74 lines
1.6 KiB
Java
74 lines
1.6 KiB
Java
// Partition a set into two subsets such that the difference of subset sums is minimum
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/*
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Input: arr[] = {1, 6, 11, 5}
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Output: 1
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Explanation:
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Subset1 = {1, 5, 6}, sum of Subset1 = 12
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Subset2 = {11}, sum of Subset2 = 11
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Input: arr[] = {36, 7, 46, 40}
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Output: 23
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Explanation:
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Subset1 = {7, 46} ; sum of Subset1 = 53
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Subset2 = {36, 40} ; sum of Subset2 = 76
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*/
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import java.util.*;
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import java.lang.*;
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import java.io.*;
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class GFG
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{
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public static void main (String[] args)
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{
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Scanner sc=new Scanner(System.in);
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int t=sc.nextInt();
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while(t-->0)
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{
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int n=sc.nextInt();
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int arr[]=new int[n];
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int sum=0;
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for(int i=0;i<n;i++)
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{
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arr[i]=sc.nextInt();
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sum+=arr[i];
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}
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int ans[]=new int[sum];
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ans=subset(arr,sum);
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int min=Integer.MAX_VALUE;
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for(int i=0;i<ans.length;i++)
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min=Math.min(min,(sum-2*ans[i]));
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System.out.println(min);
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}
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}
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static int[] subset(int arr[],int sum)
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{
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int n=arr.length;
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boolean dp[][]=new boolean[n+1][sum+1];
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for(int i=0;i<=n;i++)
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dp[i][0]=true;
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for(int i=1;i<=sum;i++)
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dp[0][i]=false;
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// subset sum concept
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for(int i=1;i<=n;i++)
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{
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for(int j=1;j<=sum;j++)
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{
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if(arr[i-1]<=j)
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dp[i][j]=dp[i-1][j-arr[i-1]] || dp[i-1][j];
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else
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dp[i][j]=dp[i-1][j];
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}
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}
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//storing last dp column whose value is true till sum/2
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int index[]=new int[sum];
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int p=0;
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for(int i=0;i<=sum/2;i++)
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{
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if(dp[n][i]==true)
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index[p++]=i;
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}
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return index;
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}
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}
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