PTA Spiral Matrix (25 points)

It is the human mind that releases infinite light, and it is also the human mind that creates boundless darkness. Light and darkness are intertwined and fight together. This is the world for which we are nostalgic and helpless.

This time your job is to fill a sequence of N positive integers into a spiral matrix in non-increasing order. A spiral matrix is filled in from the first element at the upper-left corner, then move in a clockwise spiral. The matrix has m rows and n columns, where m and n satisfy the following: m×nmust be equal to N; m≥n; and m−n is the minimum of all the possible values.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N. Then the next line contains N positive integers to be filled into the spiral matrix. All the numbers are no more than 10​4​​. The numbers in a line are separated by spaces.

Output Specification:

For each test case, output the resulting matrix in m lines, each contains n numbers. There must be exactly 1 space between two adjacent numbers, and no extra space at the end of each line.

Sample Input:

12
37 76 20 98 76 42 53 95 60 81 58 93

Sample Output:

98 95 93
42 37 81
53 20 76
58 60 76

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <string>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <vector>
#include <ctime>
#include <cctype>
#include <bitset>
#include <utility>
#include <sstream>
#include <complex>
#include <iomanip>
#include<climits>//INT_MAX
//#include<bits/stdc++.h>
#define PP pair<ll,int>
#define inf 0x3f3f3f3f
#define llinf 0x3f3f3f3f3f3f3f3fll
#define dinf 1000000000000.0
#define PI 3.1415926
typedef long long ll;
using namespace std;
int const mod=1e9+7;
const int maxn=1000100;
int N,s[10010],mp[10010][10010];
int mi=inf,m,n;
int main(){
    cin>>N;
    for(int i=1;i<=N;i++)
        cin>>s[i];
    sort(s+1,s+1+N);
    for(int i=1;i<=sqrt(N);i++){
        if(N%i==0){
            int ls=i;
            if(abs(ls-N/ls)<mi){
                n=max(ls,N/ls);
                m=min(ls,N/ls);
            }
        }
    }
//    cout<<m<<' '<<n<<endl;
    int x=0,y=1,d=1;
    for(int i=N;i>=1;i--){
        if(d==1){
            x++;
            if(x>m||mp[y][x]!=0){
                d=2;
                x--;
                y++;
            }
        }
        else if(d==2){
            y++;
            if(y>n||mp[y][x]!=0){
                d=3;
                y--;
                x--;
            }
        }
        else if(d==3){
            x--;
            if(x<1||mp[y][x]!=0){
                d=4;
                x++;
                y--;
            }
        }
        else{
            y--;
            if(y<1||mp[y][x]!=0){
                d=1;
                y++;
                x++;
            }
        }
        mp[y][x]=s[i];
    }
    for(int i=1;i<=n;i++){
        for(int j=1;j<=m;j++){
            cout<<mp[i][j];
            if(j!=m)
                cout<<' ';
            else
                cout<<endl;
        }
    }
    return 0;
}