Create 02 - Top-Down | DP | Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/03 - Climbing Stairs/02 - Top-Down | DP | Approach.cpp

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+class Solution {
+public:
+    // Function to calculate the number of ways to reach the top of the stairs using memoization
+    int solve(int n, vector<int>& dp) {
+        // Base case: If we are at the first step (n == 0), there's exactly one way to reach the top
+        if(n == 0) return 1;
+
+        // Base case: If `n` is negative, return 0 as it's an invalid path
+        if(n < 0) return 0;
+
+        // If the value for this step (`n`) is already calculated and stored in `dp`, return it (Memoization)
+        if(dp[n] != -1) return dp[n];
+
+        // Recursively calculate the number of ways to reach the top from the current step
+        // We can reach step `n` by either coming from step `n-1` or step `n-2`
+        dp[n] = solve(n - 1, dp) + solve(n - 2, dp);
+
+        // Return the calculated result for step `n`
+        return dp[n];
+    }
+
+    // Main function to start the process of calculating the number of ways to climb to the top
+    int climbStairs(int n) {
+        // Initialize a memoization array `dp` of size `n+1`, with all values set to -1
+        // `dp[i]` will store the number of ways to reach step `i`
+        vector<int> dp(n + 1, -1);
+
+        // Call the recursive function to calculate the number of ways to reach the top
+        return solve(n, dp);
+    }
+};