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.io.*;
import java.util.*;

public class MinimumSumPartition {
 public static int subSet(int[] arr) {
 int n = arr.length;
 int sum = getSum(arr);
 boolean[][] dp = new boolean[n + 1][sum + 1];
 for (int i = 0; i <= n; i++) {
 dp[i][0] = true;
 }
 for (int j = 0; j <= sum; j++) {
 dp[0][j] = false;
 }

 // fill dp array
 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 if (arr[i - 1] == j) {
 dp[i][j] = true;
 } else {
 dp[i][j] = dp[i - 1][j];
 }
 }
 }

 // fill the index array
 int[] index = new int[sum];
 int p = 0;
 for (int i = 0; i <= sum / 2; i++) {
 if (dp[n][i]) {
 index[p++] = i;
 }
 }

 return getMin(index, sum);
 }

 /**
 * Calculate sum of array elements
 *
 * @param arr the array
 * @return sum of given array
 */
 public static int getSum(int[] arr) {
 int sum = 0;
 for (int temp : arr) {
 sum += temp;
 }
 return sum;
 }

 public static int getMin(int[] arr, int sum) {
 if (arr.length == 0) {
 return 0;
 }
 int min = Integer.MAX_VALUE;
 for (int temp : arr) {
 min = Math.min(min, sum - 2 * temp);
 }
 return min;
 }

 /** Driver Code */
 public static void main(String[] args) {
 assert subSet(new int[] {1, 6, 11, 5}) == 1;
 assert subSet(new int[] {36, 7, 46, 40}) == 23;
 assert subSet(new int[] {1, 2, 3, 9}) == 3;
 }
}