C++实现托普利兹矩阵

Question

刷题的时候遇到了托普利兹矩阵，题目大概如下：
输入
3
输出
1 2 3
2 1 2
3 2 1
我写的代码如下，但是1的右上边的数字是反了的。公式实在推不出来，请大家帮助一下我～

#include <iostream>
using namespace std;

int main()
{
    int n;
    cin >> n;
    
    int matrix[105][105];
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            matrix[i][j] = (i + j) % n + 1;
        }
    }
    
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            cout << matrix[(i - j + n) % n][0] << " ";
        }
        cout << endl;
    }
    return 0;
}

Answer 1

#include <iostream>
using namespace std;
 
int main()
{
    int n;
    cin >> n;
    
    int matrix[105][105] ,i=1;
    for (int x = 1; x <= n; x++){
        i=x;
        for (int j = 1; j <= n; j++){
            matrix[i][j] = x;
            i++;
        }
    }
    int b,j;
    b=n;
    
    for(int k = 1;k <= b;k++){
        j = k,i=1;
        while(i<=b && j<=b){
            matrix[i][j]=k;
            j++,i++;
        }
    }
    
    
    for (int i = 1; i <= n; i++){
        for (int j = 1; j <= n; j++){
            cout << matrix[i][j] << " ";
        }
        cout << endl;
    }
    return 0;
}