What is the time complexity of Sort the Students by Their Kth Score?

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

What data structures are used to solve Sort the Students by Their Kth Score?

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

What are the key insights for solving Sort the Students by Their Kth Score?

Insight 1: We need to sort the rows of the matrix based on the values in the k-th column. Insight 2: A custom sorting function (comparator) is required to compare rows based on the element at the k-th index.

Which companies ask LeetCode 2545. Sort the Students by Their Kth Score in interviews?

This problem is frequently asked at IBM.

JavaScript is required for the full interactive experience. However, all content is accessible without JavaScript.

Sort the Students by Their Kth Score - LeetCode 2545 Solution

Sort the Students by Their Kth Score - Complete Solution Guide

Sort the Students by Their Kth Score is LeetCode problem 2545, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

There is a class with m students and n exams. You are given a 0-indexed m x n integer matrix score , where each row represents one student and score[i][j] denotes the score the i th student got in the j th exam. The matrix score contains distinct integers only. You are also given an integer k . Sort the students (i.e., the rows of the matrix) by their scores in the k th ( 0-indexed ) exam from the highest to the lowest. Return the matrix after sorting it. Example 1: Input: score = [[10,6,9,1],[7

Detailed Explanation

The problem asks us to sort a matrix (representing student scores on different exams) based on the scores obtained by the students in a specific exam (indicated by the index 'k'). The goal is to rearrange the rows of the matrix so that students with higher scores in the k-th exam come before students with lower scores. The input is the matrix `score` and the index `k` of the exam to sort by. The output is the sorted matrix.

Solution Approach

The provided solutions utilize the built-in sorting functions available in their respective languages, along with a custom comparator. The comparator compares two rows based on the value at the k-th column. The sorting is done in descending order, placing the rows with larger values in the k-th column earlier in the sorted matrix. The qsort_r function in the C code performs this task.

Step-by-Step Algorithm

Step 1: Define a comparison function that takes two rows and the column index `k` as input.
Step 2: Inside the comparison function, compare the elements at the k-th index of the two rows.
Step 3: The comparison function returns a negative value if the first row should come before the second, a positive value if the second row should come before the first, and zero if they are equal. Since we want descending order, we subtract the element of row A from the element of row B (B[k]-A[k] for Java and C, A[k] > B[k] in C++). Python uses a lambda function for this concisely.
Step 4: Use the language's built-in sorting function (e.g., `Arrays.sort` in Java, `sort` in C++, `sorted` in Python, `qsort_r` in C) with the matrix and the custom comparison function as arguments.
Step 5: Return the sorted matrix.

Key Insights

Insight 1: We need to sort the rows of the matrix based on the values in the k-th column.
Insight 2: A custom sorting function (comparator) is required to compare rows based on the element at the k-th index.
Insight 3: Most languages provide built-in sorting functionalities that can accept a custom comparison function, simplifying the implementation.

Complexity Analysis

Time Complexity: O(n log n)

Space Complexity: O(n)

Topics

This problem involves: Array, Sorting, Matrix.

Companies

Asked at: IBM.

Sort the Students by Their Kth Score | LeetCode 2545

Medium

Array Sorting Matrix

Time: O(n log n)Space: O(n)

Solution Code

Available in:

import java.util.Arrays;
import java.util.Comparator;

class Solution {
    public int[][] sortTheStudents(int[][] score, int k) {
        Arrays.sort(score, (a, b) -> b[k] - a[k]);
        return score;
    }
}

View Full Solution on GitHubGitHub Solution View on LeetCodeLeetCode

Problem Info

Description

Problem 2545: Sort the Students by Their Kth Score - Detailed explanation and solution approaches.

Topics

Array Sorting Matrix

Companies

IBM

Stats

Difficulty:Medium

Languages:4

Companies:1

Problem #:2545

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

5 steps

1
Step 1: Define a comparison function that takes two rows and the column index `k` as input.
2
Step 2: Inside the comparison function, compare the elements at the k-th index of the two rows.
3
Step 3: The comparison function returns a negative value if the first row should come before the second, a positive value if the second row should come before the first, and zero if they are equal. Since we want descending order, we subtract the element of row A from the element of row B (B[k]-A[k] for Java and C, A[k] > B[k] in C++). Python uses a lambda function for this concisely.
4
Step 4: Use the language's built-in sorting function (e.g., `Arrays.sort` in Java, `sort` in C++, `sorted` in Python, `qsort_r` in C) with the matrix and the custom comparison function as arguments.
5
Step 5: Return the sorted matrix.

💡

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(n log n)

✨ Log-linear - Great for sorting algorithms!

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The dominant operation is the sorting step. The comparison function has a constant time complexity (O(1)). Therefore, the overall time complexity is determined by the sorting algorithm's complexity. The space complexity depends on whether the sorting algorithm sorts in place or creates a new copy of the matrix. Python's sorted() method creates a new list, resulting in O(n) space. The Java, C++, and C versions generally sort in place, resulting in constant space or a small amount of space used by quicksort.

📖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

Radix Sort

If the range of scores in the k-th column is limited and known, radix sort could potentially be used for sorting the rows. Radix sort is a non-comparative sorting algorithm that can achieve O(nk) time complexity, where n is the number of elements to sort and k is the number of digits in the largest number. In this case, if scores are relatively small numbers, radix sort could be faster than comparison-based sorting.

Time: O(m*d), where m is the number of students and d is the maximum number of digits in the score.Space: O(m + r), where r is the radix (usually 10).

Trade-offs: Radix sort is faster when the range of values is limited and d is small. However, it's more complex to implement than comparison-based sorting and requires knowledge of the maximum value in the k-th column.

✨

Key Insights

1Insight 1: We need to sort the rows of the matrix based on the values in the k-th column.
2Insight 2: A custom sorting function (comparator) is required to compare rows based on the element at the k-th index.
3Insight 3: Most languages provide built-in sorting functionalities that can accept a custom comparison function, simplifying the implementation.

📚

Key Terms Explained

For Students

Array

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

Sorting

Arranging elements in a specific order (ascending/descending).

Edge Cases

Edge case 1: Empty matrix (score.length == 0). The code will still execute correctly because the sorting function will not be called, and the original matrix will be returned.
Edge case 2: Matrix with only one row (score.length == 1). The code will also execute correctly, returning the matrix unchanged, as there's nothing to sort.
Edge case 3: Invalid value of 'k' (k < 0 or k >= score[0].length). Although not explicitly handled in the provided solutions, it is assumed that 'k' is within the valid range according to the problem constraints. A more robust solution might include error handling for this case, such as throwing an exception or returning an error code.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly implementing the comparator function. The comparator should return a negative value if the first row should come before the second, a positive value if the second row should come before the first, and zero if they are equal. Reversing the logic will result in incorrect sorting.

✗Common mistake 2: Assuming that the built-in sort functions modify the array in place. In Python, the 'sorted' function creates a new list and does not modify the original array. For in-place modification, use the `list.sort()` method.

✗Common mistake 3: Forgetting the reverse = True parameter in Python to sort in descending order, leading to ascending sort instead.

✅

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?

💼Real-world scenario 1: Sorting student records based on their performance in a particular subject or exam.

🏦Real-world scenario 2: Ranking athletes based on their scores in a specific event in a competition.

💡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

If stuck, try working through a small example by hand. The pattern often reveals itself.

⚠️ Watch Out

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

👨‍💻 From Experience

This problem pattern appears frequently in real codebases. I've used similar logic when building production systems.

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: June 26, 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

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

@DevExpert92Jul 13

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

@AlgoMasterJul 6

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJun 29

❓

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.

How much time should I spend on a medium problem in interviews?

In a 45-minute interview, aim for: 5-10 minutes understanding and clarifying, 5-10 minutes discussing approach, 20-25 minutes coding, and 5-10 minutes testing. If stuck after 15 minutes of thinking, verbalize your thought process and ask for hints.

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 "Sort the Students by Their Kth Score"?

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

🤖 Need help with this problem?