[WikiOI] 2.2.2 蛇形矩阵

[Problem]

小明玩一个数字游戏，取个n行n列数字矩阵（其中n为不超过100的奇数），数字的填补方法为：在矩阵中心从1开始以逆时针方向绕行，逐圈扩大，直到n行n列填满数字，请输出该n行n列正方形矩阵以及其的对角线数字之和.

[Solution]

#include <iostream>
using namespace std;

int direct[4][2] = {{0, 1}, {-1, 0}, {0, -1}, {1, 0}};



/**
 * main
 */
int main(){
	int n, i, j, k = 1;
	cin >> n;

	// create array
	int **array = new int*[n];
	for(i = 0; i < n; ++i){
		array[i] = new int[n];
		for(j = 0; j < n; ++j){
			array[i][j] = 0;
		}
	}

	// init
	i = j = n / 2;
	array[i][j] = 1;

	// write data
	bool completed = false;
	int d = 0, a = 2, cnt = 0;
	while(!completed){
		cnt++;
		for(int b = 0; b < k; ++b){
			i += direct[d][0];
			j += direct[d][1];

			// completed
			if(i < 0 || i == n || j < 0 || j == n){
				completed = true;
				break;
			}
			array[i][j] = a++;
		}

		// change forward steps
		if(cnt % 2 == 0){
			k++;
		}

		// change direction
		d++;
		d %= 4;
	}

	// output result
	int sum = 0;
	for(i = 0; i < n; ++i){
		for(j = 0; j < n; ++j){
			if(i == j || i+j == n-1){
				sum += array[i][j];
			}
			cout << array[i][j] << " ";
		}
		cout << endl;
	}
	cout << sum << endl;

	return 0;
}