ACM Little Rooks 数学问题

E - Little Rooks

Time Limit:500MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Submit Status Practice SGU 222

Description

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 Input

Input

 

 

4 4 

 

 

Output

 

 

24 

 

 

 

用数学知识 c(n,k)* c(n,k) * A(k,k)

 

 

#include <iostream>
#include <cstdio>

using namespace std;

int Jiecheng(int x)
{
    int sum = 1;
    for(int i = 1;i <= x; i++)
        sum *= i;
    return sum;
}
int main()
{
    int n ,k;
    int sum;

    scanf("%d%d",&n,&k);
    if(n < k)
    {
        sum = 0;
    }
    else
    {
        sum = (Jiecheng(n)/Jiecheng(k)/Jiecheng(n - k))*(Jiecheng(n)/Jiecheng(k)/Jiecheng(n - k)) * Jiecheng(k);
    }
    printf("%d\n",sum);
}