The idea is just to generate the matrix in the spiral order. First the up-most row (u), then the right-most column (r), then the down-most row (d), and finally the left-most column (l). After generating a row or a column, update the corresponding variable to continue the generation.

The code is as follows.

1 class Solution { 2 public: 3     vector
     
      
        > generateMatrix(int n) {  4         vector
       
        
          > mat(n, vector
         
          (n)); 5         int u = 0, d = n - 1, l = 0, r = n - 1, num = 1; 6         while(true) { 7             // up 8             for(int col = l; col <= r; col++) mat[u][col] = num++; 9             if(++u > d) break;10             // right11             for(int row = u; row <= d; row++) mat[row][r] = num++;12             if(--r < l) break;13             // down14             for(int col = r; col >= l; col--) mat[d][col] = num++;15             if(--d < u) break;16             // left17             for(int row = d; row >= u; row--) mat[row][l] = num++;18             if(++l > r) break;19         }20         return mat;21     }22 };