Implement Maximum Sum of Non-Adjacent Elements (#5544)

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;
+    }
+}