A problem where the task is to find subsets of a given set whose sum equals a specified target value. Often used in dynamic programming and combinatorial optimization, aiding in resource allocation or partitioning.
Question
A problem where the task is to find subsets of a given set whose sum equals a specified target value. Often used in dynamic programming and combinatorial optimization, aiding in resource allocation or partitioning.
Solution
This seems to be a description of the Subset Sum Problem. Here's a step-by-step solution using dynamic programming:
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Initialize a boolean 2D array dp[n+1][sum+1], where n is the number of elements in the given set and sum is the target value. The size of the array is (n+1) x (sum+1) because we need to consider all subsets (including the empty set) and all possible sums (from 0 to sum).
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Set dp[i][0] = true for all i (0 <= i <= n). This represents that we can always form a sum of 0 by not including any elements.
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Set dp[0][j] = false for all j (1 <= j <= sum). This represents that we cannot form a non-zero sum using no elements.
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For each element in the set (from i=1 to n), and for each possible sum (from j=1 to sum), update dp[i][j] as follows:
- If the current element is less than or equal to the current sum, then dp[i][j] = dp[i-1][j] || dp[i-1][j - set[i-1]]. This means we can form the current sum either by excluding the current element (dp[i-1][j]) or by including the current element (dp[i-1][j - set[i-1]]).
- If the current element is greater than the current sum, then dp[i][j] = dp[i-1][j]. This means we can only form the current sum by excluding the current element.
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The answer to the problem is dp[n][sum]. If dp[n][sum] = true, then there exists a subset whose sum equals the target value. Otherwise, no such subset exists.
Similar Questions
The following paradigm can be used to find the solution of the problem in minimum time: Given a set of non-negative integer, and a value K, determine if there is a subset of the given set with sum equal to K:Group of answer choicesGreedy AlgorithmDivide and ConquerDynamic ProgrammingString Matching
The following paradigm can be used to find the solution of the problem in minimum time: Given a set of non-negative integer, and a value K, determine if there is a subset of the given set with sum equal to K:Group of answer choices
Subset SumProblem Statement:There is a subset A of n positive integers and a value sum. Find whether or not there exists any subset of the given set, the sum of whose elements is equal to the given value of sum.Time complexity of this solution is O(n*sum).Example 1:Input:sum=17 n=4 A[]={2,4,6,9} Required subset exists subset {2,6,9} has the sum 17 Example 2:Input:sum=17 n=4 A[]={2,4,6,8} No subset found with required sumYour Task:Write the program to solve this using Dynamic Programming concepts by storing the intermittent results for example for sum=1, sum=2 etc in a matrix to avoid recomputation.
Subset selection problems in machine learning
Find a subset of a given set S={sl,s2, ,sn} of n positive integers whose sum is equal to a given positive integer d. For example, if S={1,2,5,6,8}and d = 9 there are two solutions{1,2,6}and{1,8}.A suitable message is to be displayed if the given problem instance doesn't have a solution.
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