Special Positions in a Binary Matrix

Problem Description

Given an m x n binary matrix mat, 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).

Key Insights

• A special position requires the element to be 1.
• All other elements in the same row and column must be 0.
• We need to check each 1 in the matrix and verify the conditions for being a special position.

Space and Time Complexity

Time Complexity: O(m * n)
Space Complexity: O(1)

Solution

To solve the problem, we will iterate through each element in the matrix. For every element that is 1, we will check its entire row and column to ensure all other elements are 0. We will maintain a count of how many such special positions we find.

1. Loop through every element in the matrix.
2. For each element that is 1:
   • Check the entire row to see if all other elements are 0.
   • Check the entire column to see if all other elements are 0.
3. If both checks pass, increment a special position counter.
4. Return the counter at the end.

Code Solutions