Wednesday, May 8, 2013

Subset Sum

Given a set of non-negative integers, and a value sum, determine if there is a subset of the given set with sum equal to given sum.

The previous post talks about recursive approach which has exponential complexity

Lets see a dynamic programming approach which has polynomial complexity.

// Returns true if there is a subset of set[] with sun equal to given sum
public static boolean isSubsetSumDynamic(int set[], int n, int sum)
// The value of subset[i][j] will be true if there is a subset of set[0..j-1]
// with sum equal to i
boolean subset[][] = new boolean[sum+1][n+1];

// If sum is 0, then answer is true
for (int i = 0; i <= n; i++)
subset[0][i] = true;

// If sum is not 0 and set is empty, then answer is false
for (int i = 1; i <= sum; i++)
subset[i][0] = false;

// Fill the subset table in bottom up manner
for (int i = 1; i <= sum; i++)
for (int j = 1; j <= n; j++)
subset[i][j] = subset[i][j-1];
if (i >= set[j-1])
subset[i][j] = subset[i][j] || subset[i - set[j-1]][j-1];
return subset[sum][n];

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