always take worst case.', 'start': 3163.674, 'duration': 1.841}, {'end': 3169.338, 'text': 'The worst case is when you run it till 1.', 'start': 3165.855, 'duration': 3.483}, {'end': 3173.28, 'text': 'So, we saw the previous method was a brute force method and was taking linear time complexity.', 'start': 3169.338, 'duration': 3.942}, {'end': 3180.524, 'text': 'Now, there is an algorithm known as Euclidean algorithm which is going to take much much lesser time.', 'start': 3173.821, 'duration': 6.703}, {'end': 3181.785, 'text': "So, let's learn about it.", 'start': 3180.544, 'duration': 1.241}, {'end': 3184.047, 'text': 'So what is Euclidean algorithm??', 'start': 3182.285, 'duration': 1.762}, {'end': 3194.593, 'text': 'It states if a given two numbers n1 comma n2, the GCD of n1 comma n2, whatever is the GCD of n1, comma n2,', 'start': 3184.487, 'duration': 10.106}, {'end': 3202.761, 'text': "that's equivalent to the gcd of n1 minus n2 comma n2.", 'start': 3195.495, 'duration': 7.266}, {'end': 3207.005, 'text': 'where where n1 is greater than n2.', 'start': 3202.761, 'duration': 4.244}, {'end': 3218.192, 'text': 'usually in books, you will find them written as gcd of a comma b is equal to gcd of a minus b comma b where a is greater than b.', 'start': 3207.005, 'duration': 11.187}], 'summary': 'Euclidean algorithm reduces time complexity for gcd calculation.', 'duration': 37.648, 'max_score': 3148.922, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug3148922.jpg'}, {'end': 3386.703, 'src': 'embed', 'start': 3357.653, 'weight': 2, 'content': [{'end': 3360.976, 'text': 'so the gcd of 20.15 is this what do you do?', 'start': 3357.653, 'duration': 3.323}, {'end': 3364.399, 'text': 'is you take two numbers apply equal idea, get it smaller.', 'start': 3360.976, 'duration': 3.423}, {'end': 3366.14, 'text': 'apply equal idea, get it smaller.', 'start': 3364.399, 'duration': 1.741}, {'end': 3366.661, 'text': 'get it smaller.', 'start': 3366.14, 'duration': 0.521}, {'end': 3369.023, 'text': 'get it smaller till one of them is zero.', 'start': 3366.661, 'duration': 2.362}, {'end': 3371.725, 'text': 'if one of them is zero, the other is zero.', 'start': 3369.023, 'duration': 2.702}, {'end': 3374.167, 'text': 'so the algorithm is quite simple.', 'start': 3371.725, 'duration': 2.442}, {'end': 3383.862, 'text': 'start with a comma b, keep on truncating, keep on truncating with a minus b, comma b, and keep on doing till one of them,', 'start': 3374.167, 'duration': 9.695}, {'end': 3386.703, 'text': 'the greater number becomes zero.', 'start': 3383.862, 'duration': 2.841}], 'summary': 'The algorithm for finding the gcd of 20 and 15 involves repeated subtraction until one number becomes zero.', 'duration': 29.05, 'max_score': 3357.653, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug3357653.jpg'}, {'end': 3686.669, 'src': 'heatmap', 'start': 3533.462, 'weight': 0.723, 'content': [{'end': 3534.662, 'text': 'Forget about A and B.', 'start': 3533.462, 'duration': 1.2}, {'end': 3535.563, 'text': 'The logic is very simple.', 'start': 3534.662, 'duration': 0.901}, {'end': 3538.944, 'text': 'The greater module or smaller.', 'start': 3536.783, 'duration': 2.161}, {'end': 3540.505, 'text': "That's the logic.", 'start': 3539.905, 'duration': 0.6}, {'end': 3544.587, 'text': 'And you go on till one of them is 0.', 'start': 3541.005, 'duration': 3.582}, {'end': 3546.408, 'text': 'And if one of them is 0, remember this.', 'start': 3544.587, 'duration': 1.821}, {'end': 3551.791, 'text': 'If one of them is 0, the other is GCD.', 'start': 3547.189, 'duration': 4.602}, {'end': 3553.292, 'text': 'The other is GCD.', 'start': 3552.431, 'duration': 0.861}, {'end': 3556.055, 'text': 'As simple as this.', 'start': 3555.615, 'duration': 0.44}, {'end': 3563.581, 'text': 'If I try to code this up, try to code this up a given a, a given b.', 'start': 3556.676, 'duration': 6.905}, {'end': 3565.042, 'text': 'can I say you go on till.', 'start': 3563.581, 'duration': 1.461}, {'end': 3567.064, 'text': 'both of them are greater, greater than zero?', 'start': 3565.042, 'duration': 2.022}, {'end': 3568.105, 'text': 'Very simple.', 'start': 3567.805, 'duration': 0.3}, {'end': 3571.247, 'text': 'And I know one of them will be greater.', 'start': 3569.126, 'duration': 2.121}, {'end': 3572.648, 'text': 'Either a will be greater.', 'start': 3571.828, 'duration': 0.82}, {'end': 3575.911, 'text': "In that case, I'll do a modulo b.", 'start': 3573.349, 'duration': 2.562}, {'end': 3579.193, 'text': "Or else if b is greater, I'll do b modulo a.", 'start': 3575.911, 'duration': 3.282}, {'end': 3583.157, 'text': 'Instead of swapping, changing, because I did not want to get into swapping, changing.', 'start': 3579.193, 'duration': 3.964}, {'end': 3585.592, 'text': 'Why? Over here, it was 2, 10.', 'start': 3583.197, 'duration': 2.395}, {'end': 3586.633, 'text': 'So, A was this, B was this.', 'start': 3585.592, 'duration': 1.041}, {'end': 3588.335, 'text': 'And I swapped it to this.', 'start': 3587.194, 'duration': 1.141}, {'end': 3590.737, 'text': 'I did not want to implement that.', 'start': 3588.755, 'duration': 1.982}, {'end': 3594.48, 'text': 'I just, I knew, now 10 will be modulated.', 'start': 3591.157, 'duration': 3.323}, {'end': 3600.826, 'text': 'So, what I did was, I implemented it in such a way, stating, if A is greater, A will be modulated.', 'start': 3594.541, 'duration': 6.285}, {'end': 3604.049, 'text': 'If B is greater, B will be modulated.', 'start': 3601.767, 'duration': 2.282}, {'end': 3613.112, 'text': 'And once this is over, If A is 0, if A becomes 0 and the while loop is false, can I say the GCD will be B? I will.', 'start': 3604.73, 'duration': 8.382}, {'end': 3617.835, 'text': 'Or else can I say the GCD will be print of A? Simple.', 'start': 3613.893, 'duration': 3.942}, {'end': 3621.61, 'text': 'yes, you can.', 'start': 3620.049, 'duration': 1.561}, {'end': 3631.233, 'text': 'you can just take this example 52, comma 10, and you can do a dry run on this and you will see that eventually one of them will become zero,', 'start': 3621.61, 'duration': 9.623}, {'end': 3645.619, 'text': 'and that is when the looping ends and the time complexity of this euclidean algorithm is b go of log of phi minimum of a comma b y log.', 'start': 3631.233, 'duration': 14.386}, {'end': 3648.189, 'text': 'If you remember,', 'start': 3646.909, 'duration': 1.28}, {'end': 3659.492, 'text': 'I clearly stated during the digit extraction or in the pattern videos or the time complexity videos that whenever there is division happening,', 'start': 3648.189, 'duration': 11.303}, {'end': 3662.452, 'text': 'the number of iterations will be in terms of logarithm.', 'start': 3659.492, 'duration': 2.96}, {'end': 3664.953, 'text': 'Over here, there is modulo.', 'start': 3663.213, 'duration': 1.74}, {'end': 3667.334, 'text': 'You are reducing the number by division.', 'start': 3665.653, 'duration': 1.681}, {'end': 3669.934, 'text': 'The modulation operations are happening.', 'start': 3667.814, 'duration': 2.12}, {'end': 3673.235, 'text': 'Thereby, the time complexity will be in terms of logarithm.', 'start': 3670.394, 'duration': 2.841}, {'end': 3681.229, 'text': 'Now, why 5? Why not something like log base 10? In the digit extraction, it is always n by 10.', 'start': 3673.956, 'duration': 7.273}, {'end': 3686.669, 'text': "Over here, this a and b It's always changing, fluctuating.", 'start': 3681.229, 'duration': 5.44}], 'summary': 'Using euclidean algorithm, find gcd with time complexity log(min(a,b))', 'duration': 153.207, 'max_score': 3533.462, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug3533462.jpg'}, {'end': 3734.244, 'src': 'embed', 'start': 3701.136, 'weight': 1, 'content': [{'end': 3702.857, 'text': "You can read it, but it's not required.", 'start': 3701.136, 'duration': 1.721}, {'end': 3705.178, 'text': 'And minimum of A, B.', 'start': 3703.357, 'duration': 1.821}, {'end': 3707.399, 'text': 'Because that is the initial number where you start from.', 'start': 3705.178, 'duration': 2.221}, {'end': 3710.2, 'text': "That's the initial number where you start to do it.", 'start': 3707.879, 'duration': 2.321}, {'end': 3712.602, 'text': "So that's why the time complexity is this.", 'start': 3710.261, 'duration': 2.341}, {'end': 3716.089, 'text': 'No one is going to ask you how and everything.', 'start': 3713.607, 'duration': 2.482}, {'end': 3721.373, 'text': 'Just keep it in mind that the time complexity is log phi minimum of a comma b.', 'start': 3716.389, 'duration': 4.984}, {'end': 3722.354, 'text': 'This is the equality now.', 'start': 3721.373, 'duration': 0.981}, {'end': 3734.244, 'text': "I've written the same code after if I've not given else because if this line executes, the function would have end and this line will not execute.", 'start': 3724.196, 'duration': 10.048}], 'summary': 'Time complexity is log phi min of a, b; function ends if line executes.', 'duration': 33.108, 'max_score': 3701.136, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug3701136.jpg'}], 'start': 3102.99, 'title': 'Euclidean algorithm for gcd', 'summary': 'Discusses the efficiency of the euclidean algorithm for finding the greatest common divisor (gcd) of two numbers compared to the brute force method, emphasizing its o(log(phi) min(a, b)) time complexity and providing a detailed explanation of its iterative process and reduction steps.', 'chapters': [{'end': 3241.665, 'start': 3102.99, 'title': 'Euclidean algorithm for gcd', 'summary': 'Discusses the euclidean algorithm for finding the greatest common divisor (gcd) of two numbers, showcasing its efficiency in comparison to the brute force method, and explaining its mathematical basis and practical application.', 'duration': 138.675, 'highlights': ['The time complexity of the brute force method for finding GCD was linear, but the Euclidean algorithm offers a much more efficient approach, significantly reducing the time required for computation.', 'The Euclidean algorithm states that the GCD of two numbers, n1 and n2, is equivalent to the GCD of n1 minus n2 and n2, where n1 is greater than n2, providing a practical and efficient way to compute the GCD.', "The mathematical proof of the Euclidean algorithm's effectiveness in finding GCD exists, but for practical programming purposes, understanding the algorithm's concept is sufficient without delving into its mathematical intricacies."]}, {'end': 3790.209, 'start': 3242.385, 'title': 'Euclidean algorithm and time complexity', 'summary': 'Introduces the euclidean algorithm for finding the greatest common divisor (gcd) of two numbers, emphasizing the iterative process and the time complexity of the algorithm, which is o(log(phi) min(a, b)). the detailed explanation covers the step-by-step application of the algorithm, the reduction process, and the mathematical basis for the time complexity.', 'duration': 547.824, 'highlights': ['The Euclidean algorithm is used to find the GCD of two numbers iteratively, reducing the process till one of the numbers becomes zero. It emphasizes the iterative process of finding the GCD and highlights the step-by-step reduction till one of the numbers becomes zero.', 'The time complexity of the Euclidean algorithm is O(log(phi) min(a, b)), where phi is a mathematical constant and a, b are the input numbers. It explains the time complexity of the algorithm, O(log(phi) min(a, b)), and the basis for using phi as a constant due to the fluctuating nature of the input numbers.', 'The algorithm involves applying the modulo operation iteratively to reduce the larger number till one of the numbers becomes zero. It describes the reduction process involving the iterative application of the modulo operation to the larger number till one of the numbers becomes zero.']}], 'duration': 687.219, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/1xNbjMdbjug/pics/1xNbjMdbjug3102990.jpg', 'highlights': ['The Euclidean algorithm offers a much more efficient approach, significantly reducing the time required for computation.', 'The time complexity of the Euclidean algorithm is O(log(phi) min(a, b)), where phi is a mathematical constant and a, b are the input numbers.', 'The algorithm involves applying the modulo operation iteratively to reduce the larger number till one of the numbers becomes zero.', 'The Euclidean algorithm is used to find the GCD of two numbers iteratively, reducing the process till one of the numbers becomes zero.']}], 'highlights': ["The course has 455 modules, making it India's most in-depth DSA course, surpassing both paid and free courses in breadth of content.", 'The instructor focuses on teaching basic maths first to allow beginners to absorb the concepts before moving on to advanced topics.', 'The instructor follows a teaching method that starts with basic concepts, giving students ample time to absorb before moving on to advanced material.', 'The chapter emphasizes the importance of understanding the digit concept, highlighting its crucial role in solving most basic math problems.', 'The chapter introduces the concept of extraction of digits, illustrating its relevance in solving a variety of problems in basic mathematics.', 'The instructor will cover everything related to advanced mathematics that might be asked in interviews, with a focus on initially teaching basic math concepts.', 'Before solving the listed problems, the instructor will start by teaching basic math concepts, ensuring a strong foundation for problem-solving.', 'The chapter explains the concept of extracting digits from a number using modulo operator and division by 10. It demonstrates how to extract each individual digit from a number by performing modulo 10 and division by 10, providing a step-by-step explanation.', 'Demonstrates how to count the digits in a number using the extraction technique and logarithmic approach. It shows how to count the digits by using the extraction technique and then introduces an alternative approach using the logarithmic function to find the count of digits in a number.', 'Provides a pseudocode for extracting and counting the digits in a number. It offers a pseudocode to implement the process of extracting and counting the digits, providing a clear and structured approach to solving such problems.', 'The time complexity for division by 10 is log base 10n, by 2 is log base 2n, and by 5 is log base 5n, demonstrating the computation of time complexity based on division.', 'The number of iterations based on division results in a logarithmic time complexity, rather than linear time complexity.', 'Unit operations, such as divisions, have a significant impact on time complexity, especially in the case of larger numbers.', 'The process of generating the reverse of a number involves iterating through the input number, extracting the last digit, and incrementally building the reverse number by multiplying it with 10 and adding the next last digit, ultimately resulting in the reverse number 9877 from the input 7789.', 'The step-by-step explanation includes initializing the reverse number as 0, extracting the last digit from the input number, and iteratively building the reverse number by multiplying it with 10 and adding the next last digit, demonstrating a clear understanding of the reverse number generation process.', 'The reverse number algorithm involves multiplying the existing reverse number by 10 and then adding the last digit of the original number, which efficiently allows the addition of new digits in the correct place.', 'The process of determining if a number is a palindrome involves generating the reverse of the number and comparing it with the original number. Explains the process of checking for palindrome numbers and the necessary comparison step involved.', 'The definition of Armstrong number is explained using examples like 371 and 1634, emphasizing the requirement that the sum of the cubes of its digits should equal the number itself.', 'Iterating up to the square root of n and checking for factors allows for efficient factorization, as all factors can be found by the time the loop reaches the square root of n.', 'The product of a small number and a big number yields all the factors of 36, eliminating the need to go beyond the product of 1 and 36.', 'The divisors of 36, such as 1, 2, 3, 4, 6, 9, 12, 18, and 36, are printed in order using a loop from 1 to n, where n is the given number.', 'Using a list or vector data structure to store factors allows for efficient sorting and printing.', 'Emphasizes the importance of sorting the list to ensure factors are printed in a sorted fashion.', 'The time complexity in finding square roots and prime numbers is explained, emphasizing the importance of optimizing the process.', 'The definition of a prime number is clarified, emphasizing that a prime number has exactly two factors: 1 and itself.', 'The use of brute force to check for prime numbers is explained, highlighting the time complexity of the approach.', 'The square root method can be used to check for prime numbers by iterating up to the square root of n to find all factors, resulting in a time complexity of O(√n).', 'The time complexity for finding the GCD of two numbers is analyzed, with the conclusion that it is O(min(n1, n2)), addressing the scenario of handling edge cases efficiently.', 'The concept of GCD or HCF is illustrated using examples and the method to find the highest common factor for two given numbers is demonstrated.', 'The Euclidean algorithm offers a much more efficient approach, significantly reducing the time required for computation.', 'The time complexity of the Euclidean algorithm is O(log(phi) min(a, b)), where phi is a mathematical constant and a, b are the input numbers.', 'The algorithm involves applying the modulo operation iteratively to reduce the larger number till one of the numbers becomes zero.', 'The Euclidean algorithm is used to find the GCD of two numbers iteratively, reducing the process till one of the numbers becomes zero.']}