2045: [Example 5.13] Serpentine filling

topic

Time Limit: 1000 ms Memory Limit: 65536 KB
Number of Submissions: 1201 Number of Passes: 626
[Title Description]
Fill in 1,2,3,…,n×n in an n×n square matrix, and it is required to fill in a snake shape. For example, when n=4, the square matrix is:

10 11 12 1
9 16 13 2
8 15 14 3
7 6 5 4
Among them, n≤20.

【Input】
Enter n.

【Output】
Output the square matrix of the title. n lines, each number is separated by a space.

【Input example】
4
【Output example】
10 11 12 1
9 16 13 2
8 15 14 3
7 6 5 4

Topic analysis: It is difficult to directly find the data corresponding to a certain coordinate, but we can divide the square matrix into multiple layers, fill in the outermost layer first, then fill in the second layer...until the square matrix is filled. If the side length of the original square matrix is n, then it becomes a square matrix with side length (n-2) after filling the outermost layer. Through the side length of the square matrix, we can find the outermost data.

C++ code

#include<iostream>
using namespace std;
int main()
{
    
    
	int a[20][20],n;
	cin>>n;
	int c=n,temp=1;//c:当前矩阵边长;temp:当前数字
	while(c)
	{
    
    
		if(c==1)//只有一个格
		{
    
    
			a[n/2][n/2]=temp;
			break;
		}
		int y=(n-c)/2,x=(n-c)/2+c-1;
		int end=y+c-1;
		for(;y<=end;y++,temp++)//处理右面
		{
    
    
			a[y][x]=temp;
		}
		y=end;
		end=x-c+1;
		x--;
		for(;x>=end;x--,temp++)//处理下面
		{
    
    
			a[y][x]=temp;
		}
		x=end;
		end=y-c+1;
		y--;
		for(;y>=end;y--,temp++)//处理左面
		{
    
    
			a[y][x]=temp;
		}
		y=end;
		end=x+c-1;
		x++;
		for(;x<end;x++,temp++)//处理上面
		{
    
    
			a[y][x]=temp;
		}
		c-=2;//矩阵边长缩小2
	}
	for(int i=0;i<n;i++)
	{
    
    
		for(int j=0;j<n;j++)
		{
    
    
			cout<<a[i][j]<<' ';
		}
		cout<<endl;
	}
}

operation result

5*5 serpentine square