What is the time complexity of H-Index?

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

What data structures are used to solve H-Index?

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

What are the key insights for solving H-Index?

Insight 1: Sorting the citations is a common but not necessary first approach. While it helps visualize the problem, the optimal solution doesn't rely on sorting the entire array. Insight 2: Counting sort or a similar counting-based approach allows for linear time complexity by avoiding full sorting. We leverage the constraint that the maximum citation is 1000.

Which companies ask LeetCode 274. H-Index in interviews?

This problem is frequently asked at ByteDance, Nvidia, Zoox.

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H-Index - LeetCode 274 Solution

H-Index - Complete Solution Guide

H-Index is LeetCode problem 274, 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

Given an array of integers citations where citations[i] is the number of citations a researcher received for their i th paper, return the researcher's h-index . According to the definition of h-index on Wikipedia : The h-index is defined as the maximum value of h such that the given researcher has published at least h papers that have each been cited at least h times. Example 1: Input: citations = [3,0,6,1,5] Output: 3 Explanation: [3,0,6,1,5] means the researcher has 5 papers in total and each

Detailed Explanation

The H-Index problem asks us to determine a researcher's h-index given an array of citation counts for their papers. The h-index represents the maximum value 'h' such that the researcher has published at least 'h' papers with at least 'h' citations each. In simpler terms, we're looking for the largest number 'h' where at least 'h' papers have 'h' or more citations. The input is an array of integers representing citation counts, and the output is a single integer: the h-index. The constraints are: the array length (number of papers) can be up to 5000, and individual citation counts can be up to 1000.

Solution Approach

The solution uses a counting sort-like approach to efficiently determine the h-index. It creates a 'counts' array to store the number of papers with a specific citation count. It then iterates through the citations array, incrementing the corresponding count in the 'counts' array. After counting, it iterates backward from the maximum possible h-index (which is the total number of papers) down to 0. During this backward iteration, it accumulates the number of papers with at least 'h' citations. As soon as the accumulated count is greater than or equal to 'h', we've found our h-index, as there are at least 'h' papers with 'h' or more citations.

Step-by-Step Algorithm

Step 1: Determine the number of papers (n) from the length of the citations array.
Step 2: Initialize a 'counts' array of size n+1 with all elements set to 0. This array will store the frequency of papers having certain number of citations.
Step 3: Iterate through the 'citations' array. For each citation count 'c': If 'c' is greater than or equal to 'n', increment counts[n]. Otherwise, increment counts[c]. The purpose is to count the number of papers with 'n' or more citations.
Step 4: Initialize 'total_papers' to 0. This variable will track the number of papers with at least 'h' citations.
Step 5: Iterate backward from 'h = n' down to 0. In each iteration:
Step 6: Add counts[h] to 'total_papers'.
Step 7: If 'total_papers' is greater than or equal to 'h', return 'h' because we have found the h-index.
Step 8: If the loop completes without finding an h-index (total_papers never becomes >= h), return 0.

Key Insights

Insight 1: Sorting the citations is a common but not necessary first approach. While it helps visualize the problem, the optimal solution doesn't rely on sorting the entire array.
Insight 2: Counting sort or a similar counting-based approach allows for linear time complexity by avoiding full sorting. We leverage the constraint that the maximum citation is 1000.
Insight 3: Iterating from the maximum possible h-index (n) down to 0 allows us to find the largest h-index that satisfies the condition by accumulating the count of papers with at least that many citations.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Sorting, Counting Sort.

Companies

Asked at: ByteDance, Nvidia, Zoox.

H-Index | LeetCode 274

Medium

Array Sorting Counting Sort

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

Solution Code

Available in:

class Solution {
    public int hIndex(int[] citations) {
        int n = citations.length;
        int[] counts = new int[n + 1];

        for (int c : citations) {
            if (c >= n) {
                counts[n]++;
            } else {
                counts[c]++;
            }
        }

        int total_papers = 0;
        for (int h = n; h >= 0; h--) {
            total_papers += counts[h];
            if (total_papers >= h) {
                return h;
            }
        }

        return 0;
    }
}

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Problem Info

Description

Problem 274: H-Index - Detailed explanation and solution approaches.

Topics

Array Sorting Counting Sort

Companies

ByteDanceNvidiaZoox

Stats

Difficulty:Medium

Languages:4

Companies:3

Problem #:274

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

8 steps

1
Step 1: Determine the number of papers (n) from the length of the citations array.
2
Step 2: Initialize a 'counts' array of size n+1 with all elements set to 0. This array will store the frequency of papers having certain number of citations.
3
Step 3: Iterate through the 'citations' array. For each citation count 'c': If 'c' is greater than or equal to 'n', increment counts[n]. Otherwise, increment counts[c]. The purpose is to count the number of papers with 'n' or more citations.
4
Step 4: Initialize 'total_papers' to 0. This variable will track the number of papers with at least 'h' citations.
5
Step 5: Iterate backward from 'h = n' down to 0. In each iteration:
6
Step 6: Add counts[h] to 'total_papers'.
7
Step 7: If 'total_papers' is greater than or equal to 'h', return 'h' because we have found the h-index.
8
Step 8: If the loop completes without finding an h-index (total_papers never becomes >= h), return 0.

💡

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)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The dominant operations are the two loops, each iterating a maximum of 'n' times. The space complexity is determined by the 'counts' array, which requires O(n) space to store the counts of citations.

📖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

Sorting

Sort the citations array in descending order. Then, iterate through the sorted array. The h-index is the index 'i' where citations[i] is greater than or equal to i+1.

Time: O(n log n) due to sorting.Space: O(1) or O(n), depending on the sorting algorithm used (in-place vs. creating a copy).

Trade-offs: Easier to understand conceptually, but less efficient than the counting approach if n is large. Sorting becomes preferable if the range of citation values is much larger than n. For example, if n=10 but some citation values are 1000000, then the counting approach would be very inefficient in memory.

✨

Key Insights

1Insight 1: Sorting the citations is a common but not necessary first approach. While it helps visualize the problem, the optimal solution doesn't rely on sorting the entire array.
2Insight 2: Counting sort or a similar counting-based approach allows for linear time complexity by avoiding full sorting. We leverage the constraint that the maximum citation is 1000.
3Insight 3: Iterating from the maximum possible h-index (n) down to 0 allows us to find the largest h-index that satisfies the condition by accumulating the count of papers with at least that many citations.

📚

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 citations array. The code correctly handles an empty array by returning 0 because n will be 0, the counts array will be of size 1, and the total_papers will also be 0, so it immediately returns 0.
Edge case 2: All citations are 0. The counts[0] will be equal to 'n' and h will reach 0. Then total_papers will become 'n', and the h-index will be 0, which is correct.
Edge case 3: All citations are greater than or equal to n. counts[n] will become equal to 'n' and the loop will return n, which is the h-index.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly initializing the 'counts' array. It is crucial to initialize all elements to 0 to accurately count citations.

✗Common mistake 2: Not handling the case where citations are greater than the number of papers. All papers cited greater than the size of array must be grouped into `n` counts.

✗Common mistake 3: Incorrectly accumulating the papers. Ensure the iteration is backwards and you're adding the number of counts to the `total_papers`.

✅

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: Evaluating the impact of research papers. H-index is a widely used metric in academia to assess the influence and productivity of researchers.

🏦Real-world scenario 2: Ranking journals or research institutions. H-index can be aggregated to evaluate the overall performance of journals or institutions based on the citation counts of their published works.

💡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.

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 3, 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

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "H-Index"?

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.

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