[Added the Program ] -- Added the Program for the Merge Sort

C++/Merge_sort_Algorithm.cpp

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+#include <iostream>
+using namespace std;
+
+// Function to merge two subarrays of arr[]
+void merge(int arr[], int left, int mid, int right) {
+    // Find sizes of two subarrays to be merged
+    int n1 = mid - left + 1;
+    int n2 = right - mid;
+
+    // Create temporary arrays
+    int L[n1], R[n2];
+
+    // Copy data to temp arrays L[] and R[]
+    for (int i = 0; i < n1; i++)
+        L[i] = arr[left + i];
+    for (int j = 0; j < n2; j++)
+        R[j] = arr[mid + 1 + j];
+
+    // Merge the temporary arrays back into arr[left..right]
+    int i = 0; // Initial index of first subarray
+    int j = 0; // Initial index of second subarray
+    int k = left; // Initial index of merged subarray
+
+    while (i < n1 && j < n2) {
+        if (L[i] <= R[j]) {
+            arr[k] = L[i];
+            i++;
+        } else {
+            arr[k] = R[j];
+            j++;
+        }
+        k++;
+    }
+
+    // Copy the remaining elements of L[], if any
+    while (i < n1) {
+        arr[k] = L[i];
+        i++;
+        k++;
+    }
+
+    // Copy the remaining elements of R[], if any
+    while (j < n2) {
+        arr[k] = R[j];
+        j++;
+        k++;
+    }
+}
+
+// Function to implement Merge Sort
+void mergeSort(int arr[], int left, int right) {
+    if (left < right) {
+        // Find the middle point
+        int mid = left + (right - left) / 2;
+
+        // Recursively sort the two halves
+        mergeSort(arr, left, mid);
+        mergeSort(arr, mid + 1, right);
+
+        // Merge the sorted halves
+        merge(arr, left, mid, right);
+    }
+}
+
+// Utility function to print an array
+void printArray(int arr[], int size) {
+    for (int i = 0; i < size; i++)
+        cout << arr[i] << " ";
+    cout << endl;
+}
+
+int main() {
+    int arr[] = {38, 27, 43, 3, 9, 82, 10};
+    int arr_size = sizeof(arr) / sizeof(arr[0]);
+
+    cout << "Original array: \n";
+    printArray(arr, arr_size);
+
+    mergeSort(arr, 0, arr_size - 1);
+
+    cout << "Sorted array: \n";
+    printArray(arr, arr_size);
+
+    return 0;
+}

C++/Numbers_Of_Ways_to_Kth_stare.py

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+#This is a hard Leetcode Problem which uses a concept of memoization in recursion . Here is the question :
+# https://leetcode.com/problems/find-number-of-ways-to-reach-the-k-th-stair/description
+
+# this is the solution to the above leetcode problem
+
+
+def numberOfWays(k: int) -> int:
+    # dp[i] will store the number of ways to reach stair i
+    dp = [0] * (k + 1)
+
+    # Base case: 1 way to reach the first stair
+    dp[1] = 1
+
+    # Iterate over each stair up to k
+    for i in range(1, k):
+        jump = 0
+        stair = i
+        # Keep jumping upwards as long as within bounds
+        while stair <= k:
+            if stair <= k:
+                dp[stair] += dp[i]
+            jump += 1
+            stair = i + 2**jump
+
+    return dp[k]
+
+# Test the function
+k = 10  # example value
+print(numberOfWays(k))