P1978 Magical Magic Square

P1978 Magical Magic SquareDescribe

Magic Square is a very magical n∗n matrix: It is made up of numbers, ..., n∗n, and the sum of the numbers on each row, column, and two diagonal lines are the same.

When N is odd, we can construct a magic square by first writing 1 in the middle of the first line.

Then, fill in each number k (k = 2,3, ..., n∗n) according to the following way from small to large:

1. if (k−1) in the first row but not in the last column, the K is filled in the last row, (k−1) in the right column of the column;
2. if (k−1) in the last column but not in the first row, the K is filled in the first column, (k−1) on the row of the previous line;
3. if (k−1) in the last column of the first row, the K is filled directly below (k−1);
4. if (k−1) is not in the first line, nor in the last column, if (k−1) is not filled in the upper right, then K is filled in (k−1) in the upper right, otherwise k is filled in (k−1) directly below.

Now given N, please construct n∗n Magic Square according to the above method.

Format input Format

An integer N, which is the size of the magic square.

Output format

The output file contains n rows, n integers per line, that is, the magic side of the N∗n constructed by the above method. Adjacent two integers are separated by a single space.

Example 1 sample input 1[copy]

3

Sample output 1[Copy]

8 1 63 5 74 9 2

Limit

For 100% of data, 1≤n≤39 and N are odd.

Source

NOIP 2015 Raising Group Day 1 first question

Exercises

C++

#include <iostream>#include<cstdio>#include<string.h>using namespacestd;intn,a[ +][ +],x[ the],y[ the];intMain () {scanf ("%d",&N); if(n==1) {printf ("%d\n", N); return 0; } memset (A,0,sizeof(a)); a[1[N-1)/2+1]=1; x[1]=1; y[1]= (n1)/2+1;  for(intI=2; i<=n*n;i++)    {        if(x[i-1]==1&& y[i-1]!=N) {a[n][y[i-1]+1]=i; X[i]=N; Y[i]=y[i-1]+1; Continue; }        if(y[i-1]==n && x[i-1]>1) {A[x[i-1]-1][1]=i; X[i]=x[i-1]-1; Y[i]=1; Continue; }        if(x[i-1]==1&& y[i-1]==N) {a[2][n]=i; X[i]=2; Y[i]=N; Continue; }        if(x[i-1]!=1&& y[i-1]!=N) {if(a[x[i-1]-1][y[i-1]+1]==0) {A[x[i-1]-1][y[i-1]+1]=i; X[i]=x[i-1]-1; Y[i]=y[i-1]+1; Continue; }            Else{a[x[i-1]+1][y[i-1]]=i; X[i]=x[i-1]+1; Y[i]=y[i-1]; Continue; }        }    }     for(intI=1; i<=n;i++)    {         for(intj=1; j<n;j++) {printf ("%d", A[i][j]); } printf ("%d\n", A[i][n]); }    return 0;}

P1978 Magical Magic Square