Merge pull request #307 from Dhruvpatel-19/algorithms-dp/max-sum-no-consecutive

Algorithms dp/max sum no consecutive

Author: abhishektripathi66

src/algorithms/dp/MaxSumNoConsecutive.java

@@ -0,0 +1,110 @@
+package algorithms.dp;
+
+import java.util.Arrays;
+
+/*
+ * Maximum Sum of Non-Consecutive Elements
+ *
+ * Given an array of integers, find the maximum sum of elements such that
+ * no two chosen elements are adjacent in the array.
+ *
+ * This is a classic Dynamic Programming problem, often seen as a variation
+ * of the "House Robber Problem".
+ *
+ * Approaches:
+ *   1. Pure Recursion → Exponential time (O(2^n)), O(n) stack space
+ *   2. Recursion with Memoization → O(n) time, O(n) space
+ *   3. Tabulation (Bottom-Up DP) → O(n) time, O(n) space
+ *   4. Space-Optimized DP → O(n) time, O(1) space
+ *
+ * Example:
+ *   arr = [8, 7, 6, 10]
+ *   → Max sum = 18 (from 8 + 10)
+ */
+
+public class MaxSumNoConsecutive {
+    public static void main(String[] args) {
+        int[] arr = {8, 7, 6, 10};
+        int n = arr.length;
+
+        System.out.println("Max sum without taking two consecutive elements : "+maxSumRec(arr, n)); //18 (from 8 and 10)
+
+        int[] memo = new int[n+1];
+        Arrays.fill(memo, -1);
+        System.out.println("Max sum without taking two consecutive elements : "+maxSumMemo(arr, n, memo));
+
+        System.out.println("Max sum without taking two consecutive elements : "+maxSumTabulation(arr, n));
+    }
+
+    //Time Complexiy : O(2^n), Space Complexity: O(n) for recurvise call stack
+    private static int maxSumRec(int[] arr, int n){
+        if(n <= 0)
+            return 0;
+        
+        if(n == 1)
+            return arr[0];
+        
+        if(n == 2)
+            return Math.max(arr[0], arr[1]);
+        
+        //either skip curr element or take curr element and skip one before it
+        return Math.max(maxSumRec(arr, n-1), arr[n-1] + maxSumRec(arr, n-2));
+    }
+
+    //Same procedure as recursive approach
+    //Time Complexiy : O(n), Space Complexity: O(n) for memo and recurvise call stack
+    private static int maxSumMemo(int[] arr, int n, int[] memo){
+        if(n <= 0)
+            return 0;
+        
+        //returning result if computed previously
+        if(memo[n]!=-1)
+            return memo[n];
+        
+        if(n == 1)
+            return memo[n] = arr[0];
+        
+        if(n == 2)
+            return memo[n] = Math.max(arr[0], arr[1]);
+        
+        return memo[n] = Math.max(maxSumMemo(arr, n-1, memo), arr[n-1] + maxSumMemo(arr, n-2, memo));
+    }
+
+    //Time Complexiy : O(n), Space Complexity: O(n)
+    private static int maxSumTabulation(int[] arr, int n){
+
+        if(n == 0) 
+            return 0;
+        if(n == 1) 
+            return arr[0];
+        
+        if(n == 2)
+            return Math.max(arr[0], arr[1]);
+
+            
+        //It will have Space complexity O(n)
+        /*int[] dp = new int[n];
+
+        dp[0] = arr[0];
+        dp[1] = Math.max(arr[0], arr[1]);
+
+        for(int i=2; i<n; i++){
+            dp[i] = Math.max(arr[i] + dp[i-2], dp[i-1]);
+        }
+        return dp[n-1];*/
+
+        //Optimized approach with Space Complexity O(1)
+
+        int prev1 = arr[0];
+        int prev2 = Math.max(arr[0], arr[1]);
+
+        for(int i=2; i<n; i++){
+            int curr = Math.max(arr[i] + prev1, prev2);
+
+            prev1 = prev2;
+            prev2 = curr;
+        }
+
+        return prev2;
+    }
+}