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