<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;
}