Create 01 - Recursive Approach.cpp

Author: JawadSher

24 - Dynamic Programming Problems/04 - Ways to Reach the N'th Stair/01 - Recursive Approach.cpp

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+// Approach 1 : Using recursion with an index (i)
+class Solution {
+public:
+    // Function to calculate the number of ways to reach the top of the stairs starting from index `i`
+    int calculateWays(int n, int currentStep) {
+        // Base case: If we are at the top step (i == n), there's exactly one way to reach the top
+        if (currentStep == n) return 1;
+        
+        // Base case: If we've exceeded the top step (i > n), return 0 as this path is invalid
+        if (currentStep > n) return 0;
+
+        // Recursively calculate the number of ways to reach the top by taking either 1 step or 2 steps at a time
+        return calculateWays(n, currentStep + 1) + calculateWays(n, currentStep + 2);
+    }
+
+    // Main function to start the process of calculating the ways to climb to the top
+    int countWays(int n) {
+        int currentStep = 0; // Start from the first step
+        return calculateWays(n, currentStep); // Call the recursive function
+    }
+};
+
+// Approach 2 : Using recursion with step subtraction (n)
+class Solution {
+public:
+    // Function to calculate the number of ways to reach the top from step `n`
+    int calculateWays(int n) {
+        // Base case: If we're already at the top (n == 0), there's exactly one way to reach the top (no steps to take)
+        if (n == 0) return 1;
+        
+        // Base case: If `n` is negative, it's an invalid path, return 0
+        if (n < 0) return 0;
+
+        // Recursively calculate the number of ways to reach the top by subtracting either 1 step or 2 steps
+        return calculateWays(n - 1) + calculateWays(n - 2);
+    }
+
+    // Main function to start the process of calculating the ways to climb to the top
+    int countWays(int n) {
+        return calculateWays(n); // Call the recursive function to calculate the number of ways
+    }
+};