Lightoj 1005 Rooks (DP)

A rook is a piece used in the game of chess which are played on a board of square grids. A Rook can only move vertically or horizontally from its current position and A rooks attack each other if one is on the Path of the other. In the following figure, the dark squares represent the reachable locations for rook R1 from their current position . The figure also shows the rook R1 and R2 is in attacking positions where R1 and r3 is not. R2 and R3 is also in non-attacking positions.

Now, given-numbers n and K, your job is to determine the number of ways one can put K Rooks On a n x n chessboard so that no of the them is in attacking positions.

Input

Input starts with an integer T (≤350), denoting the number of test cases.

Each case contains the integers n (1≤n≤30) and K (0≤k≤n2).

Output

For each case, print the case number and total number of ways one can put the given number of rooks on a chessboard of the Given size so, no. them is in attacking positions. You may safely assume the this number would be the less than 1017.

Sample Input	Output for Sample Input
8 1 1 2 1 3 1 4 1 4 2 4 3 4 4 4 5	Case 1:1 Case 2:4 Case 3:9 Case 4:16 Case 5:72 Case 6:96 Case 7:24 Case 8:0

The title asks for a K-car on the board of the N*n, asking how many ways.

DP[I][J] represents the number of scenarios in which J cars are put in front I rows. Then dp[i][j]=dp[i-1][j]+dp[i-1][j-1]* (n (j-1));

Or use combinatorial math to do it. The answer is C (n,k) *a (n,k)

 
/* ***********************************************
Author        :guanjun
Created Time  :2016/6/9 16:02:10
File Name     :1005.cpp
************************************************ */
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <stdio.h>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <iomanip>
#include <list>
#include <deque>
#include <stack>
#define ull unsigned long long
#define ll long long
#define mod 90001
#define INF 0x3f3f3f3f
#define maxn 10010
#define cle(a) memset(a,0,sizeof(a))
const ull inf = 1LL << 61;
const double eps=1e-5;
using namespace std;
priority_queue<int,vector<int>,greater<int> >pq;
struct Node{
    int x,y;
};
struct cmp{
    bool operator()(Node a,Node b){
        if(a.x==b.x) return a.y> b.y;
        return a.x>b.x;
    }
};

bool cmp(int a,int b){
    return a>b;
}
ll dp[33][33];
int n,k;
int main()
{
    #ifndef ONLINE_JUDGE
    freopen("in.txt","r",stdin);
    #endif
    //freopen("out.txt","w",stdout);
    int T;
    cin>>T;
    for(int t=1;t<=T;t++){
        cin>>n>>k;
        printf("Case %d: ",t);
        if(k>n){
            puts("0");continue;
        }
        cle(dp);
        dp[0][0]=1;
        for(int i=1;i<=n;i++){
            for(int j=0;j<=i;j++){
                if(j)dp[i][j]=dp[i-1][j]+dp[i-1][j-1]*(n-j+1);
                else dp[i][j]=dp[i-1][j];
            }
        }
        printf("%lld\n",dp[n][k]);
    }
    return 0;
}

Lightoj 1005 Rooks (DP)