H-Index - Practice Coding Problems

H-Index - Problem

Imagine you're a researcher who has published several papers, and you want to measure your academic impact using the prestigious H-Index metric.

Given an array citations where citations[i] represents the number of citations your i-th paper has received, calculate your H-Index.

The H-Index is defined as: The maximum value h such that you have published at least h papers that have each been cited at least h times.

Example: If you have papers with citations [3, 0, 6, 1, 5], your H-Index is 3 because you have 3 papers with at least 3 citations each (papers with 3, 6, and 5 citations), but you don't have 4 papers with at least 4 citations each.

Input & Output

example_1.py — Standard Case

$ Input: [3,0,6,1,5]

› Output: 3

💡 Note: The researcher has 3 papers with at least 3 citations each (papers with 3, 6, and 5 citations), but only 2 papers with at least 4 citations each. So the H-Index is 3.

example_2.py — All High Citations

$ Input: [1,3,1]

› Output: 1

💡 Note: The researcher has only 1 paper with at least 3 citations, 2 papers with at least 1 citation. The maximum H-Index possible is 1.

example_3.py — Edge Case Single Paper

$ Input: [100]

› Output: 1

💡 Note: With only 1 paper (even with 100 citations), the maximum H-Index is 1, since we can have at most 1 paper with at least 1 citation.

Constraints

n == citations.length
1 ≤ n ≤ 5000
0 ≤ citations[i] ≤ 1000

Visualization

Tap to expand

3 papers with ≥3 citations eachBut only 2 papers with ≥4 citationsTherefore, H-Index = 3Optimal Algorithm Summary1. Create n+1 buckets for citation counts2. Count papers in each range3. Scan right-to-left to find max valid hTime: O(n) | Space: O(n)

Understanding the Visualization

Understand the Problem

We need the maximum h where we have ≥h papers with ≥h citations each

Sort by Citations

Arrange papers in descending order of citations for easier analysis

Find the Balance Point

The H-Index is where the number of papers meets the citation requirement

Optimal Counting

Use buckets to count efficiently without sorting

Key Takeaway

🎯 Key Insight: The H-Index represents the perfect balance between quantity and quality of research impact - the highest number where you have that many highly-cited papers.

Asked in

G Google 42 ⊞ Microsoft 38 a Amazon 31 Apple 24

The optimal solution uses counting sort principles to achieve O(n) time complexity. Since H-Index cannot exceed the number of papers, we create buckets to count papers in each citation range, then scan from highest to lowest to find the maximum valid H-Index. The key insight is that we only need to consider H-Index values from 0 to n.

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force (Check All Possible H-Values)	O(n²)	O(1)	Try every possible H-Index value from 0 to n and count qualifying papers
Sorting + Single Pass	O(n log n)	O(1)	Sort citations in descending order and find the optimal H-Index in one pass
Counting Sort (Optimal)	O(n)	O(n)	Use counting sort principle with buckets for O(n) time complexity

Brute Force (Check All Possible H-Values) — Algorithm Steps

Iterate through all possible H-Index values from 0 to n
For each h, count papers with citations ≥ h
Check if count ≥ h (valid H-Index condition)
Return the maximum valid h found

Visualization

Tap to expand

Step-by-Step Walkthrough

Try h=0

Count papers with ≥0 citations (all papers qualify)

Try h=1

Count papers with ≥1 citations

Try h=2

Count papers with ≥2 citations

Continue...

Keep checking until count < h

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

int hIndex(int* citations, int n) {
    int maxH = 0;
    
    // Try each possible h-index value
    for (int h = 0; h <= n; h++) {
        int count = 0;
        // Count papers with at least h citations
        for (int i = 0; i < n; i++) {
            if (citations[i] >= h) {
                count++;
            }
        }
        
        // Check if this h-index is valid
        if (count >= h) {
            maxH = h;
        }
    }
    
    return maxH;
}

int main() {
    char input[1000];
    fgets(input, sizeof(input), stdin);
    
    int citations[1000];
    int n = 0;
    
    char* token = strtok(input, "[,]");
    while (token != NULL && n < 1000) {
        citations[n++] = atoi(token);
        token = strtok(NULL, "[,]");
    }
    
    printf("%d\n", hIndex(citations, n));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n²)

For each of n possible H-Index values, we scan all n papers to count qualifying ones

⚠ Quadratic Growth

Space Complexity

O(1)

Only using a few variables for counting and tracking maximum

✓ Linear Space

73.9K Views

Medium Frequency

~18 min Avg. Time

1.8K Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force (Check All Possible H-Values) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Select Compiler