From bc34f3bd19f2231e6305f76782d302014288fd85 Mon Sep 17 00:00:00 2001
From: Ipsita Goel <45857758+ipsitagoel@users.noreply.github.com>
Date: Wed, 29 Sep 2021 18:42:42 +0530
Subject: [PATCH] chore(CPlusPlus): add binomial coefficient (#449)

Co-authored-by: Ujjwal <75884061+UG-SEP@users.noreply.github.com>
---
 .../CPlusPlus/Maths/binomial-coefficient.cpp  | 40 +++++++++++++++++++
 algorithms/CPlusPlus/README.md                |  1 +
 2 files changed, 41 insertions(+)
 create mode 100644 algorithms/CPlusPlus/Maths/binomial-coefficient.cpp

diff --git a/algorithms/CPlusPlus/Maths/binomial-coefficient.cpp b/algorithms/CPlusPlus/Maths/binomial-coefficient.cpp
new file mode 100644
index 00000000..1bab52fe
--- /dev/null
+++ b/algorithms/CPlusPlus/Maths/binomial-coefficient.cpp
@@ -0,0 +1,40 @@
+// C++ code to find the Binomial Coefficient
+// Description: Given two parameters n and r, find the value of the Binomial Coefficient i.e. C(n, r)
+// Method: Change r to n-r if r is greater than n-r and store it in a variable. Run a loop from 0 to r-1 and in every iteration update result to be (ans*(n-i))/(i+1). Hence, the result will be ((n/1)*((n-1)/2)*…*((n-r+1)/r!) i.e. nCr.
+// Time Complexity: O(r)
+// Space Complexity: O(1)
+
+#include <bits/stdc++.h>
+using namespace std;
+
+int findBinCoeff(int n, int r)
+{
+	int result = 1;
+
+	if (r > n - r)
+	{
+		r = n - r; // C(n, r) = C(n, n-r)
+	}
+
+	// Find [n*(n-1)*...*(n-r+1)]/[r*(r-1)*...*1]
+	for (int i = 0; i < r; ++i)
+	{
+		result = result * (n - i);
+		result = result / (i + 1);
+	}
+	return result;
+}
+
+int main()
+{
+	int n;
+	cout << "Enter the value of n: ";
+	cin >> n; // Eg value of n: 6
+	int r;
+	cout << "Enter the value of r: ";
+	cin >> r; // Eg value of r: 2
+	// C(6,2) = 6!/(4!*2!) = 15
+	cout << "The Binomial Coefficient is: ";
+	cout << findBinCoeff(n, r) << endl; //Eg output: 15
+	return 0;
+}
\ No newline at end of file
diff --git a/algorithms/CPlusPlus/README.md b/algorithms/CPlusPlus/README.md
index 13ee1c3b..3352545f 100644
--- a/algorithms/CPlusPlus/README.md
+++ b/algorithms/CPlusPlus/README.md
@@ -122,6 +122,7 @@
 2. [Prime Number](Maths/prime-check.cpp)
 3. [Prime Sieve](Maths/prime-sieve.cpp)
 4. [Fibonacci Series](Maths/fibonaccci-series.cpp)
+5. [Binomial Coefficient](Maths/binomial-coefficient.cpp)
 5. [Armstrong Number](Maths/armstrong.cpp)
 6. [Palindrome](Maths/palindrome.cpp)
 7. [Reverse digit of a number](Maths/reverse-digits.cpp)