Solution to Project Euler Problem 15: Lattice paths - Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner. How many such routes are there through a 20×20 grid?

• Java Code

package sikademy;
/**
 *
 * @author Archangel Macsika
 * Copyright (c) Sikademy. All rights reserved
 */

import java.math.BigInteger;

public class SikademyEulerSolution {
	
	public String run() {
		return Library.binomial(40, 20).toString();
	}

        // Returns n!.
	public static BigInteger factorial(int n) {
		if (n < 0)
			throw new IllegalArgumentException("Factorial of negative number");
		BigInteger prod = BigInteger.ONE;
		for (int i = 2; i <= n; i++)
			prod = prod.multiply(BigInteger.valueOf(i));
		return prod;
	}
	
	
	// Returns n choose k.
	public static BigInteger binomial(int n, int k) {
		if (k < 0 || k > n)
			throw new IllegalArgumentException();
		BigInteger product = BigInteger.ONE;
		for (int i = 0; i < k; i++)
			product = product.multiply(BigInteger.valueOf(n - i));
		return product.divide(factorial(k));
	}

	public static void main(String[] args) {
                SikademyEulerSolution solution = new SikademyEulerSolution();
		System.out.println(solution.run());
	}	
}

• Python Code

# 
# @author Archangel Macsika
# Copyright (c) Sikademy. All rights reserved.
# 

import math

def binomial(n, k):
	assert 0 <= k <= n
	return math.factorial(n) // (math.factorial(k) * math.factorial(n - k))

def compute():
	return str(binomial(40, 20))

if __name__ == "__main__":
	print(compute())