H-Index - Practice Coding Problems

H-Index - Problem

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.

Input & Output

Example 1 — Basic Case

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

› Output: 3

💡 Note: The researcher has 3 papers with at least 3 citations each: papers with 6, 5, and 3 citations. The 4th paper has only 1 citation and 5th has 0, so h-index is 3.

Example 2 — All High Citations

$ Input: citations = [1,3,1]

› Output: 1

💡 Note: Only 1 paper has at least 1 citation, and only 1 paper has at least 3 citations. The h-index is 1 since we have at least 1 paper with ≥1 citations.

Example 3 — All Zero Citations

$ Input: citations = [0,0]

› Output: 0

💡 Note: No papers have any citations, so the h-index is 0.

Constraints

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

Visualization

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Understanding the Visualization

Input

Array of citation counts for each paper

Process

Find maximum h satisfying the h-index condition

Output

The h-index value

Key Takeaway

🎯 Key Insight: H-index is the largest number h such that you have at least h papers with h or more citations each

Asked in

G Google 25 f Facebook 20 a Amazon 15

The h-index measures research impact by finding the maximum h where a researcher has h papers with at least h citations each. The optimal approach uses counting sort in O(n) time since h is bounded by the number of papers.

Common Approaches

Approach	Time	Space	Notes
✓ Sort First	O(n log n)	O(1)	Sort citations in descending order, then find h-index
Counting Sort Approach	O(n)	O(n)	Use counting array to avoid sorting
Brute Force	O(n²)	O(1)	Check every possible h-value from 0 to n

Sort First — Algorithm Steps

Step 1: Sort citations in descending order
Step 2: For each position i, check if (i+1) ≤ citations[i]
Step 3: Return the maximum valid h

Visualization

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Step-by-Step Walkthrough

Sort Descending

Arrange citations from highest to lowest

Check Positions

At position i, we have i+1 papers

Find h-index

Maximum h where citations[h-1] ≥ h

Code -

solution.c — C

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

int compare(const void* a, const void* b) {
    return (*(int*)b - *(int*)a);
}

int solution(int* citations, int n) {
    qsort(citations, n, sizeof(int), compare);
    int h = 0;
    for (int i = 0; i < n; i++) {
        if (citations[i] >= i + 1) {
            h = i + 1;
        } else {
            break;
        }
    }
    return h;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    int citations[1000];
    int n = 0;
    char* token = strtok(line, "[],\n ");
    while (token != NULL) {
        citations[n++] = atoi(token);
        token = strtok(NULL, "[],\n ");
    }
    printf("%d\n", solution(citations, n));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n log n)

Sorting dominates with O(n log n), then O(n) scan

⚡ Linearithmic

Space Complexity

O(1)

In-place sorting, only using constant extra variables

✓ Linear Space

28.0K Views

Medium Frequency

~15 min Avg. Time

892 Likes

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Sort First — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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