Given a rows x cols matrix mat, where mat[i][j] is either 0 or 1, return the number of special positions in mat.
A position (i,j) is called special if mat[i][j] == 1 and all other elements in row i and column j are 0 (rows and columns are 0-indexed).
 
Example 1:
Input: mat = [[1,0,0],
              [0,0,1],
              [1,0,0]]
Output: 1
Explanation: (1,2) is a special position because mat[1][2] == 1 and all other elements in row 1 and column 2 are 0.

Example 2:
Input: mat = [[1,0,0],
              [0,1,0],
              [0,0,1]]
Output: 3
Explanation: (0,0), (1,1) and (2,2) are special positions. 

Example 3:
Input: mat = [[0,0,0,1],
              [1,0,0,0],
              [0,1,1,0],
              [0,0,0,0]]
Output: 2

Example 4:
Input: mat = [[0,0,0,0,0],
              [1,0,0,0,0],
              [0,1,0,0,0],
              [0,0,1,0,0],
              [0,0,0,1,1]]
Output: 3

 
Constraints:

rows == mat.length
cols == mat[i].length
1 <= rows, cols <= 100
mat[i][j] is 0 or 1.

Difficulty: introductory

Starter code:

class Solution:
    def numSpecial(self, mat: List[List[int]]) -> int:
        

Solutions:
import itertools

class Solution:
  def numSpecial(self, mat: List[List[int]]) -> int:
    rr = [i for i, r in enumerate(mat) if sum(r) == 1]
    cc = [i for i, c in enumerate(zip(*mat)) if sum(c) == 1]
    return sum(1 for i, j in itertools.product(rr, cc) if mat[i][j] == 1)

import numpy as np

class Solution:
    def numSpecial(self, mat: List[List[int]]) -> int:
        
        mat = np.matrix(mat)
        indices_pack = np.where(mat==1)
        indices = [(i, j) for i, j in zip(indices_pack[0], indices_pack[1])]
        print(indices)
        
        count = np.array([1 for x, y in indices if mat[x,:].sum() == 1 and mat[:,y].sum() == 1])
        return int(count.sum())

class Solution:
    def numSpecial(self, mat: List[List[int]]) -> int:
        ## My original solution, not very fast
        # mat_t = list(zip(*mat))
        # row_s = [i for i in range(len(mat)) if sum(mat[i]) == 1]
        # col_s = [j for j in range(len(mat_t)) if sum(mat_t[j]) == 1]
        # return sum(mat[i][j] == 1 and i in row_s and j in col_s for i in range(len(mat)) for j in range(len(mat_t)))
        
        mat_t = list(zip(*mat))
        res = 0
        for i in range(len(mat)):
            for j in range(len(mat_t)):
                if mat[i][j] == sum(mat[i]) == sum(mat_t[j]) == 1:
                    res += 1
        return res

class Solution:
    def numSpecial(self, mat: List[List[int]]) -> int:
        ## My original solution, not very fast
        # mat_t = list(zip(*mat))
        # row_s = [i for i in range(len(mat)) if sum(mat[i]) == 1]
        # col_s = [j for j in range(len(mat_t)) if sum(mat_t[j]) == 1]
        # return sum(mat[i][j] == 1 and i in row_s and j in col_s for i in range(len(mat)) for j in range(len(mat_t)))
        
        ## Modified version, still not very fast
        mat_t = list(zip(*mat))
        res = 0
        for i in range(len(mat)):
            for j in range(len(mat_t)):
                if mat[i][j] == sum(mat[i]) == sum(mat_t[j]) == 1:
                    res += 1
        return res

class Solution:
    def numSpecial(self, mat: List[List[int]]) -> int:
        res=0
        for i in range(len(mat)):
            for j in range(len(mat[-1])):
                if mat[i][j]==1 and sum(mat[i])==1 and sum(mat[o][j] for o in range(len(mat)))==1:
                    res+=1
        return res