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7.3 Bubble Sort Algorithm| Data Structures Tutorials

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Discussed Bubble Sort Algorithm and its Program with an example.
Time complexity has also been calculated both in BEST case and WORST case.
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{'title': '7.3 Bubble Sort Algorithm| Data Structures Tutorials', 'heatmap': [{'end': 771.169, 'start': 725.72, 'weight': 0.859}, {'end': 911.808, 'start': 785.819, 'weight': 0.917}, {'end': 1199.661, 'start': 1129.095, 'weight': 0.828}, {'end': 1523.446, 'start': 1493.752, 'weight': 0.731}, {'end': 2094.853, 'start': 2047.222, 'weight': 0.903}], 'summary': 'Tutorial covers sorting techniques including bubble sort, explaining its working principle, code, and optimization. it demonstrates the process with examples and emphasizes reducing comparisons and computational operations for efficient sorting.', 'chapters': [{'end': 80.829, 'segs': [{'end': 80.829, 'src': 'embed', 'start': 0.229, 'weight': 0, 'content': [{'end': 3.992, 'text': 'are given, then you are arranging the data in either ascending order or descending order.', 'start': 0.229, 'duration': 3.763}, {'end': 4.992, 'text': 'you can say.', 'start': 3.992, 'duration': 1}, {'end': 11.337, 'text': 'and if character data is given, then sorting means to arrange that data alphabetically.', 'start': 4.992, 'duration': 6.345}, {'end': 18.042, 'text': 'fine, many sorting techniques are there bubble sort, insertion, selection, quick merge, redix, shell, heap sort.', 'start': 11.337, 'duration': 6.705}, {'end': 21.344, 'text': "okay, we'll discuss all the sorting techniques one by one in this video.", 'start': 18.042, 'duration': 3.302}, {'end': 23.846, 'text': "i'm going to discuss with you what is bubble sort.", 'start': 21.344, 'duration': 2.502}, {'end': 31.25, 'text': 'first of all we will discuss the working principle of this bubble sort with the help of an example how bubble sort works,', 'start': 24.406, 'duration': 6.844}, {'end': 34.493, 'text': 'how the data is to be sorted using this technique.', 'start': 31.25, 'duration': 3.243}, {'end': 45.96, 'text': 'then we will write down the code and after that we will see what modification we can do we can make in that algorithm of bubble sort for improving that algorithm.', 'start': 34.493, 'duration': 11.467}, {'end': 49.282, 'text': 'ok, now, first of all let us take one example.', 'start': 45.96, 'duration': 3.322}, {'end': 63.098, 'text': 'suppose data is given 15, 16, 6, 8 and five and data is stored in an array.', 'start': 49.282, 'duration': 13.816}, {'end': 69.962, 'text': 'suppose the array name is a, so the index would be from 0, 1, 2, 3, 4, something like this.', 'start': 63.098, 'duration': 6.864}, {'end': 73.985, 'text': 'okay, number of elements are 1, 2, 3, 4, 5.', 'start': 69.962, 'duration': 4.023}, {'end': 76.606, 'text': 'so suppose n is equal to 5.', 'start': 73.985, 'duration': 2.621}, {'end': 80.829, 'text': 'number of elements are n and n is equal to 5..', 'start': 76.606, 'duration': 4.223}], 'summary': 'Introduction to sorting techniques and focus on bubble sort', 'duration': 80.6, 'max_score': 0.229, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU229.jpg'}], 'start': 0.229, 'title': 'Sorting techniques', 'summary': 'Introduces various sorting techniques such as bubble sort, insertion, selection, quick merge, redix, shell, and heap sort, with a focus on discussing the working principle of bubble sort and its code with an example.', 'chapters': [{'end': 80.829, 'start': 0.229, 'title': 'Introduction to sorting techniques', 'summary': 'Covers the introduction to sorting techniques including bubble sort, insertion, selection, quick merge, redix, shell, and heap sort, with a focus on discussing the working principle of bubble sort and its code with an example.', 'duration': 80.6, 'highlights': ['The chapter covers various sorting techniques including bubble sort, insertion, selection, quick merge, redix, shell, and heap sort.', 'The focus is on discussing the working principle of bubble sort and its code with an example.', 'The data example provided for discussing bubble sort includes the elements: 15, 16, 6, 8, and 5.']}], 'duration': 80.6, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU229.jpg', 'highlights': ['The chapter covers various sorting techniques including bubble sort, insertion, selection, quick merge, redix, shell, and heap sort.', 'The focus is on discussing the working principle of bubble sort and its code with an example.', 'The data example provided for discussing bubble sort includes the elements: 15, 16, 6, 8, and 5.']}, {'end': 575.981, 'segs': [{'end': 154.737, 'src': 'embed', 'start': 129.765, 'weight': 3, 'content': [{'end': 135.089, 'text': 'you are going to sort the data in an ascending order using bubble sort.', 'start': 129.765, 'duration': 5.324}, {'end': 138.351, 'text': 'okay, now, what is the simple fundine bubble sort?', 'start': 135.089, 'duration': 3.262}, {'end': 145.194, 'text': 'we are going to start from first element and in bubble sort, this first element is compared with the second element.', 'start': 138.351, 'duration': 6.843}, {'end': 154.737, 'text': 'fine, and if these are in, these elements are in, you know, incorrect order, these are not in correct order, then we are going to swap these elements.', 'start': 146.052, 'duration': 8.685}], 'summary': 'Demonstrating bubble sort with comparison and swapping of elements.', 'duration': 24.972, 'max_score': 129.765, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU129764.jpg'}, {'end': 381.218, 'src': 'embed', 'start': 281.911, 'weight': 0, 'content': [{'end': 287.395, 'text': 'next comparison is this with this one now also swapping would be done.', 'start': 281.911, 'duration': 5.484}, {'end': 294.235, 'text': 'now the array would be 15, 6, 8, 5 and 16.', 'start': 287.395, 'duration': 6.84}, {'end': 305.381, 'text': 'okay, now this is known as this complete, is known as pass 1,', 'start': 294.235, 'duration': 11.146}, {'end': 317.668, 'text': 'and here you can see the largest element from this array has bubbled up to its right position to the end of the array.', 'start': 305.381, 'duration': 12.287}, {'end': 328.123, 'text': 'after completion of pass 1, the one element, that which is the largest element, has bubbled up to its correct position.', 'start': 317.668, 'duration': 10.455}, {'end': 331.926, 'text': 'okay, that is why it is known as bubble sort.', 'start': 328.123, 'duration': 3.803}, {'end': 342.78, 'text': 'okay, so now one element is in its correct position And this complete is known as pass 1..', 'start': 331.926, 'duration': 10.854}, {'end': 345.121, 'text': 'Now we are not still done with the sorting.', 'start': 342.78, 'duration': 2.341}, {'end': 348.583, 'text': 'Because the array is now this and this is not a sorted array.', 'start': 345.282, 'duration': 3.301}, {'end': 355.827, 'text': 'Now after this again we are going to start from first element.', 'start': 349.223, 'duration': 6.604}, {'end': 362.07, 'text': 'After pass 1 we are going to start pass 2.', 'start': 356.327, 'duration': 5.743}, {'end': 368.274, 'text': 'And now in pass 2 array is 15, 6, 8, 5 and 6.', 'start': 362.07, 'duration': 6.204}, {'end': 371.595, 'text': '16. fine, say, apply the logic of bubble.', 'start': 368.274, 'duration': 3.321}, {'end': 372.695, 'text': 'sort two adjacent.', 'start': 371.595, 'duration': 1.1}, {'end': 377.837, 'text': 'we are going to start from the zeroth element and two adjacent elements are to be compared.', 'start': 372.695, 'duration': 5.142}, {'end': 381.218, 'text': 'if they are, in, you know, correct position, then no swapping would be done.', 'start': 377.837, 'duration': 3.381}], 'summary': 'Bubble sort compares and swaps elements to move largest to end. pass 2 starts with array 15, 6, 8, 5, 16.', 'duration': 99.307, 'max_score': 281.911, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU281911.jpg'}, {'end': 545.786, 'src': 'embed', 'start': 511.916, 'weight': 2, 'content': [{'end': 517.037, 'text': 'next is this one and this one 6, 5, 8.', 'start': 511.916, 'duration': 5.121}, {'end': 518.017, 'text': 'no, swapping would be done.', 'start': 517.037, 'duration': 0.98}, {'end': 519.597, 'text': '15 and 16.', 'start': 518.017, 'duration': 1.58}, {'end': 521.638, 'text': 'now we are reached to the end of the array.', 'start': 519.597, 'duration': 2.041}, {'end': 524.318, 'text': 'now this is pass 3.', 'start': 521.638, 'duration': 2.68}, {'end': 533.5, 'text': 'now, after pass 3, 3 elements are at its correct position largest, second largest and third largest.', 'start': 524.318, 'duration': 9.182}, {'end': 536.08, 'text': 'now remaining are 2 elements.', 'start': 533.5, 'duration': 2.58}, {'end': 545.786, 'text': 'now. next pass would be pass Foo and in pass 4, array is 6, 5, 8, 15 and 16.', 'start': 536.08, 'duration': 9.706}], 'summary': 'Sorting algorithm completed 4 passes, reaching correct positions for 3 elements.', 'duration': 33.87, 'max_score': 511.916, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU511916.jpg'}], 'start': 80.829, 'title': 'Bubble sort algorithm', 'summary': 'Explains the basic principle of bubble sort, involving comparing and swapping adjacent elements to arrange data in ascending order, demonstrated through a detailed example, and further details the process with an array of 5 elements and 4 passes, ultimately achieving the sorted array.', 'chapters': [{'end': 348.583, 'start': 80.829, 'title': 'Bubble sort algorithm', 'summary': 'Explains the basic principle of bubble sort, which involves comparing and swapping adjacent elements to arrange data in ascending order, demonstrating the process through a detailed example.', 'duration': 267.754, 'highlights': ['The largest element from the array bubbles up to its correct position after completion of pass 1 in bubble sort. This is a quantifiable result of the bubble sort algorithm, indicating the progress made after the first pass of the sorting process.', 'Explanation of the process of comparing and swapping adjacent elements in bubble sort to arrange data in ascending order. This provides a detailed explanation of the key process involved in the bubble sort algorithm, contributing to the understanding of its functionality.', 'Demonstration of the comparison and swapping process through a specific example of sorting an array using bubble sort. This example showcases the practical application of the bubble sort algorithm, providing a visual representation of the sorting process.']}, {'end': 575.981, 'start': 349.223, 'title': 'Bubble sort algorithm', 'summary': 'Explains the process of bubble sort algorithm with an array of 5 elements, detailing the comparison and swapping process through 4 passes, ultimately achieving the sorted array.', 'duration': 226.758, 'highlights': ['The array is repeatedly traversed through passes, with each pass ensuring that the largest remaining element is placed in its correct position.', 'The swapping and comparison process is detailed, showcasing the step-by-step progression of the array towards being sorted.', 'The chapter concludes with the array being successfully sorted after 4 passes, demonstrating the effectiveness of the bubble sort algorithm.']}], 'duration': 495.152, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU80829.jpg', 'highlights': ['The chapter concludes with the array being successfully sorted after 4 passes, demonstrating the effectiveness of the bubble sort algorithm.', 'The largest element from the array bubbles up to its correct position after completion of pass 1 in bubble sort. This is a quantifiable result of the bubble sort algorithm, indicating the progress made after the first pass of the sorting process.', 'The array is repeatedly traversed through passes, with each pass ensuring that the largest remaining element is placed in its correct position.', 'Demonstration of the comparison and swapping process through a specific example of sorting an array using bubble sort. This example showcases the practical application of the bubble sort algorithm, providing a visual representation of the sorting process.', 'Explanation of the process of comparing and swapping adjacent elements in bubble sort to arrange data in ascending order. This provides a detailed explanation of the key process involved in the bubble sort algorithm, contributing to the understanding of its functionality.', 'The swapping and comparison process is detailed, showcasing the step-by-step progression of the array towards being sorted.']}, {'end': 924.478, 'segs': [{'end': 699.307, 'src': 'embed', 'start': 640.16, 'weight': 0, 'content': [{'end': 645.507, 'text': 'If number of elements are 6 then how many passes would be required? 5.', 'start': 640.16, 'duration': 5.347}, {'end': 651.514, 'text': 'Number of elements are 10 then number of passes would be 9.', 'start': 645.507, 'duration': 6.007}, {'end': 652.995, 'text': 'We will modify this also.', 'start': 651.514, 'duration': 1.481}, {'end': 660.001, 'text': "It's not like that if number of elements are 10, then those elements would be sorted in 9 passes only.", 'start': 653.175, 'duration': 6.826}, {'end': 661.982, 'text': 'That is not a rule.', 'start': 661.062, 'duration': 0.92}, {'end': 664.064, 'text': 'We are going to see that case also.', 'start': 662.503, 'duration': 1.561}, {'end': 666.226, 'text': 'This is the general case.', 'start': 665.065, 'duration': 1.161}, {'end': 674.153, 'text': 'If n elements are there, then in bubble sort, these steps would be repeated how many times? n minus 1 times.', 'start': 666.666, 'duration': 7.487}, {'end': 675.354, 'text': 'See now.', 'start': 675.033, 'duration': 0.321}, {'end': 682.62, 'text': 'Within this pass, how many comparisons are there? 1, 2, 3, 4.', 'start': 676.738, 'duration': 5.882}, {'end': 684.061, 'text': '4 comparisons.', 'start': 682.621, 'duration': 1.44}, {'end': 688.143, 'text': 'Within this pass also we have 1, 2, 3, 4 comparisons.', 'start': 684.542, 'duration': 3.601}, {'end': 690.604, 'text': 'Within this pass 1, 2, 3, 4.', 'start': 688.643, 'duration': 1.961}, {'end': 693.865, 'text': 'This pass 1, 2, 3, 4.', 'start': 690.604, 'duration': 3.261}, {'end': 695.367, 'text': 'So two loops would be there.', 'start': 693.866, 'duration': 1.501}, {'end': 699.307, 'text': 'One loop is for passes 1, 2, 3, 4.', 'start': 695.547, 'duration': 3.76}], 'summary': 'In bubble sort, for n elements, n-1 passes are needed with 4 comparisons in each pass.', 'duration': 59.147, 'max_score': 640.16, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU640160.jpg'}, {'end': 771.169, 'src': 'heatmap', 'start': 725.72, 'weight': 0.859, 'content': [{'end': 728.961, 'text': 'for suppose we are taking one variable.', 'start': 725.72, 'duration': 3.241}, {'end': 731.501, 'text': 'i i is equal to.', 'start': 728.961, 'duration': 2.54}, {'end': 738.616, 'text': 'outer loop is for these number of passes, and how many times this loop would be executed?', 'start': 731.501, 'duration': 7.115}, {'end': 740.857, 'text': 'n minus 1 times.', 'start': 738.616, 'duration': 2.241}, {'end': 747.879, 'text': 'right, because number of elements are here 5, number of passes are 4, that is n minus 1.', 'start': 740.857, 'duration': 7.022}, {'end': 752.961, 'text': 'so this loop would be executed for how many times n minus 1 times?', 'start': 747.879, 'duration': 5.082}, {'end': 764.024, 'text': 'so if you are going to start i from 0, then i should be less than n minus 1 and i plus plus.', 'start': 752.961, 'duration': 11.063}, {'end': 767.324, 'text': 'I hope you got the concept.', 'start': 765.962, 'duration': 1.362}, {'end': 771.169, 'text': 'Here suppose I is from 0.', 'start': 768.425, 'duration': 2.744}], 'summary': 'Outer loop executes n-1 times, given 5 elements and 4 passes.', 'duration': 45.449, 'max_score': 725.72, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU725720.jpg'}, {'end': 911.808, 'src': 'heatmap', 'start': 785.819, 'weight': 0.917, 'content': [{'end': 790.381, 'text': 'okay. that is why i am taking i is equal to from zero to less than n minus one.', 'start': 785.819, 'duration': 4.562}, {'end': 794.142, 'text': 'here n is five, five minus one, that is four.', 'start': 790.381, 'duration': 3.761}, {'end': 795.923, 'text': 'so i is less than four.', 'start': 794.142, 'duration': 1.781}, {'end': 798.024, 'text': 'it means i is equal to till.', 'start': 795.923, 'duration': 2.101}, {'end': 801.905, 'text': 'i is equal to, or you can say i is till three.', 'start': 798.024, 'duration': 3.881}, {'end': 806.467, 'text': 'if you take i is equal to one, then you can say i is less than equal to n minus one.', 'start': 801.905, 'duration': 4.562}, {'end': 810.349, 'text': 'now, within this, within this loop, one inner loop would be there.', 'start': 806.467, 'duration': 3.882}, {'end': 819.795, 'text': 'That is for suppose j is equal to 0, and this loop is for these comparisons.', 'start': 811.229, 'duration': 8.566}, {'end': 825.759, 'text': 'So how many comparisons within each pass? 1, 2, 3, 4, 4, 4, 4 and 4.', 'start': 820.716, 'duration': 5.043}, {'end': 827.901, 'text': 'It means n minus 1 comparison.', 'start': 825.759, 'duration': 2.142}, {'end': 832.904, 'text': 'So you can say j is less than n minus 1.', 'start': 827.941, 'duration': 4.963}, {'end': 836.005, 'text': 'same. fine, we are going to start from 0.', 'start': 832.904, 'duration': 3.101}, {'end': 838.645, 'text': 'that is why i am taking j is less than n minus 1.', 'start': 836.005, 'duration': 2.64}, {'end': 844.687, 'text': 'if you write here j is equal to 1, then you can say j is less than equal to n minus 1.', 'start': 838.645, 'duration': 6.042}, {'end': 849.428, 'text': 'and here you will write j plus plus.', 'start': 844.687, 'duration': 4.741}, {'end': 852.729, 'text': 'fine. now the main logic is what.', 'start': 849.428, 'duration': 3.301}, {'end': 853.289, 'text': 'now we are.', 'start': 852.729, 'duration': 0.56}, {'end': 860.411, 'text': 'we are going to check if this element is greater than this element, then you do what swapping.', 'start': 853.289, 'duration': 7.122}, {'end': 862.888, 'text': 'fine, see here this case.', 'start': 861.527, 'duration': 1.361}, {'end': 869.352, 'text': 'you can say here no swapping is done, but here this element is greater than the next element.', 'start': 862.888, 'duration': 6.464}, {'end': 872.134, 'text': 'so that is why we have done what swapping.', 'start': 869.352, 'duration': 2.782}, {'end': 873.895, 'text': 'so here what you will check.', 'start': 872.134, 'duration': 1.761}, {'end': 890.835, 'text': 'if, if name of this array is a, a of j is greater than a of j plus 1, then you do what swapping.', 'start': 873.895, 'duration': 16.94}, {'end': 892.416, 'text': 'and swapping is you?', 'start': 890.835, 'duration': 1.581}, {'end': 893.658, 'text': 'i guess you know the logic.', 'start': 892.416, 'duration': 1.242}, {'end': 896.42, 'text': 'you just take a temp variable and do the swapping.', 'start': 893.658, 'duration': 2.762}, {'end': 911.808, 'text': 'so we do what temp is equal to a of j and a of j is equal to a of j plus 1, and then a of j plus 1 is equal to 10.', 'start': 896.42, 'duration': 15.388}], 'summary': 'The algorithm involves nested loops with n-1 comparisons and swapping elements if necessary.', 'duration': 125.989, 'max_score': 785.819, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU785819.jpg'}], 'start': 582.808, 'title': 'Sorting algorithm and bubble sort', 'summary': 'Explains the concept of sorting algorithm, emphasizing on the number of passes required to sort the elements, and further discusses the bubble sort algorithm with n minus 1 comparisons within each pass and execution of outer and inner loops n minus 1 times.', 'chapters': [{'end': 666.226, 'start': 582.808, 'title': 'Sorting algorithm explanation', 'summary': 'Explains the concept of sorting algorithm, emphasizing on the number of passes required to sort the elements and clarifying that the number of passes required is always one less than the number of elements. it also highlights the special case when the number of passes is not strictly one less than the number of elements.', 'duration': 83.418, 'highlights': ['The number of passes required to sort the elements is always one less than the number of elements - for 5 elements, 4 passes are required, for 6 elements, 5 passes are required, and so on.', 'The special case where the number of elements does not strictly determine the number of passes required is highlighted, indicating that the process is not solely based on the number of elements.']}, {'end': 924.478, 'start': 666.666, 'title': 'Bubble sort algorithm', 'summary': 'Explains the bubble sort algorithm, where the number of comparisons within each pass is n minus 1, and the outer loop for passes is executed n minus 1 times, with the inner loop for comparisons executed n minus 1 times as well.', 'duration': 257.812, 'highlights': ['The number of comparisons within each pass is n minus 1. The algorithm indicates that within each pass, there are n minus 1 comparisons, providing a clear understanding of the number of comparisons made in each iteration.', 'The outer loop for passes is executed n minus 1 times. The outer loop, responsible for the number of passes, is executed n minus 1 times, illustrating the iterative process of the bubble sort algorithm.', 'The inner loop for comparisons is executed n minus 1 times as well. Similarly, the inner loop for comparisons is also executed n minus 1 times within each pass, showcasing the repetitive nature of the comparison process in bubble sort.']}], 'duration': 341.67, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU582808.jpg', 'highlights': ['The number of passes required to sort the elements is always one less than the number of elements - for 5 elements, 4 passes are required, for 6 elements, 5 passes are required, and so on.', 'The number of comparisons within each pass is n minus 1. The algorithm indicates that within each pass, there are n minus 1 comparisons, providing a clear understanding of the number of comparisons made in each iteration.', 'The special case where the number of elements does not strictly determine the number of passes required is highlighted, indicating that the process is not solely based on the number of elements.', 'The outer loop for passes is executed n minus 1 times. The outer loop, responsible for the number of passes, is executed n minus 1 times, illustrating the iterative process of the bubble sort algorithm.', 'The inner loop for comparisons is executed n minus 1 times as well. Similarly, the inner loop for comparisons is also executed n minus 1 times within each pass, showcasing the repetitive nature of the comparison process in bubble sort.']}, {'end': 1293.648, 'segs': [{'end': 955.952, 'src': 'embed', 'start': 924.478, 'weight': 1, 'content': [{'end': 928.281, 'text': 'how see here how many comparisons are there?', 'start': 924.478, 'duration': 3.803}, {'end': 934.826, 'text': 'four comparisons, but after pass one, the largest element is at its correct position, right.', 'start': 928.281, 'duration': 6.545}, {'end': 942.368, 'text': 'so in in this pass, do you really need to compare 15 with 16?', 'start': 934.826, 'duration': 7.542}, {'end': 943.129, 'text': 'i guess no.', 'start': 942.368, 'duration': 0.761}, {'end': 943.589, 'text': 'why so?', 'start': 943.129, 'duration': 0.46}, {'end': 948.15, 'text': 'because we know that the last element is the largest element.', 'start': 943.589, 'duration': 4.561}, {'end': 955.952, 'text': 'so no need to compare this element, because we know that this element is always less than this element and no swapping would be done.', 'start': 948.15, 'duration': 7.802}], 'summary': 'In the sorting process, 4 comparisons are made, but after the first pass, the largest element is in its correct position, thus eliminating the need for further comparison of certain elements.', 'duration': 31.474, 'max_score': 924.478, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU924478.jpg'}, {'end': 998.815, 'src': 'embed', 'start': 970.405, 'weight': 2, 'content': [{'end': 972.686, 'text': 'this is the second largest element.', 'start': 970.405, 'duration': 2.281}, {'end': 978.706, 'text': 'fine, then, do you really need to compare 8 with 15?', 'start': 972.686, 'duration': 6.02}, {'end': 981.727, 'text': 'No, because these elements are its correct position.', 'start': 978.706, 'duration': 3.021}, {'end': 983.948, 'text': 'These are the two largest element.', 'start': 982.128, 'duration': 1.82}, {'end': 989.011, 'text': 'So, we can say that obviously this element would not be greater than this element.', 'start': 984.569, 'duration': 4.442}, {'end': 993.713, 'text': 'So, no need to compare this and obviously then no need to do this comparison.', 'start': 989.811, 'duration': 3.902}, {'end': 998.815, 'text': 'so in this pass only two comparisons are required.', 'start': 995.351, 'duration': 3.464}], 'summary': 'In this pass, only two comparisons are required, as these are the two largest elements.', 'duration': 28.41, 'max_score': 970.405, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU970405.jpg'}, {'end': 1076.467, 'src': 'embed', 'start': 1044.471, 'weight': 3, 'content': [{'end': 1050.374, 'text': 'See, this number of comparison depends on this i value.', 'start': 1044.471, 'duration': 5.903}, {'end': 1054.557, 'text': 'Because when i value is 0, then how many comparison?', 'start': 1050.374, 'duration': 4.183}, {'end': 1056.318, 'text': 'n minus 1 comparison.', 'start': 1054.557, 'duration': 1.761}, {'end': 1062.121, 'text': 'But when i value is 1, then only 1, 2, 3, 3 comparisons.', 'start': 1056.318, 'duration': 5.803}, {'end': 1065.843, 'text': 'It means 1 comparison less.', 'start': 1062.121, 'duration': 3.722}, {'end': 1068.725, 'text': 'So when i value is 2, then how many comparisons?', 'start': 1065.843, 'duration': 2.882}, {'end': 1070.646, 'text': 'only 1, 2 comparisons.', 'start': 1068.725, 'duration': 1.921}, {'end': 1076.467, 'text': 'So you can say when I value is increasing, number of comparisons are decreasing.', 'start': 1071.621, 'duration': 4.846}], 'summary': 'As the i value increases, the number of comparisons decreases.', 'duration': 31.996, 'max_score': 1044.471, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU1044471.jpg'}, {'end': 1199.661, 'src': 'heatmap', 'start': 1129.095, 'weight': 0.828, 'content': [{'end': 1136.361, 'text': 'if you do this case, then that unnecessary comparisons can be avoided.', 'start': 1129.095, 'duration': 7.266}, {'end': 1138.022, 'text': 'so how this will work.', 'start': 1136.361, 'duration': 1.661}, {'end': 1139.383, 'text': 'see, let us take one case.', 'start': 1138.022, 'duration': 1.361}, {'end': 1143.735, 'text': 'let us take i value is equal to 2.', 'start': 1139.383, 'duration': 4.352}, {'end': 1150.197, 'text': 'fine, 2 is less than n minus 1, n minus 1 is what n is 5, 5 minus 1 is 4, yes, this condition is true.', 'start': 1143.735, 'duration': 6.462}, {'end': 1154.319, 'text': '2 is less than 4, then we will go to this loop.', 'start': 1150.197, 'duration': 4.122}, {'end': 1155.9, 'text': 'j is equal to 0.', 'start': 1154.319, 'duration': 1.581}, {'end': 1162.362, 'text': 'now j is equal to 0, so j is less than n minus 1, minus i.', 'start': 1155.9, 'duration': 6.462}, {'end': 1164.803, 'text': 'n is equal to 5, 5 minus 1, 4, 4 minus.', 'start': 1162.362, 'duration': 2.441}, {'end': 1177.096, 'text': 'i value is 2, 4 minus 2 is 2, yes, 0 is less than 2, yes, then we will enter this loop.', 'start': 1164.803, 'duration': 12.293}, {'end': 1184.082, 'text': 'now we compare what a of 0 greater than a of 1.', 'start': 1177.096, 'duration': 6.986}, {'end': 1186.445, 'text': 'now, see, i is equal to 2.', 'start': 1184.082, 'duration': 2.363}, {'end': 1189.247, 'text': 'a of 0 greater than a of 1.', 'start': 1186.445, 'duration': 2.802}, {'end': 1192.19, 'text': 'no, this condition is not true because 6 is less than 8.', 'start': 1189.247, 'duration': 2.943}, {'end': 1199.661, 'text': 'fine, so we will not enter this condition because this condition is not true, so we will not enter here.', 'start': 1192.19, 'duration': 7.471}], 'summary': 'Demonstration of avoiding unnecessary comparisons using a specific case in a loop.', 'duration': 70.566, 'max_score': 1129.095, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU1129095.jpg'}, {'end': 1298.99, 'src': 'embed', 'start': 1271.15, 'weight': 0, 'content': [{'end': 1273.592, 'text': 'this comparison is also not required.', 'start': 1271.15, 'duration': 2.442}, {'end': 1277.063, 'text': 'fine. so this is how you can.', 'start': 1274.582, 'duration': 2.481}, {'end': 1282.625, 'text': 'you can avoid the unnecessary comparisons only by writing here n minus 1 minus i.', 'start': 1277.063, 'duration': 5.562}, {'end': 1286.146, 'text': 'this is why we write here n minus 1 minus i.', 'start': 1282.625, 'duration': 3.521}, {'end': 1291.667, 'text': 'now one more modification you can do in this algorithm, and that is known as optimized bubble sort.', 'start': 1286.146, 'duration': 5.521}, {'end': 1293.648, 'text': 'now, what is that modification?', 'start': 1291.667, 'duration': 1.981}, {'end': 1298.99, 'text': 'see in this case, how many passes after how many passes you got the sorted array?', 'start': 1293.648, 'duration': 5.342}], 'summary': 'Optimize bubble sort algorithm by avoiding unnecessary comparisons and making modifications.', 'duration': 27.84, 'max_score': 1271.15, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU1271150.jpg'}], 'start': 924.478, 'title': 'Optimizing sorting algorithm', 'summary': 'Discusses optimizing comparisons in sorting algorithms by identifying unnecessary comparisons in already sorted elements, reducing required comparisons. it also explains optimizing the bubble sort algorithm by modifying the inner loop to n minus 1 minus i, resulting in a significant decrease in comparisons as the i value increases.', 'chapters': [{'end': 1042.564, 'start': 924.478, 'title': 'Optimizing comparison in sorting algorithm', 'summary': 'Discusses the optimization of comparisons in a sorting algorithm by identifying unnecessary comparisons based on the already sorted elements, reducing the number of required comparisons to sort the elements.', 'duration': 118.086, 'highlights': ['Identifying unnecessary comparisons based on already sorted elements, reducing the number of required comparisons to sort the elements.', 'Explaining the concept using examples of largest and second largest elements to omit comparisons and optimize computation.', 'Discussing the process of identifying correct positions of elements after each pass to minimize unnecessary comparisons.']}, {'end': 1293.648, 'start': 1044.471, 'title': 'Optimized bubble sort', 'summary': 'Explains how to optimize the bubble sort algorithm by reducing unnecessary comparisons by modifying the inner loop to n minus 1 minus i, resulting in a significant decrease in the number of comparisons as the i value increases.', 'duration': 249.177, 'highlights': ['By modifying the inner loop to n minus 1 minus i, unnecessary comparisons can be avoided, resulting in a significant reduction in the number of comparisons as the i value increases.', 'The number of comparisons in the algorithm depends on the i value, with n minus 1 comparisons when i equals 0 and decreasing as i increases.', 'Illustration of the optimization with i value equal to 2, showing a decrease in the number of comparisons and the avoidance of unnecessary comparisons.']}], 'duration': 369.17, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU924478.jpg', 'highlights': ['Modifying inner loop to n minus 1 minus i reduces unnecessary comparisons as i increases.', 'Identifying correct positions of elements after each pass minimizes unnecessary comparisons.', 'Explanation using examples of largest and second largest elements to omit comparisons.', 'Illustration of optimization with i value equal to 2, showing decrease in comparisons.', 'Number of comparisons in algorithm depends on i value, decreasing as i increases.']}, {'end': 1617.107, 'segs': [{'end': 1399.889, 'src': 'embed', 'start': 1293.648, 'weight': 0, 'content': [{'end': 1298.99, 'text': 'see in this case, how many passes after how many passes you got the sorted array?', 'start': 1293.648, 'duration': 5.342}, {'end': 1305.594, 'text': 'after 4 passes you can say after n-1 passes, but every time this is not true,', 'start': 1299.89, 'duration': 5.704}, {'end': 1315.139, 'text': 'may be sometimes 10 elements are there and only after executing 3 passes you got the sorted array.', 'start': 1305.594, 'duration': 9.545}, {'end': 1321.683, 'text': 'fine, but when you apply this logic, then this program would be executed.', 'start': 1315.139, 'duration': 6.544}, {'end': 1325.005, 'text': 'for how many times n-1?', 'start': 1321.683, 'duration': 3.322}, {'end': 1333.539, 'text': 'you can say if n is equal to 10, then for nine times this is to be executed.', 'start': 1325.005, 'duration': 8.534}, {'end': 1344.523, 'text': 'fine. and if, suppose this this, all the elements, all the elements has been sorted after the third pass, only then remaining passes are wasted.', 'start': 1333.539, 'duration': 10.984}, {'end': 1346.903, 'text': 'wastage of time now.', 'start': 1344.523, 'duration': 2.38}, {'end': 1351.325, 'text': 'so what you can do is so, to get this point, let us take one more example.', 'start': 1346.903, 'duration': 4.422}, {'end': 1359.385, 'text': 'see, now we are going to take one more example see, suppose this is the array 16, 14, 5, 6 and 8.', 'start': 1352.441, 'duration': 6.944}, {'end': 1360.105, 'text': 'how many elements?', 'start': 1359.385, 'duration': 0.72}, {'end': 1361.286, 'text': '5 elements.', 'start': 1360.105, 'duration': 1.181}, {'end': 1364.888, 'text': 'ok, now, according to this case, how many passes would be required?', 'start': 1361.286, 'duration': 3.602}, {'end': 1368.39, 'text': 'this, this numerical or you can say this program would be executed?', 'start': 1364.888, 'duration': 3.502}, {'end': 1369.671, 'text': 'for how many passes?', 'start': 1368.39, 'duration': 1.281}, {'end': 1374.675, 'text': 'four passes n minus one, n minus one.', 'start': 1370.973, 'duration': 3.702}, {'end': 1383.159, 'text': 'fine, now see, when you apply the bubble sort, then you see that you see that in pass one, yes, swapping is done.', 'start': 1374.675, 'duration': 8.484}, {'end': 1384.9, 'text': 'we got the largest element here.', 'start': 1383.159, 'duration': 1.741}, {'end': 1390.043, 'text': 'in pass two, we have just done three comparisons and two largest element are there.', 'start': 1384.9, 'duration': 5.143}, {'end': 1397.127, 'text': 'and in pass 3, see when you are comparing 5 with 6, no swapping is there.', 'start': 1391.361, 'duration': 5.766}, {'end': 1399.889, 'text': 'when you are comparing 6 with 8, no swapping is there.', 'start': 1397.127, 'duration': 2.762}], 'summary': 'Bubble sort may require fewer passes than n-1 for sorting, leading to potential time wastage.', 'duration': 106.241, 'max_score': 1293.648, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU1293648.jpg'}, {'end': 1526.787, 'src': 'heatmap', 'start': 1485.401, 'weight': 4, 'content': [{'end': 1488.943, 'text': 'if see in this pass one swapping is there, 14 and 15.', 'start': 1485.401, 'duration': 3.542}, {'end': 1490.523, 'text': 'yes, this swapping was there.', 'start': 1488.943, 'duration': 1.58}, {'end': 1492.424, 'text': 'so here we got one swapping.', 'start': 1490.523, 'duration': 1.901}, {'end': 1498.533, 'text': 'here also we got swapping, but in this pass no swapping is there.', 'start': 1493.752, 'duration': 4.781}, {'end': 1502.735, 'text': 'so we can say that now the array is sorted, no need to do any other passes.', 'start': 1498.533, 'duration': 4.202}, {'end': 1504.295, 'text': 'so how to check that condition?', 'start': 1502.735, 'duration': 1.56}, {'end': 1506.796, 'text': 'so we can take one flag variable.', 'start': 1504.295, 'duration': 2.501}, {'end': 1514.338, 'text': 'fine, now, in starting we in this loop, suppose after this loop we are going to set this flag.', 'start': 1506.796, 'duration': 7.542}, {'end': 1523.446, 'text': 'variable is equal to 0 and now, if swapping is done, then you can set this variable as 1.', 'start': 1514.338, 'duration': 9.108}, {'end': 1526.787, 'text': 'so the code for swapping is here only.', 'start': 1523.446, 'duration': 3.341}], 'summary': 'The array is sorted after 2 passes with swapping at 14 and 15.', 'duration': 41.386, 'max_score': 1485.401, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU1485401.jpg'}], 'start': 1293.648, 'title': 'Sorting algorithm efficiency and bubble sort optimization', 'summary': 'Explains the efficiency of sorting algorithms by discussing the number of passes required and highlights the potential time wastage. it also discusses the optimization of the bubble sort algorithm, emphasizing reduced comparisons and unnecessary pass stoppage, with an example of a sorted array of 5, 6, 8, 14, and 16.', 'chapters': [{'end': 1374.675, 'start': 1293.648, 'title': 'Sorting algorithm efficiency', 'summary': 'Explains the efficiency of a sorting algorithm by discussing the number of passes required to sort an array, highlighting the potential wastage of time if the remaining passes are executed after the array is already sorted.', 'duration': 81.027, 'highlights': ['The number of passes required to sort an array using a sorting algorithm is not always equal to n-1, as demonstrated by the example with 10 elements being sorted after only 3 passes.', 'The potential wastage of time in sorting algorithms is illustrated by the scenario where all elements are sorted after a certain pass, resulting in the remaining passes being unnecessary.', "The concept of the number of passes needed to sort an array is further exemplified using a specific array of 5 elements, demonstrating the variation in the required number of passes based on the array's initial state."]}, {'end': 1617.107, 'start': 1374.675, 'title': 'Bubble sort algorithm optimization', 'summary': 'Discusses the optimization of the bubble sort algorithm, highlighting the reduced comparisons and the modification of the program to stop unnecessary passes based on the presence of swapping, with an example of a sorted array of 5, 6, 8, 14, and 16.', 'duration': 242.432, 'highlights': ['The chapter explains the optimization of the bubble sort algorithm by modifying the program to stop unnecessary passes, reducing the number of comparisons and iterations, as demonstrated by the example of a sorted array of 5, 6, 8, 14, and 16.', 'It introduces the concept of a flag variable to track swapping and illustrates how the program can be modified to break the loop and declare the array as sorted when no swapping occurs in a pass, effectively reducing the computational overhead.', 'The technique of using a flag variable to identify the presence of swapping in each pass is demonstrated, showcasing its role in determining whether the array is sorted and breaking the loop accordingly, leading to improved efficiency in sorting.']}], 'duration': 323.459, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU1293648.jpg', 'highlights': ['The number of passes required to sort an array is not always equal to n-1, as demonstrated by the example with 10 elements being sorted after only 3 passes.', 'The potential wastage of time in sorting algorithms is illustrated by the scenario where all elements are sorted after a certain pass, resulting in the remaining passes being unnecessary.', "The concept of the number of passes needed to sort an array is further exemplified using a specific array of 5 elements, demonstrating the variation in the required number of passes based on the array's initial state.", 'The chapter explains the optimization of the bubble sort algorithm by modifying the program to stop unnecessary passes, reducing the number of comparisons and iterations, as demonstrated by the example of a sorted array of 5, 6, 8, 14, and 16.', 'It introduces the concept of a flag variable to track swapping and illustrates how the program can be modified to break the loop and declare the array as sorted when no swapping occurs in a pass, effectively reducing the computational overhead.', 'The technique of using a flag variable to identify the presence of swapping in each pass is demonstrated, showcasing its role in determining whether the array is sorted and breaking the loop accordingly, leading to improved efficiency in sorting.']}, {'end': 2135.235, 'segs': [{'end': 1645.577, 'src': 'embed', 'start': 1617.107, 'weight': 1, 'content': [{'end': 1621.368, 'text': 'this is not the complete code, i am just writing the logic.', 'start': 1617.107, 'duration': 4.261}, {'end': 1628.65, 'text': 'obviously you have to declare one array, a size of the array, n, flag variable and something like this.', 'start': 1621.368, 'duration': 7.282}, {'end': 1632.071, 'text': 'so this is the optimized bubble sort.', 'start': 1628.65, 'duration': 3.421}, {'end': 1636.452, 'text': 'so now let us trace out this thing, this program, with the help of one example.', 'start': 1632.071, 'duration': 4.381}, {'end': 1638.032, 'text': 'let us take one i value.', 'start': 1636.452, 'duration': 1.58}, {'end': 1642.075, 'text': 'i value is equal to suppose 2.', 'start': 1638.032, 'duration': 4.043}, {'end': 1643.496, 'text': 'see when i value is 0.', 'start': 1642.075, 'duration': 1.421}, {'end': 1645.577, 'text': 'so i value is 0 for this pass.', 'start': 1643.496, 'duration': 2.081}], 'summary': 'Optimized bubble sort logic explained with an example.', 'duration': 28.47, 'max_score': 1617.107, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU1617107.jpg'}, {'end': 1692.242, 'src': 'embed', 'start': 1668.663, 'weight': 2, 'content': [{'end': 1677.129, 'text': "because according to, because if we don't write this flag variable, this will this flag variable, this this code, then how many passes would be there?", 'start': 1668.663, 'duration': 8.466}, {'end': 1682.013, 'text': 'four passes would be there and i would be increased from zero to three.', 'start': 1677.129, 'duration': 4.884}, {'end': 1687.437, 'text': 'but if you write down this code and if this code is correct, then i value would not be increased to 3.', 'start': 1682.013, 'duration': 5.424}, {'end': 1692.242, 'text': 'the outer loop would be executed for i value 0, 1 and 2.', 'start': 1687.437, 'duration': 4.805}], 'summary': 'Without the flag variable, the code would have four passes with i increasing from 0 to 3, but with the flag variable correctly implemented, the outer loop would execute for i values 0, 1, and 2.', 'duration': 23.579, 'max_score': 1668.663, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU1668663.jpg'}, {'end': 1992.128, 'src': 'embed', 'start': 1959.7, 'weight': 5, 'content': [{'end': 1961.2, 'text': 'this array is already sorted.', 'start': 1959.7, 'duration': 1.5}, {'end': 1962.141, 'text': 'how many elements are there?', 'start': 1961.2, 'duration': 0.941}, {'end': 1962.741, 'text': '1, 2, 3, 4, 5, 6, 7, 8.', 'start': 1962.141, 'duration': 0.6}, {'end': 1967.338, 'text': 'n is equal to 8.', 'start': 1962.741, 'duration': 4.597}, {'end': 1973.605, 'text': "now, if you don't apply this logic, if you don't apply this flag variable, then how many times how many passes would be there?", 'start': 1967.338, 'duration': 6.267}, {'end': 1977.969, 'text': '7 passes.', 'start': 1973.605, 'duration': 4.364}, {'end': 1982.734, 'text': 'fine, this program would be executed for 7 passes again and again.', 'start': 1977.969, 'duration': 4.765}, {'end': 1986.579, 'text': 'but no need to execute for 7 passes, because this array is already sorted.', 'start': 1982.734, 'duration': 3.845}, {'end': 1992.128, 'text': 'na in one pass only we can come to know that this array is already sorted.', 'start': 1986.579, 'duration': 5.549}], 'summary': 'Array of 8 elements, already sorted, requires 1 pass to verify.', 'duration': 32.428, 'max_score': 1959.7, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU1959700.jpg'}, {'end': 2094.853, 'src': 'heatmap', 'start': 2008.101, 'weight': 0, 'content': [{'end': 2014.427, 'text': 'and if in any pass you find out that no swapping has been done, then you can say that this array is already sorted.', 'start': 2008.101, 'duration': 6.326}, {'end': 2022.498, 'text': 'fine, so no need to do seven passes, no need to execute this program for seven passes.', 'start': 2015.691, 'duration': 6.807}, {'end': 2025.621, 'text': 'just in one pass only you can come to know that array is sorted.', 'start': 2022.498, 'duration': 3.123}, {'end': 2032.629, 'text': 'but only if you apply this logic, if you apply this flag variable, then only you can come to know, in in one pass only,', 'start': 2025.621, 'duration': 7.008}, {'end': 2034.331, 'text': 'that this array is already sorted.', 'start': 2032.629, 'duration': 1.702}, {'end': 2036.633, 'text': 'so this is the best case.', 'start': 2034.331, 'duration': 2.302}, {'end': 2039.255, 'text': 'so best case is then array is already sorted.', 'start': 2036.633, 'duration': 2.622}, {'end': 2042.238, 'text': 'so in this case the time complexity is what.', 'start': 2039.255, 'duration': 2.983}, {'end': 2043.839, 'text': 'how to find out time complexity?', 'start': 2042.238, 'duration': 1.601}, {'end': 2047.222, 'text': 'see how many for loops are there one and two.', 'start': 2043.839, 'duration': 3.383}, {'end': 2054.608, 'text': 'so to find out the time complexity you just have to check out how many times, how many calculations are there,', 'start': 2047.222, 'duration': 7.386}, {'end': 2058.429, 'text': 'how many computations are there within this inner for loop?', 'start': 2054.608, 'duration': 3.821}, {'end': 2061.813, 'text': 'so the best case is array is already sorted.', 'start': 2058.429, 'duration': 3.384}, {'end': 2065.614, 'text': 'so in one pass only you can come to know that array is already sorted.', 'start': 2061.813, 'duration': 3.801}, {'end': 2068.717, 'text': 'so this loop will be executed for one time only.', 'start': 2065.614, 'duration': 3.103}, {'end': 2074.661, 'text': 'and this loop would be executed for how many times for n minus 1?', 'start': 2068.717, 'duration': 5.944}, {'end': 2076.623, 'text': 'n minus 1 comparison would be there.', 'start': 2074.661, 'duration': 1.962}, {'end': 2082.768, 'text': 'so the time complexity would be order of n in best case when you apply this logic.', 'start': 2076.623, 'duration': 6.145}, {'end': 2089.857, 'text': 'but in worst case, worst case means the array is given in descending order and you are supposed to arrange the array in ascending order.', 'start': 2082.768, 'duration': 7.089}, {'end': 2094.853, 'text': 'in that case the time complexity would be order of n square.', 'start': 2089.857, 'duration': 4.996}], 'summary': 'Best case: array already sorted, time complexity o(n). worst case: descending order, time complexity o(n^2).', 'duration': 46.507, 'max_score': 2008.101, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU2008101.jpg'}, {'end': 2101.097, 'src': 'embed', 'start': 2076.623, 'weight': 4, 'content': [{'end': 2082.768, 'text': 'so the time complexity would be order of n in best case when you apply this logic.', 'start': 2076.623, 'duration': 6.145}, {'end': 2089.857, 'text': 'but in worst case, worst case means the array is given in descending order and you are supposed to arrange the array in ascending order.', 'start': 2082.768, 'duration': 7.089}, {'end': 2094.853, 'text': 'in that case the time complexity would be order of n square.', 'start': 2089.857, 'duration': 4.996}, {'end': 2095.632, 'text': 'why so?', 'start': 2094.853, 'duration': 0.779}, {'end': 2101.097, 'text': 'because outer loop would all would be executed for how many times n minus 1 times?', 'start': 2095.632, 'duration': 5.465}], 'summary': 'Time complexity: o(n) best case, o(n^2) worst case', 'duration': 24.474, 'max_score': 2076.623, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU2076623.jpg'}], 'start': 1617.107, 'title': 'Bubble sort optimization and time complexity', 'summary': 'Covers the optimized bubble sort logic, illustrating the use of a flag variable to minimize passes and iterations through the array. additionally, it discusses the time complexity of bubble sort, emphasizing the importance of reducing computational operations for sorting.', 'chapters': [{'end': 1930.061, 'start': 1617.107, 'title': 'Optimized bubble sort logic', 'summary': 'Covers the optimized bubble sort logic, tracing the program with an example and discussing the use of a flag variable to reduce the number of passes and iterations through the array.', 'duration': 312.954, 'highlights': ['The use of a flag variable to optimize the bubble sort and reduce the number of passes and iterations through the array.', "Tracing the program with an example and discussing the value of 'i' for each pass, emphasizing the impact of the flag variable on the value of 'i' and the number of passes.", 'Explanation of the control flow within the nested for loops, highlighting the conditions and iterations during the sorting process.']}, {'end': 2135.235, 'start': 1930.061, 'title': 'Bubble sort time complexity', 'summary': 'Discusses the time complexity of bubble sort, highlighting the best and worst case scenarios and the corresponding time complexities, with an emphasis on reducing the number of passes and computational operations required for sorting.', 'duration': 205.174, 'highlights': ['The best case scenario for bubble sort is when the array is already sorted, leading to a time complexity of O(n) as the loop is executed only once, reducing the number of comparisons to n-1.', 'The worst case scenario for bubble sort is when the array is given in descending order, resulting in a time complexity of O(n^2) due to the polynomial nature of the computational operations within the nested loops.', 'The chapter emphasizes the importance of applying a flag variable to reduce the number of passes required for sorting, highlighting the efficiency gained by identifying the sorted array in just one pass.']}], 'duration': 518.128, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/o4bAoo_gFBU/pics/o4bAoo_gFBU1617107.jpg', 'highlights': ['The chapter emphasizes the importance of applying a flag variable to reduce the number of passes required for sorting, highlighting the efficiency gained by identifying the sorted array in just one pass.', 'The use of a flag variable to optimize the bubble sort and reduce the number of passes and iterations through the array.', "Tracing the program with an example and discussing the value of 'i' for each pass, emphasizing the impact of the flag variable on the value of 'i' and the number of passes.", 'The best case scenario for bubble sort is when the array is already sorted, leading to a time complexity of O(n) as the loop is executed only once, reducing the number of comparisons to n-1.', 'The worst case scenario for bubble sort is when the array is given in descending order, resulting in a time complexity of O(n^2) due to the polynomial nature of the computational operations within the nested loops.', 'Explanation of the control flow within the nested for loops, highlighting the conditions and iterations during the sorting process.']}], 'highlights': ['The chapter covers various sorting techniques including bubble sort, insertion, selection, quick merge, redix, shell, and heap sort.', 'The focus is on discussing the working principle of bubble sort and its code with an example.', 'The data example provided for discussing bubble sort includes the elements: 15, 16, 6, 8, and 5.', 'The chapter concludes with the array being successfully sorted after 4 passes, demonstrating the effectiveness of the bubble sort algorithm.', 'The largest element from the array bubbles up to its correct position after completion of pass 1 in bubble sort. This is a quantifiable result of the bubble sort algorithm, indicating the progress made after the first pass of the sorting process.', 'The array is repeatedly traversed through passes, with each pass ensuring that the largest remaining element is placed in its correct position.', 'Demonstration of the comparison and swapping process through a specific example of sorting an array using bubble sort. This example showcases the practical application of the bubble sort algorithm, providing a visual representation of the sorting process.', 'Explanation of the process of comparing and swapping adjacent elements in bubble sort to arrange data in ascending order. This provides a detailed explanation of the key process involved in the bubble sort algorithm, contributing to the understanding of its functionality.', 'The swapping and comparison process is detailed, showcasing the step-by-step progression of the array towards being sorted.', 'The number of passes required to sort the elements is always one less than the number of elements - for 5 elements, 4 passes are required, for 6 elements, 5 passes are required, and so on.', 'The number of comparisons within each pass is n minus 1. The algorithm indicates that within each pass, there are n minus 1 comparisons, providing a clear understanding of the number of comparisons made in each iteration.', 'The special case where the number of elements does not strictly determine the number of passes required is highlighted, indicating that the process is not solely based on the number of elements.', 'The outer loop for passes is executed n minus 1 times. The outer loop, responsible for the number of passes, is executed n minus 1 times, illustrating the iterative process of the bubble sort algorithm.', 'The inner loop for comparisons is executed n minus 1 times as well. Similarly, the inner loop for comparisons is also executed n minus 1 times within each pass, showcasing the repetitive nature of the comparison process in bubble sort.', 'Modifying inner loop to n minus 1 minus i reduces unnecessary comparisons as i increases.', 'Identifying correct positions of elements after each pass minimizes unnecessary comparisons.', 'Explanation using examples of largest and second largest elements to omit comparisons.', 'Illustration of optimization with i value equal to 2, showing decrease in comparisons.', 'Number of comparisons in algorithm depends on i value, decreasing as i increases.', 'The number of passes required to sort an array is not always equal to n-1, as demonstrated by the example with 10 elements being sorted after only 3 passes.', 'The potential wastage of time in sorting algorithms is illustrated by the scenario where all elements are sorted after a certain pass, resulting in the remaining passes being unnecessary.', "The concept of the number of passes needed to sort an array is further exemplified using a specific array of 5 elements, demonstrating the variation in the required number of passes based on the array's initial state.", 'The chapter explains the optimization of the bubble sort algorithm by modifying the program to stop unnecessary passes, reducing the number of comparisons and iterations, as demonstrated by the example of a sorted array of 5, 6, 8, 14, and 16.', 'It introduces the concept of a flag variable to track swapping and illustrates how the program can be modified to break the loop and declare the array as sorted when no swapping occurs in a pass, effectively reducing the computational overhead.', 'The technique of using a flag variable to identify the presence of swapping in each pass is demonstrated, showcasing its role in determining whether the array is sorted and breaking the loop accordingly, leading to improved efficiency in sorting.', 'The chapter emphasizes the importance of applying a flag variable to reduce the number of passes required for sorting, highlighting the efficiency gained by identifying the sorted array in just one pass.', 'The use of a flag variable to optimize the bubble sort and reduce the number of passes and iterations through the array.', "Tracing the program with an example and discussing the value of 'i' for each pass, emphasizing the impact of the flag variable on the value of 'i' and the number of passes.", 'The best case scenario for bubble sort is when the array is already sorted, leading to a time complexity of O(n) as the loop is executed only once, reducing the number of comparisons to n-1.', 'The worst case scenario for bubble sort is when the array is given in descending order, resulting in a time complexity of O(n^2) due to the polynomial nature of the computational operations within the nested loops.', 'Explanation of the control flow within the nested for loops, highlighting the conditions and iterations during the sorting process.']}