title

Dp 16. Partition A Set Into Two Subsets With Minimum Absolute Sum Difference | DP on Subsequences

description

Lecture Notes/C++/Java Codes: https://takeuforward.org/dynamic-programming/striver-dp-series-dynamic-programming-problems/
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a
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In this video, we solve the problem of Partition a set into two subsets such that the difference of subset sums is minimum. This problem is the third problem on DP on Subsequences Pattern. Please watch DP 14 before watching this.
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detail

{'title': 'Dp 16. Partition A Set Into Two Subsets With Minimum Absolute Sum Difference | DP on Subsequences', 'heatmap': [{'end': 724.565, 'start': 669.888, 'weight': 0.804}, {'end': 1682.836, 'start': 1659.084, 'weight': 1}], 'summary': "Discusses minimizing the absolute difference between two subsets' sums using subset sum and pick and non-pick concepts, implementing memoization and tabulation in dynamic programming, explaining the tabulation method for finding target sum, and exploring the tabulation approach for subset sum problem to achieve a minimal difference of 2.", 'chapters': [{'end': 317.127, 'segs': [{'end': 68.179, 'src': 'embed', 'start': 23.576, 'weight': 0, 'content': [{'end': 31.881, 'text': 'so the question says partition a set into two subsets such that the difference of subset sums is minimum.', 'start': 23.576, 'duration': 8.305}, {'end': 39.486, 'text': "so you're given an array containing n non-negative integers again very important, it has all non-negative integers.", 'start': 31.881, 'duration': 7.605}, {'end': 46.23, 'text': 'your task is to partition that array into two subsets, so basically subset one and subset two,', 'start': 39.486, 'duration': 6.744}, {'end': 52.174, 'text': 'such that the absolute difference between both of the subset sums is as minimal as possible.', 'start': 46.23, 'duration': 5.944}, {'end': 60.528, 'text': 'Your task is to find the minimum absolute difference, considering any valid division of array elements.', 'start': 53.459, 'duration': 7.069}, {'end': 62.651, 'text': "So let's quickly check out an example.", 'start': 61.089, 'duration': 1.562}, {'end': 66.373, 'text': 'So if we see this example 1, 2, 3, 4.', 'start': 62.872, 'duration': 3.501}, {'end': 68.179, 'text': "Let's discuss over here.", 'start': 66.376, 'duration': 1.803}], 'summary': 'Partition a set into two subsets to minimize absolute difference in subset sums.', 'duration': 44.603, 'max_score': 23.576, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc23576.jpg'}, {'end': 219.289, 'src': 'embed', 'start': 166.568, 'weight': 4, 'content': [{'end': 171.991, 'text': 'because this is something different than what we have been doing.', 'start': 166.568, 'duration': 5.423}, {'end': 173.332, 'text': 'what have we done till now?', 'start': 171.991, 'duration': 1.341}, {'end': 174.953, 'text': 'we have done a lecture 14.', 'start': 173.332, 'duration': 1.621}, {'end': 177.694, 'text': 'yes, we have done a lecture 14 over there.', 'start': 174.953, 'duration': 2.741}, {'end': 179.095, 'text': 'what have we discussed?', 'start': 177.694, 'duration': 1.401}, {'end': 181.557, 'text': 'we have discussed a given an array.', 'start': 179.095, 'duration': 2.462}, {'end': 191.182, 'text': 'yes, given an array, and i will give you a target, and your task is to tell me if this target like, if there is a subset,', 'start': 181.557, 'duration': 9.625}, {'end': 197.917, 'text': 'if there is a subset whose sum is equal to this target.', 'start': 191.182, 'duration': 6.735}, {'end': 199.418, 'text': 'so you are given an array.', 'start': 197.917, 'duration': 1.501}, {'end': 206.523, 'text': 'we have already done a problem where we have to tell is there a subset which is equivalent to the given some target?', 'start': 199.418, 'duration': 7.105}, {'end': 209.145, 'text': 'and if you remember, what concept did we use?', 'start': 206.523, 'duration': 2.622}, {'end': 215.768, 'text': 'we use the concept of pick and non-pick, or take or non take, the concept that we used.', 'start': 209.145, 'duration': 6.623}, {'end': 219.289, 'text': 'So if you remember the reference, it was something like this.', 'start': 216.308, 'duration': 2.981}], 'summary': 'Lecture 14 covered finding a subset in an array that sums up to a given target using the pick and non-pick concept.', 'duration': 52.721, 'max_score': 166.568, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc166568.jpg'}], 'start': 0.689, 'title': 'Minimal subset sum difference', 'summary': "Discusses how to minimize the absolute difference between two subsets' sums, using subset sum and pick and non-pick concepts, with an example of achieving a minimal difference of 0 in the set {1, 2, 3, 4}.", 'chapters': [{'end': 138.982, 'start': 0.689, 'title': 'Partition set for minimal subset sum difference', 'summary': 'Discusses how to partition a set into two subsets to minimize the absolute difference between their sums, using the idea of subset sum, with an example of dividing the set {1, 2, 3, 4} into subsets to achieve minimal difference of 0.', 'duration': 138.293, 'highlights': ['The chapter discusses the idea of partitioning a set into two subsets to minimize the absolute difference between their sums, based on the subset sum problem.', 'The example of dividing the set {1, 2, 3, 4} into subsets to achieve a minimal absolute difference of 0 is presented, demonstrating different possible partitions and their respective subset sums.', 'The problem involves finding the minimum absolute difference between the subset sums of a given array, with the requirement that the array contains non-negative integers.']}, {'end': 317.127, 'start': 139.403, 'title': 'Minimum subset sum difference', 'summary': "Discusses the concept of finding the minimum absolute difference between two subsets of an array, and the application of the pick and non-pick concept in determining if a subset's sum equals a given target.", 'duration': 177.724, 'highlights': ["The chapter discusses the concept of finding the minimum absolute difference between two subsets of an array, and the application of the pick and non-pick concept in determining if a subset's sum equals a given target.", 'The lecture also revisits a previous problem where the task was to determine if there exists a subset in the array with a sum equal to a given target.', 'The lecture provides a detailed explanation of the pick and non-pick concept, outlining the base cases and the recursive approach to solve the problem.']}], 'duration': 316.438, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc689.jpg', 'highlights': ['The chapter discusses the idea of partitioning a set into two subsets to minimize the absolute difference between their sums, based on the subset sum problem.', 'The problem involves finding the minimum absolute difference between the subset sums of a given array, with the requirement that the array contains non-negative integers.', 'The example of dividing the set {1, 2, 3, 4} into subsets to achieve a minimal absolute difference of 0 is presented, demonstrating different possible partitions and their respective subset sums.', "The chapter discusses the concept of finding the minimum absolute difference between two subsets of an array, and the application of the pick and non-pick concept in determining if a subset's sum equals a given target.", 'The lecture provides a detailed explanation of the pick and non-pick concept, outlining the base cases and the recursive approach to solve the problem.', 'The lecture also revisits a previous problem where the task was to determine if there exists a subset in the array with a sum equal to a given target.']}, {'end': 714.321, 'segs': [{'end': 372.136, 'src': 'embed', 'start': 343.388, 'weight': 0, 'content': [{'end': 352.674, 'text': 'so we went on to write the tabulation, as, firstly, though, we declared a dp of n of target, and then we went on to write f of index,', 'start': 343.388, 'duration': 9.286}, {'end': 355.138, 'text': 'equal to 0 till n minus 1.', 'start': 352.674, 'duration': 2.464}, {'end': 366.634, 'text': 'and over here we went on to write dp of i and every index, rather dp of index, and every target, 0 as true.', 'start': 355.138, 'duration': 11.496}, {'end': 372.136, 'text': "so this is what we wrote, because it's almost equivalent to this if target is zero, return true.", 'start': 366.634, 'duration': 5.502}], 'summary': 'Wrote tabulation for dynamic programming, setting dp of n of target and f of index to 0 till n-1.', 'duration': 28.748, 'max_score': 343.388, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc343388.jpg'}, {'end': 697.084, 'src': 'embed', 'start': 669.888, 'weight': 1, 'content': [{'end': 683.111, 'text': 'So assume the array to be something as 1, 3, probably 2, 5, and 6, and the target to be 7, okay, and the target to be 7.', 'start': 669.888, 'duration': 13.223}, {'end': 686.655, 'text': "let's assume this is the array that we have taken and this is the target.", 'start': 683.111, 'duration': 3.544}, {'end': 689.637, 'text': 'so what is the first tabulation that you wrote over here?', 'start': 686.655, 'duration': 2.982}, {'end': 692.7, 'text': "this is done, and the next thing you're writing is dp of 0.", 'start': 689.637, 'duration': 3.063}, {'end': 694.382, 'text': 'array of 0 is equal to true.', 'start': 692.7, 'duration': 1.682}, {'end': 695.283, 'text': 'so what is array of 0?', 'start': 694.382, 'duration': 0.901}, {'end': 697.084, 'text': 'over here, it is 1.', 'start': 695.283, 'duration': 1.801}], 'summary': 'Given an array [1, 3, 2, 5, 6] and target 7, discussing dynamic programming for array subset sum', 'duration': 27.196, 'max_score': 669.888, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc669888.jpg'}], 'start': 317.127, 'title': 'Dynamic programming techniques', 'summary': 'Discusses the implementation of memoization and tabulation in dynamic programming, focusing on base cases and array initialization, as well as explaining the tabulation format for solving the subset sum problem with a 5x8 dp table and an array of 5 elements, finding the answer at dp of 4 with the target being 7.', 'chapters': [{'end': 418.75, 'start': 317.127, 'title': 'Memoization and tabulation in dynamic programming', 'summary': 'Discusses the implementation of memoization and tabulation in dynamic programming, with a focus on base cases and array initialization.', 'duration': 101.623, 'highlights': ['The tabulation involves initializing a dp array of size n and setting dp[i][0] to true, equivalent to the base case if the target is zero, return true.', 'The next base case involves setting dp[0][target] to true if the target is equal to the first element of the array, ensuring that if the target is equivalent to array[0], then it will be true.', 'The first step in tabulation is to declare a dp array of size n and set dp[index][target] to true for every index and target, akin to if target is zero, return true.']}, {'end': 714.321, 'start': 419.11, 'title': 'Tabulation for subset sum problem', 'summary': 'Explains the tabulation format for solving the subset sum problem, where the dp table signifies whether a particular subset can achieve the target, demonstrated using a 5x8 dp table and an array of 5 elements, with the answer found at dp of 4 and the target being 7.', 'duration': 295.211, 'highlights': ['The chapter explains the tabulation format for solving the subset sum problem, where the DP table signifies whether a particular subset can achieve the target, demonstrated using a 5x8 DP table and an array of 5 elements, with the answer found at dp of 4 and the target being 7.', 'The base cases are filled first in the tabulation form, where the index is equal to something and target is true, and then the DP array is filled based on the given array and target, with the answer found at dp of 4 and the target being 7.', 'The tabulation format involves filling the DP table with true for the base cases, then filling the rest of the table based on the given array and target, with the answer found at dp of 4 and the target being 7.']}], 'duration': 397.194, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc317127.jpg', 'highlights': ['The tabulation involves initializing a dp array of size n and setting dp[i][0] to true, equivalent to the base case if the target is zero, return true.', 'The tabulation format involves filling the DP table with true for the base cases, then filling the rest of the table based on the given array and target, with the answer found at dp of 4 and the target being 7.', 'The base cases are filled first in the tabulation form, where the index is equal to something and target is true, and then the DP array is filled based on the given array and target, with the answer found at dp of 4 and the target being 7.']}, {'end': 865.986, 'segs': [{'end': 841.626, 'src': 'embed', 'start': 787.185, 'weight': 0, 'content': [{'end': 800.764, 'text': 'from 1 to 7, i can definitely say yes or no if i write the tabulation, because the tabulation makes sure that i fill the entire Yes,', 'start': 787.185, 'duration': 13.579}, {'end': 810.391, 'text': 'entire matrix and eventually I will get to know if I can achieve 1, if I can achieve 2, if I can achieve 3, if I can achieve 4, if I can achieve 5,', 'start': 800.764, 'duration': 9.627}, {'end': 814.008, 'text': 'if I can achieve 6, if I can achieve 7..', 'start': 810.391, 'duration': 3.617}, {'end': 820.793, 'text': 'And just because the question asked 7, we picked up this guy and we said, this is our answer.', 'start': 814.008, 'duration': 6.785}, {'end': 825.336, 'text': 'This is our answer, DP of 4 of 7.', 'start': 821.133, 'duration': 4.203}, {'end': 830.479, 'text': 'If someone comes up and gives you a different target, now you still can say without calling the tabulation again.', 'start': 825.336, 'duration': 5.143}, {'end': 836.823, 'text': 'This DP will strictly help you to tell if you can achieve a target 5 or not.', 'start': 831.079, 'duration': 5.744}, {'end': 838.905, 'text': 'So, this is what I wanted to portray you.', 'start': 837.103, 'duration': 1.802}, {'end': 841.626, 'text': 'This is what tabulation signifies.', 'start': 839.285, 'duration': 2.341}], 'summary': 'Using tabulation, we can achieve targets 1 to 7 with dp of 4 of 7.', 'duration': 54.441, 'max_score': 787.185, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc787185.jpg'}], 'start': 714.321, 'title': 'Tabulation method for target sum', 'summary': 'Explains the tabulation method for finding target sum, demonstrating its ability to provide yes or no answers for values 1 to 7 and to determine if a specific target can be achieved without repetitive tabulation.', 'chapters': [{'end': 865.986, 'start': 714.321, 'title': 'Tabulation method for target sum', 'summary': 'Explains the tabulation method for finding target sum, showing how tabulation can answer yes or no for every target value from 1 to 7 and how it can help determine if a specific target can be achieved without having to call tabulation again.', 'duration': 151.665, 'highlights': ['The tabulation method enables determining if a specific target can be achieved for values from 1 to 7 without calling tabulation again, ensuring efficient computation.', 'By using the tabulation method, it is possible to answer yes or no for every target value from 1 to 7, providing a clear indication of achievability.', 'The significance of DP values in tabulation is demonstrated by showing how it can help determine if a specific target, such as 5 or 4, can be achieved without needing to call tabulation again.', "The explanation of how each row in tabulation signifies the ability to achieve a specific target value provides a clear understanding of the method's functionality."]}], 'duration': 151.665, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc714321.jpg', 'highlights': ['The tabulation method enables determining if a specific target can be achieved for values from 1 to 7 without calling tabulation again, ensuring efficient computation.', 'By using the tabulation method, it is possible to answer yes or no for every target value from 1 to 7, providing a clear indication of achievability.', 'The significance of DP values in tabulation is demonstrated by showing how it can help determine if a specific target, such as 5 or 4, can be achieved without needing to call tabulation again.', "The explanation of how each row in tabulation signifies the ability to achieve a specific target value provides a clear understanding of the method's functionality."]}, {'end': 1780.951, 'segs': [{'end': 932.343, 'src': 'embed', 'start': 865.986, 'weight': 0, 'content': [{'end': 871.352, 'text': 'so just keep this in your mind, that As of now, from subset sum, what we have derived?', 'start': 865.986, 'duration': 5.366}, {'end': 877.035, 'text': 'From subset sum, the tabulation one.', 'start': 871.992, 'duration': 5.043}, {'end': 877.896, 'text': 'what have we derived?', 'start': 877.035, 'duration': 0.861}, {'end': 885.501, 'text': 'We can like if we check.', 'start': 880.658, 'duration': 4.843}, {'end': 893.266, 'text': 'if we check for a target equal to k, we can derive.', 'start': 885.501, 'duration': 7.765}, {'end': 912.349, 'text': 'we can derive if every possible target i repeat, if every possible target between 1 and k is possible or is not possible.', 'start': 895.339, 'duration': 17.01}, {'end': 919.595, 'text': "if i'm just checking for target equal to k, the tabulation automatically will tell me for every value between 1 to k,", 'start': 912.349, 'duration': 7.246}, {'end': 923.078, 'text': "i don't need to do any extra steps, make sense.", 'start': 919.595, 'duration': 3.483}, {'end': 926.341, 'text': "so with the help of this i'll solve the next problem, okay.", 'start': 923.078, 'duration': 3.263}, {'end': 930.422, 'text': "so now let's come back to the dp 16, which was the original problem.", 'start': 926.341, 'duration': 4.081}, {'end': 932.343, 'text': 'what did the original problem state?', 'start': 930.422, 'duration': 1.921}], 'summary': 'Deriving possible targets between 1 and k using tabulation for solving the next problem.', 'duration': 66.357, 'max_score': 865.986, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc865986.jpg'}, {'end': 1293.826, 'src': 'embed', 'start': 1263.223, 'weight': 1, 'content': [{'end': 1272.708, 'text': 'so i figured out what values are possible and this can easily be done with the help of the last row that has been generated in this dp array,', 'start': 1263.223, 'duration': 9.485}, {'end': 1277.57, 'text': 'if i call the tabulation method of subset sum.', 'start': 1272.708, 'duration': 4.862}, {'end': 1286.283, 'text': 'so can i say, can i say that 0 is possible, 4 is possible, 6 is possible, 8 is possible, 11 is possible.', 'start': 1277.57, 'duration': 8.713}, {'end': 1290.305, 'text': 'So these are the valid S1s which are possible.', 'start': 1286.723, 'duration': 3.582}, {'end': 1293.826, 'text': 'These are the partitions that are possible for S1.', 'start': 1290.545, 'duration': 3.281}], 'summary': 'Values 0, 4, 6, 8, and 11 are possible for s1 in subset sum problem.', 'duration': 30.603, 'max_score': 1263.223, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc1263223.jpg'}, {'end': 1356.989, 'src': 'embed', 'start': 1326.783, 'weight': 2, 'content': [{'end': 1328.784, 'text': 'For every S1, I got the corresponding S2.', 'start': 1326.783, 'duration': 2.001}, {'end': 1340.425, 'text': 'Can I say the difference, the absolute difference over here is 12? Absolute difference over here is 8, 6, 2, 2, 6, 8, 12.', 'start': 1329.544, 'duration': 10.881}, {'end': 1342.108, 'text': 'What do I need? The minimal.', 'start': 1340.427, 'duration': 1.681}, {'end': 1344.489, 'text': "And what's the minimal that I see? It's 2.", 'start': 1342.228, 'duration': 2.261}, {'end': 1345.729, 'text': "So that's my answer.", 'start': 1344.489, 'duration': 1.24}, {'end': 1348.761, 'text': 'using subset sum.', 'start': 1347.299, 'duration': 1.462}, {'end': 1352.665, 'text': "i did it super duper easily, i don't know.", 'start': 1348.761, 'duration': 3.904}, {'end': 1356.989, 'text': "i don't find any problem in this and this is definitely going to be my answer.", 'start': 1352.665, 'duration': 4.324}], 'summary': 'The absolute differences are 12, 8, 6, 2, 2, 6, 8, and 12; the minimal difference is 2.', 'duration': 30.206, 'max_score': 1326.783, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc1326783.jpg'}, {'end': 1682.836, 'src': 'heatmap', 'start': 1659.084, 'weight': 1, 'content': [{'end': 1671.305, 'text': 'comma, total sum, minus s1 is what your s2 will be minus of s1 and an absolute of the entire stuff.', 'start': 1659.084, 'duration': 12.221}, {'end': 1673.487, 'text': 'yes, an absolute of the entire stuff.', 'start': 1671.305, 'duration': 2.182}, {'end': 1676.79, 'text': 'at the end of the day can i say i will return the mini.', 'start': 1673.487, 'duration': 3.303}, {'end': 1682.836, 'text': "so if i just write this and let's run this off, let's see if it's running fine, it does run.", 'start': 1676.79, 'duration': 6.046}], 'summary': 'The total sum minus s1 will be the absolute of the entire stuff.', 'duration': 23.752, 'max_score': 1659.084, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc1659084.jpg'}, {'end': 1759.362, 'src': 'embed', 'start': 1724.59, 'weight': 4, 'content': [{'end': 1726.431, 'text': 'you can also try it with the space optimization.', 'start': 1724.59, 'duration': 1.841}, {'end': 1727.972, 'text': "that's your choice.", 'start': 1726.431, 'duration': 1.541}, {'end': 1736.957, 'text': 'so if we do the space optimization, it will take a bit lesser space complexity, but the time complexity still will be equivalent to n into target,', 'start': 1727.972, 'duration': 8.985}, {'end': 1741.478, 'text': 'plus total sum by 2 plus a big of n linear loop.', 'start': 1736.957, 'duration': 4.521}, {'end': 1748.46, 'text': 'so a couple of linear loops and the totals are n into k and the time space complexity will be b go of, uh, these guys,', 'start': 1741.478, 'duration': 6.982}, {'end': 1750.14, 'text': "that's a single linear loop that you.", 'start': 1748.46, 'duration': 1.68}, {'end': 1752.38, 'text': "uh, single linear array that you're using.", 'start': 1750.14, 'duration': 2.24}, {'end': 1759.362, 'text': 'so, guys, i hope i was able to make this tough problem easy and just in case i was able to make it, please please like this video,', 'start': 1752.38, 'duration': 6.982}], 'summary': 'Space optimization reduces space complexity, but time complexity remains n * target. total sum is n * k, and time space complexity is o(n) with a single linear array.', 'duration': 34.772, 'max_score': 1724.59, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc1724590.jpg'}], 'start': 865.986, 'title': 'Subset sum problem', 'summary': 'Explores tabulation approach for subset sum problem, demonstrating automatic determination of every value between 1 and k without additional steps. it also discusses optimizing the problem to minimize absolute difference between subsets, achieving a minimal difference of 2, and demonstrates implementation using dynamic programming and space optimization.', 'chapters': [{'end': 932.343, 'start': 865.986, 'title': 'Subset sum tabulation derivation', 'summary': 'Explores the derivation of tabulation approach for subset sum problem, where it is demonstrated that the tabulation method can automatically determine the possibility of every value between 1 and k without the need for additional steps.', 'duration': 66.357, 'highlights': ['The tabulation method for subset sum problem can automatically determine the possibility of every value between 1 and k without additional steps.', 'The tabulation approach provides a solution without the need for extra steps or checks.']}, {'end': 1780.951, 'start': 932.343, 'title': 'Optimizing subset sum problem', 'summary': 'Discusses optimizing the subset sum problem to minimize the absolute difference between two subsets, achieving the minimal difference of 2, and demonstrates the implementation using dynamic programming and space optimization.', 'duration': 848.608, 'highlights': ['Using dynamic programming to find valid S1s for the subset sum problem The lecture explains how to use dynamic programming and the last row of the generated dp array to determine the valid S1s for the subset sum problem, with 0, 4, 6, 8, and 11 identified as valid S1s.', 'Identifying corresponding S2 for each S1 to obtain minimal absolute difference The lecture demonstrates identifying the corresponding S2 for each S1, resulting in an absolute difference of 12, 8, 6, 2, and 2, and emphasizes the goal of minimizing the absolute difference to achieve the optimal solution.', 'Implementing space optimization for the subset sum problem The lecture illustrates the implementation of space optimization for the subset sum problem, reducing the space complexity while maintaining the time complexity equivalent to n into target, plus total sum by 2.']}], 'duration': 914.965, 'thumbnail': 'https://coursnap.oss-ap-southeast-1.aliyuncs.com/video-capture/GS_OqZb2CWc/pics/GS_OqZb2CWc865986.jpg', 'highlights': ['The tabulation method for subset sum problem can automatically determine the possibility of every value between 1 and k without additional steps.', 'Using dynamic programming to find valid S1s for the subset sum problem The lecture explains how to use dynamic programming and the last row of the generated dp array to determine the valid S1s for the subset sum problem, with 0, 4, 6, 8, and 11 identified as valid S1s.', 'Identifying corresponding S2 for each S1 to obtain minimal absolute difference The lecture demonstrates identifying the corresponding S2 for each S1, resulting in an absolute difference of 12, 8, 6, 2, and 2, and emphasizes the goal of minimizing the absolute difference to achieve the optimal solution.', 'The tabulation approach provides a solution without the need for extra steps or checks.', 'Implementing space optimization for the subset sum problem The lecture illustrates the implementation of space optimization for the subset sum problem, reducing the space complexity while maintaining the time complexity equivalent to n into target, plus total sum by 2.']}], 'highlights': ['The tabulation approach provides a solution without the need for extra steps or checks.', 'The tabulation method for subset sum problem can automatically determine the possibility of every value between 1 and k without additional steps.', 'The lecture illustrates the implementation of space optimization for the subset sum problem, reducing the space complexity while maintaining the time complexity equivalent to n into target, plus total sum by 2.', 'The lecture demonstrates identifying the corresponding S2 for each S1, resulting in an absolute difference of 12, 8, 6, 2, and 2, and emphasizes the goal of minimizing the absolute difference to achieve the optimal solution.', "The explanation of how each row in tabulation signifies the ability to achieve a specific target value provides a clear understanding of the method's functionality.", 'By using the tabulation method, it is possible to answer yes or no for every target value from 1 to 7, providing a clear indication of achievability.', 'The tabulation method enables determining if a specific target can be achieved for values from 1 to 7 without calling tabulation again, ensuring efficient computation.', 'The lecture also revisits a previous problem where the task was to determine if there exists a subset in the array with a sum equal to a given target.', 'The lecture provides a detailed explanation of the pick and non-pick concept, outlining the base cases and the recursive approach to solve the problem.', "The chapter discusses the concept of finding the minimum absolute difference between two subsets of an array, and the application of the pick and non-pick concept in determining if a subset's sum equals a given target.", 'The example of dividing the set {1, 2, 3, 4} into subsets to achieve a minimal absolute difference of 0 is presented, demonstrating different possible partitions and their respective subset sums.', 'The problem involves finding the minimum absolute difference between the subset sums of a given array, with the requirement that the array contains non-negative integers.', 'The chapter discusses the idea of partitioning a set into two subsets to minimize the absolute difference between their sums, based on the subset sum problem.']}