输出模魔方矩阵

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魔方矩阵的一般定义：将自然数 1 到 N^2， 排列 N 行 N 列的方阵，使每行、每列及两条主对角线上的 N 个数的和都等于N (N^2+1)/2，这样的方阵称为 N 阶幻方。

#include<iostream>
using namespace std;
int count_dig(int n)//计算整数的位数，因为15的平方才225，所以最多3位
{for(int i = 100, j = 3; i >=1 ; i /= 10, j--){if(n / i >= 1)return j;}
}
int main()
{int n;int matrix[15][15];bool first = true;while(cin >> n){if(!first)cout << endl;else first = false;for(int i = 0; i < n; i++)for(int j = 0; j < n; j++)matrix[i][j] = 0;//清零int x = 0, y = n / 2;matrix[x][y] = 1;int next = 2;int max = n * n;while(next <= max){int tmp_x = x - 1;//往右上角走int tmp_y = y + 1;if(tmp_x < 0)tmp_x = tmp_x + n;//超出边界则会绕if(tmp_y > n - 1)tmp_y = tmp_y - n;if(matrix[tmp_x][tmp_y] != 0 || (x == 0 && y == n - 1))//若右上角位置有数或前一个数位置是最右上角，则下一个数填在前一个数下面x++;else {x = tmp_x;y = tmp_y;}matrix[x][y] = next++;}int length = count_dig(n * n);cout << "n=" << n << ',' << " sum=" << (1 + n * n) * n / 2 << endl;//输出矩阵for(int i = 0; i < n; i++){for(int j = 0; j < n; j++){cout << ' ';for(int space = 0; space < length - count_dig(matrix[i][j]); space++)cout << ' ';cout << matrix[i][j];}cout << endl;}}
}

题目：

Constraints

Time Limit: 1 secs, Memory Limit: 32 MB

Description

If you have good observations skills, you may found that building a Magic Square is simple. A Magic Square has only an odd number N of rows and columns. For this problem you could expect the values to be 3N15 . A Magic Square is created by integer numbers in the range from 1 to N² , with a peculiar property, the ``sum of the numbers" in each row, column and diagonal is the same value.

For example the case for n = 3 is:

M. Square                Rows          Columns       Diagonals
8 1 6                   8+1+6 = 15    8+3+4 = 15    8+5+2 = 15
3 5 7                   3+5+7 = 15    1+5+9 = 15    4+5+6 = 15
4 9 2                   4+9+2 = 15    6+7+2 = 15

Input

A file with several lines, each line has the value of n .

Output

For each input line, print N and the sum in the first line, followed by the magic square. To see a nice looking square, take into account the maximum length in characters of N² and print each number with the maximum length preceded by one space or blank character. Print one line between squares.

Sample Input

3
5

Sample Output

n=3, sum=158 1 63 5 74 9 2n=5, sum=6517 24  1  8 1523  5  7 14 164  6 13 20 2210 12 19 21  311 18 25  2  9

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