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## Project Euler 15–Lattice paths

By Wu Yudong on December 13, 2017

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?

#include<iostream>
#include<cmath>
using namespace std;

long long a[21][21];

int main()
{
int i;
for (i = 0; i < 21; i++) {
a[0][i] = 1;
a[i][0] = 1;
}
for (i = 1; i < 21; i++)
for (int j = 1; j < 21; j++)
a[i][j] = a[i][j - 1] + a[i - 1][j];
cout << a[20][20] << endl;
return 0;
}