What is the time complexity of Find the Width of Columns of a Grid?

The optimal solution has a time complexity of O(m*n).

What data structures are used to solve Find the Width of Columns of a Grid?

This problem uses Array, Matrix. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Find the Width of Columns of a Grid?

Iterate through each column of the matrix to find the maximum width for each column. Convert each integer to a string to easily determine its length. Account for the extra character for negative numbers.

Which companies ask LeetCode 2639. Find the Width of Columns of a Grid in interviews?

This problem is frequently asked at Atlassian, Samsung.

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Find the Width of Columns of a Grid - LeetCode 2639 Solution

Find the Width of Columns of a Grid - Complete Solution Guide

Find the Width of Columns of a Grid is LeetCode problem 2639, a Easy level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given a 0-indexed m x n integer matrix grid . The width of a column is the maximum length of its integers. For example, if grid = [[-10], [3], [12]] , the width of the only column is 3 since -10 is of length 3 . Return an integer array ans of size n where ans[i] is the width of the i th column . The length of an integer x with len digits is equal to len if x is non-negative, and len + 1 otherwise. Example 1: Input: grid = [[1],[22],[333]] Output: [3] Explanation: In the 0 th column, 333

Detailed Explanation

The problem asks you to find the maximum width of each column in a given integer matrix. The width of an integer is its number of digits, plus one if the integer is negative. The input is a 2D integer array (matrix), and the output is a 1D integer array where each element represents the maximum width of the corresponding column in the input matrix.

Solution Approach

The solution uses a nested loop approach. The outer loop iterates through each column, and the inner loop iterates through each row in that column. For each integer encountered, the solution converts it to a string, calculates its length (adding 1 if negative), and updates the maximum width for that column if necessary. Finally, the array containing the maximum widths for each column is returned.

Step-by-Step Algorithm

Initialize an integer array `ans` of the same length as the number of columns in the input `grid` to store the maximum width of each column. Initialize each element to 0.
Iterate through each column `j` of the `grid` (outer loop).
For each column `j`, initialize a variable `max_width` to 0.
Iterate through each row `i` in column `j` (inner loop).
Convert the integer `grid[i][j]` to a string using `str()` (Python) or `String.valueOf()` (Java) or `to_string()` (C++).
Calculate the length of the string. Add 1 to the length if the number is negative.
Update `max_width` with the maximum of `max_width` and the calculated length.
After the inner loop, assign `max_width` to `ans[j]`.
After the outer loop, return the array `ans`.

Key Insights

Iterate through each column of the matrix to find the maximum width for each column.
Convert each integer to a string to easily determine its length. Account for the extra character for negative numbers.
Use a simple array to store the maximum width for each column. This array will be the same length as the number of columns in the input matrix.

Complexity Analysis

Time Complexity: O(m*n)

Space Complexity: O(n)

Topics

This problem involves: Array, Matrix.

Companies

Asked at: Atlassian, Samsung.

Find the Width of Columns of a Grid | LeetCode 2639

Easy

Array Matrix

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

Solution Code

Available in:

class Solution {
    public int[] findColumnWidth(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[] ans = new int[n];
        for (int j = 0; j < n; j++) {
            int maxLen = 0;
            for (int i = 0; i < m; i++) {
                int num = grid[i][j];
                int len = String.valueOf(num).length();
                if (num < 0) {
                    len++;
                }
                maxLen = Math.max(maxLen, len);
            }
            ans[j] = maxLen;
        }
        return ans;
    }
}

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Problem Info

Description

Problem 2639: Find the Width of Columns of a Grid - Detailed explanation and solution approaches.

Topics

Array Matrix

Companies

AtlassianSamsung

Stats

Difficulty:Easy

Languages:4

Companies:2

Problem #:2639

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

9 steps

1
Initialize an integer array `ans` of the same length as the number of columns in the input `grid` to store the maximum width of each column. Initialize each element to 0.
2
Iterate through each column `j` of the `grid` (outer loop).
3
For each column `j`, initialize a variable `max_width` to 0.
4
Iterate through each row `i` in column `j` (inner loop).
5
Convert the integer `grid[i][j]` to a string using `str()` (Python) or `String.valueOf()` (Java) or `to_string()` (C++).
6
Calculate the length of the string. Add 1 to the length if the number is negative.
7
Update `max_width` with the maximum of `max_width` and the calculated length.
8
After the inner loop, assign `max_width` to `ans[j]`.
9
After the outer loop, return the array `ans`.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(m*n)

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The nested loops iterate through each cell of the matrix once, resulting in O(m*n) time complexity. The space complexity is O(n) because we are creating an array of size 'n' to store the widths of each column.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Without String Conversion

Instead of converting to strings, manually calculate the number of digits by repeatedly dividing by 10. This avoids the overhead of string conversion, but may be slightly more complex to implement.

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

Trade-offs: May be slightly faster in some cases due to avoiding string conversion, but potentially less readable and more prone to errors.

✨

Key Insights

1Iterate through each column of the matrix to find the maximum width for each column.
2Convert each integer to a string to easily determine its length. Account for the extra character for negative numbers.
3Use a simple array to store the maximum width for each column. This array will be the same length as the number of columns in the input matrix.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Edge Cases

Empty matrix: The solution handles an empty matrix gracefully, by either returning an empty array (if the first row check passes) or providing a proper error handling mechanism (which is implicit by using the length of the first row)
Matrix with only one row or column: The solution works correctly for matrices with only one row or one column.

⚠️

Common Mistakes to Avoid

✗Forgetting to add 1 to the length for negative numbers: This is a crucial step that many beginners might overlook.

✗Incorrectly handling the case of zero: Zero has a length of 1, but might be missed if not handled separately during calculation of the length of the number.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Data formatting and presentation: Determining the appropriate width for displaying columns of data in a table or spreadsheet.

🏦Database design: Estimating the size needed for storing columns of varying integer sizes in a database, to optimize storage space.

🎮GUI design: Dynamically adjusting the size of column widths in a user interface based on the length of data displayed.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: September 28, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

In a real interview, always clarify constraints first. Ask about input size and value ranges.

@TechLeadJul 14

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 7

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJun 30

❓

Frequently Asked Questions

When should I use in-place modification vs creating a new array?

Use in-place modification when space complexity matters (O(1) space requirement) and the original array can be modified. Create a new array when you need to preserve the original data or when the problem involves significant restructuring that would complicate in-place logic.

What should I learn from easy problems?

Easy problems introduce core patterns that appear in harder problems. Master basic operations (iteration, conditionals, simple data structures), recognize common patterns (counting, searching, basic transformations), and practice explaining your thought process clearly.

What is the importance of time and space complexity analysis?

Complexity analysis is crucial because: 1) Interviewers always ask about it, 2) It helps you choose between approaches, 3) It demonstrates CS fundamentals. Always state both time and space complexity, and be prepared to explain how you derived them.

What is the optimal approach for "Find the Width of Columns of a Grid"?

For this easy-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether matrix techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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