HDU 5755 Gambler Bo

可以设n*m个未知量，建立n*m个方程。位置i，j可以建立方程 (2*x[i*m+j]+x[(i-1)*m+j]+x[(i+1)*m+j]+x[i*m+j-1]+x[i*m+j+1])%3=3-b[i][j]; 套了个高斯消元的板子过了。

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<iostream>
using namespace std;
typedef long long LL;
const double pi=acos(-1.0),eps=1e-8;
void File()
{
    freopen("D:\in.txt","r",stdin);
    freopen("D:\out.txt","w",stdout);
}
inline int read()
{
    char c = getchar();  while(!isdigit(c)) c = getchar();
    int x = 0;
    while(isdigit(c)) { x = x * 10 + c - '0'; c = getchar(); }
    return x;
}

const int mod = 3;
int exgcd(int a,int b,int &x,int &y){
    if(!b){x = 1; y = 0; return a;}
    else{
        int r = exgcd(b,a%b,y,x);
        y -= x * (a/b);
        return r;
    }
}
int lcm(int a,int b){
    int x = 0, y =0;
    return a / exgcd(a,b,x,y) * b;
}
const int MAXN=1000;

int A[MAXN][MAXN],free_x[MAXN],x[MAXN];
void Gauss(int n,int m){
    int r,c;
    for(r=0,c=0;r<n && c<m;c++){
        int maxr = r;
        for(int i=r+1;i<n;i++) if(abs(A[i][c]) > abs(A[maxr][c])) maxr = i;
        if(maxr != r) for(int i=c;i<=m;i++) swap(A[r][i],A[maxr][i]);
        if(!A[r][c]) continue;
        for(int i=r+1;i<n;i++) if(A[i][c]){
            int d = lcm(A[i][c],A[r][c]);
            int t1 = d / A[i][c], t2 = d / A[r][c];
            for(int j=c;j<=m;j++)
                A[i][j] = ((A[i][j] * t1 - A[r][j] * t2) % mod + mod) % mod;
        }
        r++;
    }
    for(int i=r;i<n;i++) if(A[i][m]) return ;
    for(int i=r-1;i>=0;i--){
        x[i] = A[i][m];
        for(int j=i+1;j<m;j++){
            x[i] = ((x[i] - A[i][j] * x[j]) % mod + mod) % mod;
        }
        int x1 = 0,y1 = 0;
        int d = exgcd(A[i][i],mod,x1,y1);
        x1 = ((x1 % mod) + mod) % mod;
        x[i] = x[i] * x1 % mod;
    }
}
void Gauss_init(){
    memset(A,0,sizeof A); memset(free_x,0,sizeof free_x); memset(x,0,sizeof x);
}
int T,n,m;
int b[MAXN][MAXN];

bool check(int a,int b)
{
    if(a>=0&&a<n&&b>=0&&b<m) return 1;
    return 0;
}

int main()
{
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d",&n,&m);
        for(int i=0;i<n;i++) for(int j=0;j<m;j++) scanf("%d",&b[i][j]);
        Gauss_init();
        for(int i=0;i<n;i++) for(int j=0;j<m;j++)
        {
            A[i*m+j][i*m+j]=2;
            if(check(i-1,j)) A[i*m+j][(i-1)*m+j]=1;
            if(check(i+1,j)) A[i*m+j][(i+1)*m+j]=1;
            if(check(i,j-1)) A[i*m+j][i*m+j-1]=1;
            if(check(i,j+1)) A[i*m+j][i*m+j+1]=1;
            A[i*m+j][n*m]=(3-b[i][j])%3;
        }
        Gauss(n*m,n*m);
        int ans=0; for(int i=0;i<n*m;i++) ans=ans+x[i]; printf("%d
",ans);
        for(int i=0;i<n*m;i++) while(x[i]) { printf("%d %d
",i/m+1,i%m+1); x[i]--; }
    }
    return 0;
}