
Problem Statement
The h-index is an academic metric that measures the productivity and citation impact of the publications of a researcher. The h-index is defined as the maximum value ( h ), such that a researcher has published at least ( h ) papers that have each received ( h ) or more citations. In other words, if a researcher's h-index is ( h ), they have ( h ) papers which have been cited at least ( h ) times.
In this problem, you are provided an array citations
where citations[i]
represents the number of citations that the ( i )th paper has received. Your task is to determine the researcher's h-index from this data.
Examples
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 of them had received 3, 0, 6, 1, 5 citations respectively. Since the researcher has 3 papers with at least 3 citations each and the remaining two with no more than 3 citations each, their h-index is 3.
Example 2
Input:
citations = [1,3,1]
Output:
1
Constraints
n == citations.length
1 <= n <= 5000
0 <= citations[i] <= 1000
Approach and Intuition
To solve this problem, understanding exactly how the h-index is calculated with respect to a list of citation counts is key. Let's break down the steps:
Sorting the Citations:
Start by sorting the citations array in descending order. This arrangement ensures that higher citation counts are considered first for higher possible values of ( h ).Calculating the h-Index:
Iterate through the sorted list, checking at each point whether the count of papers (indexed from 1 in a 0-based index system) is at least as great as the number of citations at the current index. This is crucial because, for any position ( i ) in the sorted list, if ( i+1 ) (which represents the number of papers in a 1-based index system) is greater than or equal tocitations[i]
, the h-index is determined based on this count.Edge Cases and Complexity:
Consider edge cases where all papers have zero citations, or all papers have a number of citations higher than the number of papers. The algorithm should still efficiently produce the correct h-index.
- For example, in the citation array [3,0,6,1,5]:
- Sorted, this becomes [6,5,3,1,0]
- Here, the algorithm will confirm that the h-index 3 is correct because there are at least 3 papers that have received 3 or more citations (6, 5, and 3).
This approach runs efficiently within the given constraints, operating primarily with a time complexity of ( O(n \log n) ) due to the sorting step. The subsequent iteration to determine the h-index is linear, ( O(n) ).
Solutions
- Java
public class Solution {
public int calculateHIndex(int[] refs) {
int len = refs.length;
int[] counts = new int[len + 1];
for (int cite : refs)
counts[Math.min(len, cite)]++;
int index = len;
for (int accumulated = counts[len]; index > accumulated; accumulated += counts[index])
index--;
return index;
}
}
The provided Java solution calculates the H-Index, which is a metric used to measure the impact and relevance of a researcher's publications. The H-Index quantifies both the number of publications and the number of citations per publication.
- The
calculateHIndex
method takes an array of integersrefs
, representing the number of citations each publication has received. - An auxiliary array
counts
of sizelen + 1
(wherelen
is the number of publications), increments counts for each citation number up to the maximumlen
to handle cases where citations exceed the number of publications. - Iterate through each citation in
refs
and increment thecounts
array usingMath.min(len, cite)
to ensure the index doesn't exceed the length of thecounts
array. - Calculate the H-Index by checking from the highest possible index (
len
) downwards, accumulating counts from thecounts
array until theindex
is less than or equal to the number of accumulated values. - The final
index
value, when the loop ceases, represents the H-Index of the researcher, defined as the maximum number of papers that have received at least that number of citations.
This method efficiently computes the H-Index in a time complexity linearly dependent on the number of publications, utilizing an array-based counting approach. The solution's auxiliary space is also linearly dependent on the number of publications.
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