Daily question - leecode59 (spiral matrix II)

difficulty ： secondary  ( It's not easy to see clearly , Stop talking about my hydrology ~)

Give you a positive integer  n , Generate a include  1  To  n2  All the elements , And the elements are arranged in a clockwise spiral order  n x n  square matrix  matrix .

Example  1：

Input ：n = 3

Output ：[[1,2,3],[8,9,4],[7,6,5]]

Example  2：

Input ：n = 1

Output ：[[1]]

Ideas ：

A simulation problem , Medium difficulty , The frequency of interviews is very high .

The simulation problem itself does not involve algorithm , It is to simulate the whole process simply according to the description of the topic, so as to get the final result .

This kind of questions naturally examine your code strength , That is, the ability to master the programming language , If you're not careful, you'll have all kinds of problems  bug.

The key point of doing this kind of simulation problem is to draw more on the paper , Don't think you're dizzy , Write the code clean , Behind  debug...

This question is based on “ Clockwise ” Fill the matrix sequentially , The direction is nothing more than “ The up and down or so ”, Clockwise , Filling is according to “ On -> Right -> Next -> Left ”, The specific point is ：

On ： Fill from left to right .

Right ： Fill from top to bottom .

Next ： Fill from right to left .

Left ： Fill... From bottom to top .

At the same time, find the boundary of each filling , For example, at the beginning, the leftmost boundary  left = 0, The rightmost boundary  right = n-1, Uppermost boundary  up = 0, The lowest boundary  down = n-1.

Let me explain here ：（ Because I didn't understand at first ）

Here is a suggestion , I didn't understand the analysis , Just run separately , It's not clear, and you should not be ashamed to ask ！

Code implementation ：

round() Method returns a floating-point number x Round the value of .

class Solution:
 
 def generateMatrix(self, n: int) -> List[List[int]]:
 #  Initialize the square to fill
 matrix = [[0] * n for _ in range(n)]
 
 left, right, up, down = 0, n - 1, 0, n - 1
 number = 1 #  Number to fill
 
 while left < right and up < down:
 
 #  Fill the upper edge from left to right
 for x in range(left, right):
 matrix[up][x] = number
 number += 1
 
 #  Fill the right side from top to bottom
 for y in range(up, down):
 matrix[y][right] = number
 number += 1
 
 #  Fill the bottom from right to left
 for x in range(right, left, -1):
 matrix[down][x] = number
 number += 1
 
 #  Fill the left side from bottom to top
 for y in range(down, up, -1):
 matrix[y][left] = number
 number += 1
 
 #  Narrow the range to fill
 left += 1
 right -= 1
 up += 1
 down -= 1
 
 #  If the order is odd , Fill the center once more
 if n % 2:
 matrix[round(n // 2)][round(n // 2)] = number
 #round()  Method returns a floating-point number x Round the value of .
 
 return matrix