【算法】蛇形矩阵

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<span style="font-family: Arial, Helvetica, sans-serif; background-color: rgb(255, 255, 255);">昨晚参加了腾讯的笔试。其中有一道算法题：生成N*N的矩阵，具体规则是：输入一个正整数N，然后生成一个矩阵，并输出矩阵。</span>

生成矩阵的规则是：

例如输入N=3，则生成：
1 2 3

8 9 4

7 6 5.

若输入N=4，则生成：

1 2 3 4

12 13 14 5

11 16 15 6

10 9 8 7

今早仔细思考之后，使用了两种算法实习。（小弟不才，和做ACM的同学有些差距...）

No.1 主要是思想是：一次循环填完一圈。因为给定N值，所以圈数 = N/2 + N%2；下边是代码：

#include<iostream>using namespace std;#include<Windows.h>int a[100][100] = {0};void getValue(int number){int i,j,flag = 0, m = 0;m = 0;int roll = 0;roll = number / 2;if(number % 2 == 1)roll += 1;while(m < roll){for(j = m; j < number - m; j++){if(m == 0)a[m][j] = j+1;else{a[m][j] = a[m][j-1] + 1;}}flag = m + 1;for(j = flag; j < number - m; j++){if(a[j][number - flag] == 0){a[j][number - flag] = a[j-1][number - flag]+1;}}for(j = number - flag - 1; j >= flag-1; j--){if(a[number - flag][j] == 0){a[number - flag][j] = a[number - flag][j+1]+1;}}flag += 1;for( j = number - flag; j > 0; j--){if(a[j][m] == 0){a[j][m] = a[j+1][m] + 1;}}m++;}for(i = 0; i < number; i++){for(j = 0;j < number; j++)cout<<a[i][j]<<"\t";cout << endl;}for(i = 0; i < number; i++){for(j = 0;j < number; j++)cout<<a[i][j]<<" ";}cout << endl;return;}int main(){int number;cin >> number;getValue(number);system("pause");return 0;}

No.2 另外一种是更为广知的DFS深度优先搜索方法。代码如下：

#include<iostream>using namespace std;#include<Windows.h>int my[] = {1,0,-1,0};int mx[] = {0,1,0,-1};int map[9999][9999] = {0};int num = 0;int n = 0;int rec = 0;void dfs(int x, int y,int sum){if(sum > num)return;map[x][y] = sum;sum++;int nx = x + mx[(rec)%4];int ny = y + my[(rec)%4];if( ny > 0 && nx>0 && nx<=n && ny <= n){if(map[nx][ny] == 0){dfs(nx,ny,sum);}else{rec++;dfs(x+mx[(rec)%4],y+my[(rec)%4],sum);}}else{rec++;dfs(x+mx[(rec)%4],y+my[(rec)%4],sum);}return;}int main(){cin >> n;num = n*n;dfs(1,1,1);for(int i = 1; i <= n; i++){for(int j = 1; j <= n ; j++){cout << map[i][j]<<" ";}cout << endl;}system("pause");return 0;}

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