H-Index

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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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

✓ Brute Force

⏱️ Time: O(n²) Space: O(1)

For each possible h-value from 0 to n, count how many papers have at least h citations. Return the maximum h where we have at least h such papers.

Counting Sort Approach

⏱️ Time: O(n) Space: O(n)

Since h-index is bounded by the number of papers, we can use a counting array of size n+1. Count papers for each citation level, then scan from right to left to find the h-index.

Sort First

⏱️ Time: O(n log n) Space: O(1)

Sort the citations array in descending order, then iterate through it. At position i, we have (i+1) papers with at least citations[i] citations. Find the maximum h where h ≤ citations[h-1].

Brute Force — Algorithm Steps

Step 1: Try each h from n down to 0
Step 2: Count papers with at least h citations
Step 3: Return first h where count >= h

Visualization

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Step-by-Step Walkthrough

Try h=5

Count papers with ≥5 citations

Try h=4

Count papers with ≥4 citations

Found h=3

3 papers have ≥3 citations

Code -

solution.c — C

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

int solution(int* citations, int n) {
    for (int h = n; h >= 0; h--) {
        int count = 0;
        for (int i = 0; i < n; i++) {
            if (citations[i] >= h) {
                count++;
            }
        }
        if (count >= h) {
            return h;
        }
    }
    return 0;
}

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(n²)

For each of n possible h-values, we scan the entire array

⚡ Linearithmic

Space Complexity

O(1)

Only using a few variables

✓ Linear Space

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Related Problems

Common Approaches

Brute Force — Algorithm Steps

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Code -

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