Add Space Optimized Solution to Subset sum problem (#5612)

src/main/java/com/thealgorithms/dynamicprogramming/SubsetSumSpaceOptimized.java

@@ -0,0 +1,35 @@
+package com.thealgorithms.dynamicprogramming;
+/*
+The Sum of Subset problem determines whether a subset of elements from a
+given array sums up to a specific target value.
+*/
+public final class SubsetSumSpaceOptimized {
+    private SubsetSumSpaceOptimized() {
+    }
+    /**
+     * This method checks whether the subset of an array
+     * contains a given sum or not. This is an space
+     * optimized solution using 1D boolean array
+     * Time Complexity: O(n * sum), Space complexity: O(sum)
+     *
+     * @param arr An array containing integers
+     * @param sum The target sum of the subset
+     * @return True or False
+     */
+    public static boolean isSubsetSum(int[] arr, int sum) {
+        int n = arr.length;
+        // Declare the boolean array with size sum + 1
+        boolean[] dp = new boolean[sum + 1];
+
+        // Initialize the first element as true
+        dp[0] = true;
+
+        // Find the subset sum using 1D array
+        for (int i = 0; i < n; i++) {
+            for (int j = sum; j >= arr[i]; j--) {
+                dp[j] = dp[j] || dp[j - arr[i]];
+            }
+        }
+        return dp[sum];
+    }
+}