Nash Matrix（dfs+构造）

#include<bits/stdc++.h>
typedef long long ll ;
#define int ll
#define mod 1000000007
#define gcd __gcd
#define rep(i , j , n) for(int i = j ; i <= n ; i++)
#define red(i , n , j)  for(int i = n ; i >= j ; i--)
#define ME(x , y) memset(x , y , sizeof(x))
//ll lcm(ll a , ll b){return a*b/gcd(a,b);}
//ll quickpow(ll a , ll b){ll ans=1;while(b){if(b&1)ans=ans*a%mod;b>>=1,a=a*a%mod;}return ans;}
//int euler1(int x){int ans=x;for(int i=2;i*i<=x;i++)if(x%i==0){ans-=ans/i;while(x%i==0)x/=i;}if(x>1)ans-=ans/x;return ans;}
//const int N = 1e7+9; int vis[n],prime[n],phi[N];int euler2(int n){ME(vis,true);int len=1;rep(i,2,n){if(vis[i]){prime[len++]=i,phi[i]=i-1;}for(int j=1;j<len&&prime[j]*i<=n;j++){vis[i*prime[j]]=0;if(i%prime[j]==0){phi[i*prime[j]]=phi[i]*prime[j];break;}else{phi[i*prime[j]]=phi[i]*phi[prime[j]];}}}return len}
#define INF  0x3f3f3f3f
#define PI acos(-1)
#define pii pair<int,int>
#define fi first
#define se second
#define lson l,mid,root<<1
#define rson mid+1,r,root<<1|1
#define cin(x) scanf("%lld" , &x);
using namespace std;
const int maxn = 1e3+9;
pii a[maxn][maxn];
char s[maxn][maxn];
int dir[4][2] = {{-1 , 0},{1 , 0},{0 , -1},{0 , 1}};
char str1[5] = {'U' , 'D' , 'L' , 'R'};
char str2[5] = {'D' , 'U' , 'R' , 'L'};
int vis[maxn][maxn];
int n , flag = 1 , flag1;
void dfs(int vax , int vay , int x , int y , int di){
    if(di == 0) s[x][y] = 'D';
    if(di == 1) s[x][y] = 'U';
    if(di == 2) s[x][y] = 'R';
    if(di == 3) s[x][y] = 'L';
    for(int i = 0 ; i < 4 ; i++){
        int xx = x + dir[i][0];
        int yy = y + dir[i][1];
        if(xx < 1 || xx > n || yy < 1 || yy > n || vis[xx][yy] || a[xx][yy].fi != vax || a[xx][yy].se != vay) continue;
        vis[xx][yy] = 1 ;
        dfs(vax , vay , xx , yy , i);
    }
}

void connect(int x , int y , int xx , int yy , char c , char st){
    s[x][y] = c ;
    if(!vis[xx][yy]) s[xx][yy] = st;
    vis[x][y] = vis[xx][yy] = 1;
}

void solve(){
    cin >> n ;
    rep(i , 1 , n){
        rep(j , 1 , n){
            cin >> a[i][j].fi >> a[i][j].se;
            if(a[i][j].fi == i && a[i][j].se == j){
                s[i][j] = 'X';
            }
        }
    }
    rep(i , 1 , n){
        rep(j , 1 , n){
            if(s[i][j] == 'X'){
                vis[i][j] = 1 ;
                dfs(a[i][j].fi , a[i][j].se , i , j , -1);
            }
        }
    }
    rep(i , 1 , n){
        rep(j , 1 , n){
            if(a[i][j].fi == -1  && !vis[i][j]){
                int flag = 0 ;
                for(int k = 0 ; k < 4 ; k++){
                    int xx = i + dir[k][0];
                    int yy = j + dir[k][1];
                    if(xx < 1 || xx > n || yy < 1 || yy > n || a[xx][yy].fi != -1) continue;
                    connect(i , j , xx , yy , str1[k] , str2[k]);
                    flag = 1 ;
                    break;

                }
                if(!flag){
                    cout << "INVALID" << endl;
                    return ;
                }
            }
        }
    }
    rep(i , 1 , n){
        rep(j , 1 , n){
            if(!vis[i][j]){
                cout << "INVALID" << endl;
                return ;
            }
        }
    }
    cout << "VALID" << endl;
    rep(i , 1 , n){
        rep(j , 1 , n){
            cout << s[i][j] ;
        }
        cout << endl;
    }

}

signed main()
{
    ios::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    //int t ;
    //cin(t);
    //while(t--){
        solve();
    //}
}