diff --git a/src/main/java/com/thealgorithms/dynamicprogramming/MinimumSumPartition.java b/src/main/java/com/thealgorithms/dynamicprogramming/MinimumSumPartition.java index c15c0186fc62..52308c23cf1c 100644 --- a/src/main/java/com/thealgorithms/dynamicprogramming/MinimumSumPartition.java +++ b/src/main/java/com/thealgorithms/dynamicprogramming/MinimumSumPartition.java @@ -1,89 +1,57 @@ package com.thealgorithms.dynamicprogramming; -// Partition a set into two subsets such that the difference of subset sums is minimum +import java.util.Arrays; /* -Input: arr[] = {1, 6, 11, 5} -Output: 1 +Given an array of non-negative integers , partition the array in two subset that +difference in sum of elements for both subset minimum. +Return the minimum difference in sum of these subsets you can achieve. + +Input: array[] = {1, 6, 11, 4} +Output: 0 Explanation: -Subset1 = {1, 5, 6}, sum of Subset1 = 12 +Subset1 = {1, 4, 6}, sum of Subset1 = 11 Subset2 = {11}, sum of Subset2 = 11 -Input: arr[] = {36, 7, 46, 40} +Input: array[] = {36, 7, 46, 40} Output: 23 Explanation: Subset1 = {7, 46} ; sum of Subset1 = 53 Subset2 = {36, 40} ; sum of Subset2 = 76 */ -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); +public final class MinimumSumPartition { + private MinimumSumPartition() { } - /** - * 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; + private static void throwIfInvalidInput(final int[] array) { + if (Arrays.stream(array).anyMatch(a -> a < 0)) { + throw new IllegalArgumentException("Input array should not contain negative number(s)."); } - 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; - } + public static int minimumSumPartition(final int[] array) { + throwIfInvalidInput(array); + int sum = Arrays.stream(array).sum(); + boolean[] dp = new boolean[sum / 2 + 1]; + dp[0] = true; // Base case , don't select any element from array - /** - * 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; + // Find the closest sum of subset array that we can achieve which is closest to half of sum of full array + int closestPartitionSum = 0; + + for (int i = 0; i < array.length; i++) { + for (int j = sum / 2; j > 0; j--) { + if (array[i] <= j) { + dp[j] = dp[j] || dp[j - array[i]]; + } + if (dp[j]) { + closestPartitionSum = Math.max(closestPartitionSum, j); + } + } + } + /* + Difference in sum = Big partition sum - Small partition sum + = ( Total sum - Small partition sum) - Small partition sum + */ + return sum - (2 * closestPartitionSum); } } diff --git a/src/test/java/com/thealgorithms/dynamicprogramming/MinimumSumPartitionTest.java b/src/test/java/com/thealgorithms/dynamicprogramming/MinimumSumPartitionTest.java new file mode 100644 index 000000000000..1f14320244ea --- /dev/null +++ b/src/test/java/com/thealgorithms/dynamicprogramming/MinimumSumPartitionTest.java @@ -0,0 +1,44 @@ +package com.thealgorithms.dynamicprogramming; + +import static org.junit.jupiter.api.Assertions.assertEquals; +import static org.junit.jupiter.api.Assertions.assertThrows; + +import org.junit.jupiter.api.Test; + +class MinimumSumPartitionTest { + @Test + public void testMinimumSumPartitionWithEvenSum() { + int[] array = {1, 6, 11, 4}; + assertEquals(0, MinimumSumPartition.minimumSumPartition(array)); + } + + @Test + public void testMinimumSumPartitionWithOddSum() { + int[] array = {36, 7, 46, 40}; + assertEquals(23, MinimumSumPartition.minimumSumPartition(array)); + } + + @Test + public void testMinimumSumPartitionWithSingleElement() { + int[] array = {7}; + assertEquals(7, MinimumSumPartition.minimumSumPartition(array)); + } + + @Test + public void testMinimumSumPartitionWithLargeNumbers() { + int[] array = {100, 200, 300, 400, 500}; + assertEquals(100, MinimumSumPartition.minimumSumPartition(array)); + } + + @Test + public void testMinimumSumPartitionWithEmptyArray() { + int[] array = {}; + assertEquals(0, MinimumSumPartition.minimumSumPartition(array)); + } + + @Test + public void testMinimumSumPartitionThrowsForNegativeArray() { + int[] array = {4, 1, -6, 7}; + assertThrows(IllegalArgumentException.class, () -> { MinimumSumPartition.minimumSumPartition(array); }); + } +}