UvaLive 6600 Spanning trees in a secure lock pattern matrix, uvalivespanning

UvaLive 6600 Spanning trees in a secure lock pattern matrix, uvalivespanning

Link: https://icpcarchive.ecs.baylor.edu/index.php? Option = com_onlinejudge & Itemid = 8 & page = show_problem & problem = 4611

Question: Give a matrix of N * N vertices (N <= 6). Each vertex can only be connected to eight neighboring vertices and ask how many tree generation methods are available.

Idea: The question is very clear, that is, to list a matrix of the edge of each vertex, and then obtain the determinant of the submatrix. Because N is only 6, you can create a table.

Code for table creation:

#include <algorithm>#include <cmath>#include <cstdio>#include <cstdlib>#include <cstring>#include <ctime>#include <ctype.h>#include <iostream>#include <map>#include <queue>#include <set>#include <stack>#include <string>#include <vector>#define eps 1e-8#define INF 0x7fffffff#define PI acos(-1.0)#define seed 31//131,1313typedef long long LL;typedef unsigned long long ULL;using namespace std;#define MOD 1000#define maxn 40#define maxm 40struct Matrix{    int n,m;    double a[maxn][maxm];    void change(int c,int d)    {        n=c;        m=d;        for(int i=0; i<n; i++)            for(int j=0; j<m; j++)                a[i][j]=0;    }    void Copy(const Matrix &x)    {        n=x.n;        m=x.m;        for(int i=0; i<n; i++)            for(int j=0; j<m; j++)                a[i][j]=x.a[i][j];    }    void build(int n)    {        change(n*n,n*n);        for(int i=0; i<n*n; i++)        {            if(i%n!=0)            {                a[i][i-1]=-1;                a[i-1][i]=-1;                a[i][i]++;                a[i-1][i-1]++;            }            if(i%n!=0&&i/n!=0)            {                a[i][i-n-1]=-1;                a[i-n-1][i]=-1;                a[i][i]++;                a[i-n-1][i-n-1]++;            }            if(i%n!=0&&i/n!=n-1)            {                a[i][i+n-1]=-1;                a[i+n-1][i]=-1;                a[i][i]++;                a[i+n-1][i+n-1]++;            }            if(i/n!=n-1)            {                a[i][i+n]=-1;                a[i+n][i]=-1;                a[i][i]++;                a[i+n][i+n]++;            }        }    }    double det()    {        for(int i=1; i<n; i++)        {            for(int j=0; j<i; j++)                if(a[i][j]!=0)                {                    for(int k=j+1; k<m; k++)                        a[i][k]-=(a[j][k]*a[i][j]/a[j][j]);                    a[i][j]=0;                }        }        double ans=1;        for(int i=0; i<n-1; i++)            ans*=a[i][i];        return ans;    }};int main(){    int t;    scanf("%d",&t);    Matrix A;    A.build(t);    printf("%.0f\n",A.det());    return 0;}

AC code:

int main(){    char ss[10][40]={"1","16","17745","1064918960","3271331573452806","504061943351319050000000"};    int T;    scanf("%d",&T);    while(T--)    {        int a;        scanf("%d",&a);        puts(ss[a-1]);    }}