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preface

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Difficulty level: Medium

1. Describe

Given a positive integer n, generate an n x n square matrix matrix containing all elements from 1 to n2 in a clockwise spiral order.

Example 2.

Example 1

Input: n = 3 output: [[1,2,3],[8,9,4],[7,6,5]]Copy the code

Example 2

Input: n = 1 Output: [[1]]Copy the code

Constraints:

  • 1 <= n <= 20

3. The answer

class SpiralMatrixII {
    func generateMatrix(_ n: Int)- > [[Int]] {
        guard n > 0 else {
            return [[Int]]()
        }
    
        var num = 1
        var res = Array(repeating: Array(repeating: 0, count: n), count: n)
        
        for layer in 0..<n / 2 {
            let start = layer
            let end = n - layer - 1
            
            // top
            for i in start..<end {
                res[start][i] = num
                num + = 1
            }
            
            // right
            for i in start..<end {
                res[i][end] = num
                num + = 1
            }
            
            // bottom
            for i in stride(from: end, to: start, by: -1) {
                res[end][i] = num
                num + = 1
            }
            
            // left
            for i in stride(from: end, to: start, by: -1) {
                res[i][start] = num
                num + = 1}}// handle the center one
        if n % 2 ! = 0 {
            res[n / 2][n / 2] = n * n
        }
        
        return res
    }
}
Copy the code
  • Main idea: Start clockwise and fill in the numbers, remembering to work with the middle one.
  • Time complexity: O(n^2)
  • Space complexity: O(1)

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