F. Unusual Matrix(Codeforces Round #697 (Div. 3)题解)

题目链接：F. Unusual Matrix
思路：我们可以发现，如果\(a_{i,j}\)不等于\(b_{i,j}\)那么他们变化的次数一定是奇数次，否则一定是偶数次，而该元素变化的总次数是行变化次数+列变化次数，所以我们通过\(a_{1,1}\)就能将1行和1列的情况枚举出来，进一步，因为我们知道其他元素的情况，所以我们就可以推出来其他行和其他列的变化次数的情况，然后再带入矩阵进行验证。
\(Code:\)

#include<set>
#include<iostream>
#include<cstring>
#include<cmath>
#include<cstdio>
#include<cstdlib>
#include<map>
#include<algorithm>
#include<vector>
#include<queue>
#define ch() getchar()
#define pc(x) putchar(x)
#include<stack>
#include<unordered_map>
#define rep(i,a,b) for(auto i=a;i<=b;++i)
#define bep(i,a,b) for(auto i=a;i>=b;--i)
#define lowbit(x) x&(-x)
#define ll long long
#define ull unsigned long long
#define pb emplace_back
#define mp make_pair
#define PI acos(-1)
using namespace std;
template<typename T>void read(T&x){
    static char c;
    static int f;
    for(c=ch(),f=1; c<'0'||c>'9'; c=ch())if(c=='-')f=-f;
    for(x=0; c>='0'&&c<='9'; c=ch())x=x*10+(c&15);
    x*=f;
}
template<typename T>void write(T x){
    static char q[65];
    int cnt=0;
    if(x<0)pc('-'),x=-x;
    q[++cnt]=x%10,x/=10;
    while(x)
        q[++cnt]=x%10,x/=10;
    while(cnt)pc(q[cnt--]+'0');
}

const int N = 1e3+10;
int _,n;
char a[N][N],b[N][N];
int row[N],col[N];
bool check(int x,int y){
    row[1] = x;
    col[1] = y;
    rep(i,2,n){
        if(b[1][i] == a[1][i])row[i] = col[1];
        else row[i] = !col[1];
    }
    rep(i,2,n){
        if(b[i][1] == a[i][1])col[i] = row[1];
        else col[i] = !row[1];
    }
    rep(i,1,n){
        rep(j,1,n){
            if(b[i][j] == a[i][j] and col[i]!=row[j])return false;
            if(b[i][j] != a[i][j] and col[i]==row[j])return false;
        }
    }
    return true;
}
void solve(){
    read(_);
    while(_--){
        read(n);
        rep(i,1,n)scanf("%s",a[i]+1);
        rep(i,1,n)scanf("%s",b[i]+1);
        //rep(i,1,n)puts(b[i]+1);
        bool flag = false;
        if(b[1][1] == a[1][1]){
            if(check(1,1) or check(0,0))flag = true;
        }
        else if(check(1,0) or check(0,1))flag = true;
        if(flag)puts("YES");
        else puts("NO");
    }
}


signed main(){solve();return 0; }