Original title:

Given a positive integer n, we generate a square matrix containing all the elements from 1 to n2, and the elements are arranged in a clockwise order.

Example:

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

Source: LeetCode
Link: https://leetcode-cn.com/problems/spiral-matrix-ii
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Solution 1:

Idea: Similar to peeling onions, it needs to be filled clockwise layer by layer.

Procedure 1:

First, the first layer is filled when temp = 1, then the second layer is filled when temp = 2, layer by layer. At the same time, the spiral matrix of 54 can also be traversed by this method.
** I think the most clever part of this program is the use of temp to control the number of layers traversed. * *

class Solution(object):
    def generateMatrix(self, n):
        """
        :type n: int
        :rtype: List[List[int]]
        """
        temp = 1
        start = 0
        mat = [[0 for _ in range(n)] for _ in range(n)]
        while temp <= n:
            for i in range(temp-1, n - temp+1): # left to right
                start  += 1
                mat[temp-1][i] = start
            for i in range(temp, n - temp + 1): # top to bottom
                start  += 1
                mat[i][n-temp] = start
            for i in range(n - temp -1 , temp-2, -1): # right to left
                start  += 1
                mat[n-temp][i] = start
            for i in range(n - temp - 1, temp-1, -1): # bottom to top
                start  += 1
                mat[i][temp-1] = start
            temp  += 1
        return mat

Procedure two:

Thought: It is also a step-by-step traversal, but the implementation method of the program is to use four variables for boundary control, which is different from the previous program using only one temp variable.

class Solution(object):
    def generateMatrix(self, n):
        """
        :type n: int
        :rtype: List[List[int]]
        """
        l, r, t, b = 0, n - 1, 0, n - 1
        mat = [[0 for _ in range(n)] for _ in range(n)]
        num, tar = 1, n * n
        while num <= tar:
            for i in range(l, r + 1): # left to right
                mat[t][i] = num
                num += 1
            t += 1
            for i in range(t, b + 1): # top to bottom
                mat[i][r] = num
                num += 1
            r -= 1
            for i in range(r, l - 1, -1): # right to left
                mat[b][i] = num
                num += 1
            b -= 1
            for i in range(b, t - 1, -1): # bottom to top
                mat[i][l] = num
                num += 1
            l += 1
        return mat