add solution for lab 6

labs/recursion/checkpoint1.cpp

@@ -0,0 +1,27 @@
+#include <iostream>
+using namespace std;
+
+int countPaths(int x, int y) {
+    // if we are at the origin, there is 1 path
+    if (x == 0 && y == 0) return 1;
+    
+    int paths = 0;
+
+    // Move left if x > 0
+    if (x > 0) paths += countPaths(x - 1, y);
+    
+    // Move up if y > 0
+    if (y > 0) paths += countPaths(x, y - 1);
+    
+    return paths;
+}
+
+int main() {
+    int start_x, start_y;
+    cout << "Enter the starting coordinates (x, y): ";
+    cin >> start_x >> start_y;
+    
+    int result = countPaths(start_x, start_y);
+    cout << "Number of paths to the origin: " << result << endl;
+    return 0;
+}