add code for computing Combinations(nCr)

Author: OmarKimo

Math/Combinations (nCr)/nCr.cpp

@@ -0,0 +1,25 @@
+#include <iostream>
+using namespace std;
+
+// Returns n choose r. (i.e. The number of distinct sets of size k chosen from n items). [O(r)]
+// Note that C(n, r) = C(n, n - r)
+// So call the function with nCr(n, min(r, n-r)) for better performance.
+int nCr(int n, int r) {
+    if (n < r)
+        return 0;
+
+    if (r == 0)
+        return 1;
+
+    return n * nCr(n - 1, r - 1) / r;
+}
+
+int main(int argc, char** argv){
+
+    if(argc > 2){
+        int n = atoi(argv[1]), r = atoi(argv[2]);
+        printf("%d choose %d = %d\n", n, r, nCr(n,r));
+    }
+
+    return 0;
+}