Find the Width of Columns of a Grid

Problem Description

You are given a 0-indexed integer matrix grid of size m x n. The width of a column is defined as the maximum length of its integers. Return an integer array ans of size n where ans[i] is the width of the i-th column.

Key Insights

• The width of an integer is determined by its digit count; negative integers have an extra digit due to the minus sign.
• We need to calculate the width for each column independently.
• We can iterate through each column and each row to find the maximum width.

Space and Time Complexity

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

Solution

To solve the problem, we will:

1. Initialize an array ans of size n to store the maximum width of each column.
2. Iterate through each column index j.
3. For each column, iterate through every row i to find the maximum length of integers in that column.
4. For each integer, calculate its width based on whether it is negative or non-negative.
5. Update ans[j] with the maximum width found for column j.
6. Return the ans array.

Code Solutions