Skip to content

2482. Difference Between Ones and Zeros in Row and Column

Difficulty Topics

Description

You are given a 0-indexed m x n binary matrix grid.

A 0-indexed m x n difference matrix diff is created with the following procedure:

  • Let the number of ones in the ith row be onesRowi.
  • Let the number of ones in the jth column be onesColj.
  • Let the number of zeros in the ith row be zerosRowi.
  • Let the number of zeros in the jth column be zerosColj.
  • diff[i][j] = onesRowi + onesColj - zerosRowi - zerosColj

Return the difference matrix diff.

 

Example 1:

Input: grid = [[0,1,1],[1,0,1],[0,0,1]]
Output: [[0,0,4],[0,0,4],[-2,-2,2]]
Explanation:
- diff[0][0] = onesRow0 + onesCol0 - zerosRow0 - zerosCol0 = 2 + 1 - 1 - 2 = 0 
- diff[0][1] = onesRow0 + onesCol1 - zerosRow0 - zerosCol1 = 2 + 1 - 1 - 2 = 0 
- diff[0][2] = onesRow0 + onesCol2 - zerosRow0 - zerosCol2 = 2 + 3 - 1 - 0 = 4 
- diff[1][0] = onesRow1 + onesCol0 - zerosRow1 - zerosCol0 = 2 + 1 - 1 - 2 = 0 
- diff[1][1] = onesRow1 + onesCol1 - zerosRow1 - zerosCol1 = 2 + 1 - 1 - 2 = 0 
- diff[1][2] = onesRow1 + onesCol2 - zerosRow1 - zerosCol2 = 2 + 3 - 1 - 0 = 4 
- diff[2][0] = onesRow2 + onesCol0 - zerosRow2 - zerosCol0 = 1 + 1 - 2 - 2 = -2
- diff[2][1] = onesRow2 + onesCol1 - zerosRow2 - zerosCol1 = 1 + 1 - 2 - 2 = -2
- diff[2][2] = onesRow2 + onesCol2 - zerosRow2 - zerosCol2 = 1 + 3 - 2 - 0 = 2

Example 2:

Input: grid = [[1,1,1],[1,1,1]]
Output: [[5,5,5],[5,5,5]]
Explanation:
- diff[0][0] = onesRow0 + onesCol0 - zerosRow0 - zerosCol0 = 3 + 2 - 0 - 0 = 5
- diff[0][1] = onesRow0 + onesCol1 - zerosRow0 - zerosCol1 = 3 + 2 - 0 - 0 = 5
- diff[0][2] = onesRow0 + onesCol2 - zerosRow0 - zerosCol2 = 3 + 2 - 0 - 0 = 5
- diff[1][0] = onesRow1 + onesCol0 - zerosRow1 - zerosCol0 = 3 + 2 - 0 - 0 = 5
- diff[1][1] = onesRow1 + onesCol1 - zerosRow1 - zerosCol1 = 3 + 2 - 0 - 0 = 5
- diff[1][2] = onesRow1 + onesCol2 - zerosRow1 - zerosCol2 = 3 + 2 - 0 - 0 = 5

 

Constraints:

  • m == grid.length
  • n == grid[i].length
  • 1 <= m, n <= 105
  • 1 <= m * n <= 105
  • grid[i][j] is either 0 or 1.

Solution

difference-between-ones-and-zeros-in-row-and-column.py
class Solution:
    def onesMinusZeros(self, grid: List[List[int]]) -> List[List[int]]:
        rows, cols = len(grid), len(grid[0])
        res = [[0] * cols for _ in range(rows)]
        rowOnes = defaultdict(int)
        colOnes = defaultdict(int)

        for i in range(rows):
            count = grid[i].count(1)
            rowOnes[i] = count

        for i, col in enumerate(zip(*grid)):
            count = col.count(1)
            colOnes[i] = count

        # print(rowOnes, colOnes)
        for i in range(rows):
            for j in range(cols):
                rone = rowOnes[i]
                rzero = rows - rone
                cone = colOnes[j]
                czero = cols - cone
                # print(i, j, rone, cone, rzero, czero)
                res[i][j] = rone + cone - rzero - czero

        return res