Arrays | 59. Spiral Matrix II

Topic Link: 59. Spiral Matrix II

zero, description

Given a positive integer n, generate an array containing 1 to $n^2$ all elements, and the nxn square matrix matrix with elements spirally arranged in clockwise order

Example:
Example 1:

Input: n = 3
Output: [[1,2,3],[8,9,4],[7,6,5]]

Example 2:
Input: n = 1
Output: [[1]]

1. Solution: Simulation

Simulation matrix generation.
The initial position is set to the upper left corner of the matrix, and the initial direction is set to the right.
If the position of the next step exceeds the boundary of the matrix, or is a previously visited position, rotate clockwise and enter the next direction. Repeat this until $n^2$ elements.

Key: logic in circles

• Create a two-dimensional array vector<vector<int>> res(n,vector<int>(n));
• Clockwise order, first fix the number of rows, from (top, left) to (top, right)
• Then fix the number of columns, from (top+1, right) to (bottom, right) [Note: top needs +1]
• Then fix the number of rows, from (bottom, right-1) to (bottom, left)
• Then fix the number of columns, from (bottom-1, left) to (top+1, left) [Note: At this time, due to the top+1 above, the arrival is top+1 at this time]
• complete a lap
• Note that it is (top+1, left) at this time, not the starting point of the next cycle, but left+1
• The starting point is (top+1, left+1)
  

class Solution {
    
    
public:
    vector<vector<int>> generateMatrix(int n) {
    
    
        vector<vector<int>> res(n,vector<int>(n));
        int up = 0, down = n - 1, left = 0, right = n - 1, index = 1;
        while(index <= n * n){
    
    
            for(int i = left; i <= right; i++){
    
    
                res[up][i] = index++;
            }
            up++;
            for(int i = up; i <= down; i++){
    
    
                res[i][right] = index++;
            }
            right--;
            for(int i = right; i >= left; i--){
    
    
                res[down][i] = index++;
            }
            down--;
            for(int i = down; i >= up; i--){
    
    
                res[i][left] = index++;
            }
            left++;
        }
        return res;
    }
};