Red Huang

Red Huang

uva 12036

Each column can be freely replaced, and if each number exceeds five, using the pigeonhole principle, it can be found that there will definitely be a collision in the column.

And it will not affect other numbers. The example below has four types of numbers, each appearing four times.

1 2 3 4
4 1 2 3
3 4 1 2
2 3 4 1

Just place them diagonally downwards.

//  
//        GGGGGGGGGGGGG        CCCCCCCCCCCCC               AAA  
//     GGG::::::::::::G     CCC::::::::::::C              A:::A  
//   GG:::::::::::::::G   CC:::::::::::::::C             A:::::A  
//  G:::::GGGGGGGG::::G  C:::::CCCCCCCC::::C            A:::::::A  
// G:::::G       GGGGGG C:::::C       CCCCCC           A:::::::::A  
//G:::::G              C:::::C                        A:::::A:::::A  
//G:::::G              C:::::C                       A:::::A A:::::A  
//G:::::G    GGGGGGGGGGC:::::C                      A:::::A   A:::::A  
//G:::::G    G::::::::GC:::::C                     A:::::A     A:::::A  
//G:::::G    GGGGG::::GC:::::C                    A:::::AAAAAAAAA:::::A  
//G:::::G        G::::GC:::::C                   A:::::::::::::::::::::A  
// G:::::G       G::::G C:::::C       CCCCCC    A:::::AAAAAAAAAAAAA:::::A  
//  G:::::GGGGGGGG::::G  C:::::CCCCCCCC::::C   A:::::A             A:::::A  
//   GG:::::::::::::::G   CC:::::::::::::::C  A:::::A               A:::::A  
//     GGG::::::GGG:::G     CCC::::::::::::C A:::::A                 A:::::A  
//        GGGGGG   GGGG        CCCCCCCCCCCCCAAAAAAA                   AAAAAAA  
#include <iostream>  
#include <cstdio>  
#include <cstring>  
#include <algorithm>  
#include <cmath>  
#include <climits>  
#include <vector>  
#include <set>  
#include <map>  
#include <queue>  
#include <cctype>  
#include <utility>  
#include <ctime>  
using namespace std;  
#ifdef DEBUG  
#define VAR(a,b) decltype(b) a=(b)  
#define debug(...) printf("DEBUG: "),printf(__VA_ARGS__)  
#define gettime() end_time=clock();printf("now running time is %.7f\\n",(float)(end_time - start_time)/CLOCKS_PER_SEC);  
#else  
#define VAR(a,b) __typeof(b) a=(b)  
#define debug(...)  
#define gettime()  
#endif  
typedef unsigned int uint;  
typedef long long int Int;  
typedef unsigned long long int UInt;  
#define Set(a,s) memset(a,s,sizeof(a))  
#define Write(w) freopen(w,"w",stdout)  
#define Read(r) freopen(r,"r",stdin)  
#define Pln() printf("\\n")  
#define I_de(x,n)for(int i=0;i<n;i++)printf("%d ",x[i]);Pln()  
#define De(x)printf(#x"%d\\n",x)  
#define For(i,x)for(int i=0;i<x;i++)  
#define CON(x,y) x##y  
#define Pmz(dp,nx,ny)for(int hty=0;hty<ny;hty++){for(int htx=0;htx<nx;htx++){\\  
    printf("%d ",dp[htx][hty]);}Pln();}  
#define M 30005  
#define PII pair<int,int>  
#define PB push_back  
#define oo INT_MAX  
#define Set_oo 0x3f  
#define FOR(a,b) for(VAR(a,(b).begin());a!=(b).end();++a)  
#define eps 1e-6  
#define X first  
#define Y second  
clock_t start_time=clock(), end_time;  
bool xdy(double x,double y){return x>y+eps;}  
bool xddy(double x,double y){return x>y-eps;}  
bool xcy(double x,double y){return x<y-eps;}  
bool xcdy(double x,double y){return x<y+eps;}  
int min3(int x,int y,int z){  
    int tmp=min(x,y);  
    return min(tmp,z);  
}  
int max3(int x,int y,int z){  
    int tmp=max(x,y);  
    return max(tmp,z);  
}  
int n;  
int w[104];  
bool solve(){  
    int t;  
    bool suc=true;  
    for(int i=0;i<n;i++){  
        for(int j=0;j<n;j++){  
            scanf("%d",&t);  
            w[t]++;  
            if(w[t]>n)suc=false;  
        }  
    }  
    return suc;  
}  
int main() {  
    ios_base::sync_with_stdio(0);  
    int test,ff=0;  
    scanf("%d",&test);  
    while(test--){  
        Set(w,0);  
        scanf("%d",&n);  
        printf("Case %d: %s\\n",++ff,(solve())?"yes":"no");  
    }  
}  

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