Create 01 - Recursive Approach (caused TLE).cpp

Author: JawadSher

24 - Dynamic Programming Problems/26 - Longest Arithmetic Subsequence/01 - Recursive Approach (caused TLE).cpp

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+class Solution {
+  public:
+    // Helper function to recursively find the length of the longest arithmetic progression (AP)
+    // ending at the current index with a given common difference `diff`.
+    int solve(vector<int>& arr, int index, int diff) {
+        // Base case: if the index goes out of bounds, return 0
+        if(index < 0) return 0;
+
+        int ans = 0;
+        // Iterate backwards from the current index to find elements that can form an AP
+        for(int j = index - 1; j >= 0; j--) {
+            // Check if the difference between arr[index] and arr[j] matches the given `diff`
+            if(arr[index] - arr[j] == diff) {
+                // Recursively find the length of AP ending at arr[j] and update `ans`
+                ans = max(ans, 1 + solve(arr, j, diff));
+            }
+        }
+        
+        // Return the maximum length of AP found
+        return ans;
+    }
+    
+    // Function to find the length of the longest arithmetic progression in the array
+    int lengthOfLongestAP(vector<int>& arr) {
+        int n = arr.size();
+        
+        // If the array has 2 or fewer elements, the entire array is an AP
+        if(n <= 2) return n;
+
+        int ans = 0;
+        // Iterate through all pairs of elements to calculate the common difference `diff`
+        for(int i = 0; i < n; i++) {
+            for(int j = i + 1; j < n; j++) {
+                // Calculate the common difference and start a recursive search
+                // The length of the AP is at least 2 (the current pair)
+                ans = max(ans, 2 + solve(arr, i, arr[j] - arr[i]));
+            }
+        }
+        
+        // Return the maximum length of the AP found
+        return ans;
+    }
+};