Find the Row with the Maximum Number of 1’s

In this article, we will solve the problem of finding the row with the maximum number of 1’s in a binary matrix.

Problem Statement: Given a binary matrix (a matrix containing only 0s and 1s), find the row with the maximum number of 1’s. Each row in the matrix is sorted in non-decreasing order (i.e., all the 0s will be followed by all the 1s).

Solution:

To solve this problem, we can take advantage of the fact that each row is sorted. We can use the following approach:

1.    Initialize Variables:

• Keep track of the maximum number of 1's found so far and the corresponding row index.

2.    Traverse Each Row:

• For each row, use binary search to find the first occurrence of 1.

• Calculate the number of 1's in the row by subtracting the index of the first 1 from the total number of columns.

• Update the maximum number of 1's and the row index if the current row has more 1's than the previous maximum.

3.    Return the Row Index:

• After traversing all rows, return the index of the row with the maximum number of 1's.

Time Complexity: O(n log m)

Space Complexity: O(1)