euler15

Starting in the top left corner of a 2×2 grid, there are 6 routes (without backtracking) to the bottom right corner.

How many routes are there through a 20×20 grid?
--------------------

#include

#define M 20
#define N 20


long long  cal(int m, int n)
{
    if (m == 0 || n==0) return 1;

    return cal(m-1, n) + cal(m, n-1);
}


int main(int argc, const char *argv[])
{

    printf("%lld\n", cal(M, N));

    return 0;
}

    耗费了46m，应该有更快更好的办法。

#include<stdio.h>

#define N 20
int main()
{
    long long result=1;
    int i;

    for (i=1;i<=N;i++) {
        result = result*(N+i);
        result /= i;

    }

    printf("result: %lld\n",result);

    return 0;

}

排列组合！ perfect!