96 lines
2.3 KiB
Java
96 lines
2.3 KiB
Java
package DynamicProgramming;
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// 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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public class MinimumSumPartition
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{
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public static int subSet(int[] arr) {
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int n = arr.length;
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int sum = getSum(arr);
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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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}
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for (int j = 0; j <= sum; j++) {
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dp[0][j] = false;
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}
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//fill dp array
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for(int i = 1; i <= n; i++){
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for(int j = 1; j <= sum; j++){
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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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}
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else if(arr[i-1] == j){
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dp[i][j] = true;
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}
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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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}
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// fill the index array
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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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if(dp[n][i]){
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index[p++] = i;
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}
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}
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return getMin(index, sum);
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}
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/**
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* Calculate sum of array elements
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*
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* @param arr the array
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* @return sum of given array
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*/
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public static int getSum(int[] arr) {
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int sum = 0;
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for (int temp : arr) {
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sum += temp;
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}
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return sum;
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}
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public static int getMin(int[] arr, int sum) {
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if (arr.length == 0) {
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return 0;
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}
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int min = Integer.MAX_VALUE;
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for (int temp : arr) {
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min = Math.min(min, sum - 2 * temp);
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}
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return min;
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}
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public static void main(String args[]){
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Scanner in = new Scanner(System.in);
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int n = in.nextInt();
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int arr[] = new int[n];
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for(int i = 0 ; i<n; i++){
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arr[i] = in.nextInt();
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}
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System.out.println(subSet(arr));
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}
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}
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