diff --git a/src/main/java/com/thealgorithms/dynamicprogramming/SubsetSumSpaceOptimized.java b/src/main/java/com/thealgorithms/dynamicprogramming/SubsetSumSpaceOptimized.java new file mode 100644 index 000000000000..946da46cb292 --- /dev/null +++ b/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]; + } +} diff --git a/src/test/java/com/thealgorithms/dynamicprogramming/SubsetSumSpaceOptimizedTest.java b/src/test/java/com/thealgorithms/dynamicprogramming/SubsetSumSpaceOptimizedTest.java new file mode 100644 index 000000000000..3a965f4e68b8 --- /dev/null +++ b/src/test/java/com/thealgorithms/dynamicprogramming/SubsetSumSpaceOptimizedTest.java @@ -0,0 +1,18 @@ +package com.thealgorithms.dynamicprogramming; + +import static org.junit.jupiter.api.Assertions.assertFalse; +import static org.junit.jupiter.api.Assertions.assertTrue; + +import org.junit.jupiter.api.Test; + +public class SubsetSumSpaceOptimizedTest { + + @Test + void basicCheck() { + assertTrue(SubsetSumSpaceOptimized.isSubsetSum(new int[] {7, 3, 2, 5, 8}, 14)); + assertTrue(SubsetSumSpaceOptimized.isSubsetSum(new int[] {4, 3, 2, 1}, 5)); + assertTrue(SubsetSumSpaceOptimized.isSubsetSum(new int[] {1, 7, 2, 9, 10}, 13)); + assertFalse(SubsetSumSpaceOptimized.isSubsetSum(new int[] {1, 2, 7, 10, 9}, 14)); + assertFalse(SubsetSumSpaceOptimized.isSubsetSum(new int[] {2, 15, 1, 6, 7}, 4)); + } +}