leetcode 1277. Count Square Submatrices with All Ones（python）

描述

Given a m * n matrix of ones and zeros, return how many square submatrices have all ones.

Example 1:

Input: matrix =
[
  [0,1,1,1],
  [1,1,1,1],
  [0,1,1,1]
]
Output: 15
Explanation: 
There are 10 squares of side 1.
There are 4 squares of side 2.
There is  1 square of side 3.
Total number of squares = 10 + 4 + 1 = 15.	

Example 2:

Input: matrix = 
[
  [1,0,1],
  [1,1,0],
  [1,1,0]
]
Output: 7
Explanation: 
There are 6 squares of side 1.  
There is 1 square of side 2. 
Total number of squares = 6 + 1 = 7.

Note:

1 <= arr.length <= 300
1 <= arr[0].length <= 300
0 <= arr[i][j] <= 1

解析

根据题意，只需要找出 matrix 中由 1 组成的任意大小的正方形个数即可。其实只要找规律就可以发现，设计一个 m*n 的 new 矩阵来存放数量值，其中的 new[i][j] 表示以此单元格为右下角的正方形的个数可以有几个，然后遍历比较所有的 matrix 的值，