#4387 Enhance Minimum sum partition problem implementation (#4394)

* Enhance Minimum sum partition problem implementation

* Linter resolved

* Linter resolved

* Code review comments

* Code review comments

* Add validation for non-negative numbers

* Linter resolved

* style: fix formiatting

---------

Co-authored-by: Piotr Idzik <65706193+vil02@users.noreply.github.com>

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;
+public final class MinimumSumPartition {
+    private MinimumSumPartition() {
     }
 
-        // 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];
-                }
+    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).");
         }
     }
 
-        // 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;
-            }
-        }
+    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
 
-        return getMin(index, sum);
-    }
+        // Find the closest sum of subset array that we can achieve which is closest to half of sum of full array
+        int closestPartitionSum = 0;
 
-    /**
-     * Calculate sum of array elements
-     *
-     * @param arr the array
-     * @return sum of given array
+        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
          */
-    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;
+        return sum - (2 * closestPartitionSum);
     }
 }

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); });
+    }
+}