Project Euler 15 solution

Lattice paths

Problem 15

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?

Link: https://projecteuler.net/problem=15

My solution:

Using recursie function to find out the routes.

Implemented by Lu.Qian. using C++:

 1 #include <iostream>
 2 //#include <cstring>
 3 //#include <cmath>
 4 //#include <map>
 5 using namespace std;
 6
 7 unsigned long long int num = 0;
 8 void find_route(int len, int wid){
 9     if(len == 0 || wid == 0){
10         num++;
11     }
12     find_route(len - 1, wid);
13     find_route(len, wid - 1);
14 }
15
16 int main()
17 {
18
19     find_route(20,20);
20     cout<<num<<endl;
21     return 0;
22 }

However, this project I worte will take so much cost on recurive funciton, and the running time it take will be unacceptable.

So I‘ll wirite another function by using simple iteration.