diff --git a/src/main/java/com/thealgorithms/dynamicprogramming/MaximumSumOfNonAdjacentElements.java b/src/main/java/com/thealgorithms/dynamicprogramming/MaximumSumOfNonAdjacentElements.java new file mode 100644 index 000000000..49af3ae3d --- /dev/null +++ b/src/main/java/com/thealgorithms/dynamicprogramming/MaximumSumOfNonAdjacentElements.java @@ -0,0 +1,95 @@ +package com.thealgorithms.dynamicprogramming; + +/** + * Class to find the maximum sum of non-adjacent elements in an array. This + * class contains two approaches: one with O(n) space complexity and another + * with O(1) space optimization. For more information, refer to + * https://takeuforward.org/data-structure/maximum-sum-of-non-adjacent-elements-dp-5/ + */ +final class MaximumSumOfNonAdjacentElements { + + private MaximumSumOfNonAdjacentElements() { + } + + /** + * Approach 1: Uses a dynamic programming array to store the maximum sum at + * each index. Time Complexity: O(n) - where n is the length of the input + * array. Space Complexity: O(n) - due to the additional dp array. + * @param arr The input array of integers. + * @return The maximum sum of non-adjacent elements. + */ + public static int getMaxSumApproach1(int[] arr) { + if (arr.length == 0) { + return 0; // Check for empty array + } + + int n = arr.length; + int[] dp = new int[n]; + + // Base case: Maximum sum if only one element is present. + dp[0] = arr[0]; + + for (int ind = 1; ind < n; ind++) { + + // Case 1: Do not take the current element, carry forward the previous max + // sum. + int notTake = dp[ind - 1]; + + // Case 2: Take the current element, add it to the max sum up to two + // indices before. + int take = arr[ind]; + if (ind > 1) { + take += dp[ind - 2]; + } + + // Store the maximum of both choices in the dp array. + dp[ind] = Math.max(take, notTake); + } + + return dp[n - 1]; + } + + /** + * Approach 2: Optimized space complexity approach using two variables instead + * of an array. Time Complexity: O(n) - where n is the length of the input + * array. Space Complexity: O(1) - as it only uses constant space for two + * variables. + * @param arr The input array of integers. + * @return The maximum sum of non-adjacent elements. + */ + public static int getMaxSumApproach2(int[] arr) { + if (arr.length == 0) { + return 0; // Check for empty array + } + + int n = arr.length; + + // Two variables to keep track of previous two results: + // prev1 = max sum up to the last element (n-1) + // prev2 = max sum up to the element before last (n-2) + + int prev1 = arr[0]; // Base case: Maximum sum for the first element. + int prev2 = 0; + + for (int ind = 1; ind < n; ind++) { + // Case 1: Do not take the current element, keep the last max sum. + int notTake = prev1; + + // Case 2: Take the current element and add it to the result from two + // steps back. + int take = arr[ind]; + if (ind > 1) { + take += prev2; + } + + // Calculate the current maximum sum and update previous values. + int current = Math.max(take, notTake); + + // Shift prev1 and prev2 for the next iteration. + prev2 = prev1; + prev1 = current; + } + + return prev1; + } +} diff --git a/src/test/java/com/thealgorithms/dynamicprogramming/MaximumSumOfNonAdjacentElementsTest.java b/src/test/java/com/thealgorithms/dynamicprogramming/MaximumSumOfNonAdjacentElementsTest.java new file mode 100644 index 000000000..3f312d864 --- /dev/null +++ b/src/test/java/com/thealgorithms/dynamicprogramming/MaximumSumOfNonAdjacentElementsTest.java @@ -0,0 +1,52 @@ +package com.thealgorithms.dynamicprogramming; + +import static org.junit.jupiter.api.Assertions.assertEquals; + +import org.junit.jupiter.api.Test; + +public class MaximumSumOfNonAdjacentElementsTest { + + // Tests for Approach1 + @Test + public void testGetMaxSumApproach1WithEmptyArray() { + assertEquals(0, MaximumSumOfNonAdjacentElements.getMaxSumApproach1(new int[] {})); // Empty array + } + + @Test + public void testGetMaxSumApproach1WithSingleElement() { + assertEquals(1, MaximumSumOfNonAdjacentElements.getMaxSumApproach1(new int[] {1})); // Single element + } + + @Test + public void testGetMaxSumApproach1WithTwoElementsTakeMax() { + assertEquals(2, MaximumSumOfNonAdjacentElements.getMaxSumApproach1(new int[] {1, 2})); // Take max of both + } + + @Test + public void testGetMaxSumApproach1WithMultipleElements() { + assertEquals(15, MaximumSumOfNonAdjacentElements.getMaxSumApproach1(new int[] {3, 2, 5, 10, 7})); // 3 + 7 + 5 + assertEquals(10, MaximumSumOfNonAdjacentElements.getMaxSumApproach1(new int[] {5, 1, 1, 5})); // 5 + 5 + } + + // Tests for Approach2 + @Test + public void testGetMaxSumApproach2WithEmptyArray() { + assertEquals(0, MaximumSumOfNonAdjacentElements.getMaxSumApproach2(new int[] {})); // Empty array + } + + @Test + public void testGetMaxSumApproach2WithSingleElement() { + assertEquals(1, MaximumSumOfNonAdjacentElements.getMaxSumApproach2(new int[] {1})); // Single element + } + + @Test + public void testGetMaxSumApproach2WithTwoElementsTakeMax() { + assertEquals(2, MaximumSumOfNonAdjacentElements.getMaxSumApproach2(new int[] {1, 2})); // Take max of both + } + + @Test + public void testGetMaxSumApproach2WithMultipleElements() { + assertEquals(15, MaximumSumOfNonAdjacentElements.getMaxSumApproach2(new int[] {3, 2, 5, 10, 7})); // 3 + 7 + 5 + assertEquals(10, MaximumSumOfNonAdjacentElements.getMaxSumApproach2(new int[] {5, 1, 1, 5})); // 5 + 5 + } +}