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  • URAL

    Join

    题目链接https://vjudge.net/problem/URAL-1627

    Description:

    Businessman Petya recently bought a new house. This house has one floor with n × m square rooms, placed in rectangular lattice. Some rooms are pantries and the other ones are bedrooms. Now he wants to join all bedrooms with doors in such a way that there will be exactly one way between any pair of them. He can make doors only between neighbouring bedrooms (i.e. bedrooms having a common wall). Now he wants to count the number of different ways he can do it.

    Input:

    First line contains two integers n and m (1 ≤ nm ≤ 9)  — the number of lines and columns in the lattice. Next n lines contain exactly m characters representing house map, where "." means bedroom and "*" means pantry. It is guaranteed that there is at least one bedroom in the house.

    Output:

    Output the number of ways to join bedrooms modulo 10 9.

    Sample Input:

    2 2
    .*
    *.

    Sample Output:

    0

    题意:

    给出一个n*m的矩阵,然后"*"表示障碍物。现在可以在两个"."之间搭桥,问有多少种方式将所有的"."连通。

    题解:

    直接给所有能够搭桥的点建边,然后就是个生成树计数问题了。

    代码如下:

    #include <cstdio>
    #include <cstring>
    #include <algorithm>
    #include <iostream>
    #include <cmath>
    using namespace std;
    typedef long long ll;
    const int N = 105,MOD = 1e9;
    char mp[N][N];
    int g[N][N],num[N][N];
    ll b[N][N];
    int tot=0;
    ll Det(int n){
        int i,j,k;
        ll ret = 1;
        if(n==0) return 0;
        for(i=2;i<=n;i++){
            for(j = i+1;j <= n;j++){
                while(b[j][i]){
                    ll tmp=b[i][i]/b[j][i];//不存在除不尽的情况
                    for(k = i;k <= n;k++)
                        b[i][k] = ((b[i][k] - tmp*b[j][k])%MOD+MOD)%MOD;
                    for(k=i;k<=n;k++)
                        swap(b[i][k],b[j][k]);
                    ret = -ret;
                }
            }
            if(!b[i][i]) return 0;
            ret = ret * b[i][i]%MOD;
            if(ret<0) ret+=MOD;
        }
        if(ret < 0) ret += MOD;
        return ret;
    }
    int main(){
        int n,m;
        scanf("%d%d",&n,&m);
        for(int i=1;i<=n;i++){
            scanf("%s",mp[i]+1);
            for(int j=1;j<=m;j++){
                if(mp[i][j]=='.') num[i][j]=++tot;
            }
        }
        for(int i=1;i<=n;i++){
            for(int j=1;j<=m;j++){
                if(mp[i][j]=='*') continue ;
                if(j>1&&mp[i][j-1]=='.') g[num[i][j-1]][num[i][j]]=1;
                if(i<n&&mp[i+1][j]=='.') g[num[i+1][j]][num[i][j]]=1;
            }
        }
        for(int i=1;i<=tot;i++){
            for(int j=1;j<=tot;j++){
                if(g[i][j]){
                    b[i][i]++;b[j][j]++;
                    b[i][j]=b[j][i]=-1;
                }
            }
        }
        cout<<Det(tot);
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/heyuhhh/p/10392763.html
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