sgu 222. Little Rooks 组合数学

222. Little Rooks

time limit per test: 0.25 sec.
memory limit per test: 65536 KB

input: standard
output: standard

Inspired by a "Little Bishops" problem, Petya now wants to solve problem for rooks. 

A rook is a piece used in the game of chess which is played on a board of square grids. A rook can only move horizontally and vertically from its current position and two rooks attack each other if one is on the path of the other. 

Given two numbers n and k, your job is to determine the number of ways one can put k rooks on an n × n chessboard so that no two of them are in attacking positions. 

Input

The input file contains two integers n (1 ≤ n ≤ 10) and k (0 ≤ k ≤ n2). 

Output

Print a line containing the total number of ways one can put the given number of rooks on a chessboard of the given size so that no two of them are in attacking positions. 

Sample test(s)

Input

4 4 

Output

24 

题意每行每列选一个，所以首先排除k>n的情况。

先看n==k的情况，从1到n可以得到递推关系n!。

如果有空行（空列）C(x,y);x 空行 y 总行数 。

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
ll nn[11]={1,1,2,6,24,120,720,5040,40320,362880,3628800};
int main(){
    int n,k;scanf("%d%d",&n,&k);
    if(k>n)printf("0");else printf("%I64d",nn[k]*(nn[n]/nn[n-k]/nn[k])*(nn[n]/nn[n-k]/nn[k]));
	return 0;
}