CF 632F Magic Matrix

You’re given a matrix A of size n × n.

Let’s call the matrix with nonnegative elements magic if it is symmetric (so ai,j = aj,i), ai,i = 0 and ai,j ≤ max(ai,k, aj,k)for all triples i, j, k. Note that i, j, k do not need to be distinct.

Determine if the matrix is magic.

论bitset的重要性

#include<cmath>
#include<queue>
#include<stack>
#include<cstdio>
#include<bitset>
#include<cstring>
#include<complex>
#include<iostream>
#include<algorithm>
#define pi acos(-1)
#define inf (1<<30)
#define INF (1<<62)
#define fi first
#define se second
#define CLR(x,f) memset(x,f,sizeof(x))
#define CPY(x,y) memcpy(x,y,sizeof(x))
#define prt(x) cout<<#x<<": "<<x<<endl
#define Har(x) printf("--------DEBUG(%d)--------\n",x)
//#define TL
using namespace std;
const int M=2500;
bitset<M>b[M];
typedef long long ll;
int a[M][M],n;
typedef pair<int,int> ii;
typedef pair<int,ii> iii;
iii dat[M*M];
bool judge(){
for(int i=0;i<n;i++)if(a[i][i])return 0;
for(int i=0;i<n;i++)for(int j=0;j<n;j++)if(a[i][j]-a[j][i])return 0;
int tot=0;
for(int i=0;i<n;i++){
for(int j=0;j<n;j++){
dat[tot++]=iii(a[i][j],ii(i,j));
}
}
sort(dat,dat+tot);
for(int j,i=0;i<tot;i++){
for(j=i;j<tot&&dat[j].fi==dat[i].fi;j++);
for(int k=i;k<j;k++){
ii v=dat[k].se;
if((b[v.fi]&b[v.se]).any())return false;
}
for(int k=i;k<j;k++){
ii v=dat[k].se;
b[v.fi][v.se]=true;
}
i=j-1;
}
return true;
}
int main(){
#ifdef TL
#endif
scanf("%d",&n);
for(int i=0;i<n;i++)
for(int j=0;j<n;j++)
scanf("%d",&a[i][j]);
if(judge())puts("MAGIC");
else puts("NOT MAGIC");
return 0;
}