Merge pull request #232 from i-priyanshu/master

Binomial Coefficient in C++ using DP  fixes #222

Author: smv1999

Dynamic Programming/binomial_coefficient.cpp

@@ -0,0 +1,43 @@
+// Write a function that takes two parameters n and k and returns the value of Binomial Coefficient C(n, k).
+//  For example, our function should return 6 for n = 4 and k = 2, and it should return 10 for n = 5 and k = 2.
+
+// The idea we have used here is inspired by the pascal triangle.
+/*
+                    1
+                 1     1
+               1  2  2  1
+             1   3  4  3  1  */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+int binomial(int n, int r)
+{
+    if (r > n)
+        return 0;
+    if (r == 0 || r == n)
+        return 1;
+
+    int dp[n + 1][r + 1];
+    for (int i = 1; i <= n; i++)
+    {
+        for (int j = 1; j <= r; j++)
+        {
+            if (i == j || j == 0) // Base Condition
+                dp[i][j] = 1;
+            else
+            { //  we have taken a mod, so that higher results can be calculted too.
+                dp[i][j] = (dp[i - 1][j - 1] + dp[i - 1][j]) % 10000007;
+            }
+        }
+    }
+    return dp[n][r];
+}
+
+int main()
+{
+    int n;
+    int r;
+    cin >> n >> r;
+    return binomial(n, r);
+}