275. H-Index II
Description
Given an array of integers citations
where citations[i]
is the number of citations a researcher received for their ith
paper and citations
is sorted in ascending order, 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.
You must write an algorithm that runs in logarithmic time.
Example 1:
Input: citations = [0,1,3,5,6] Output: 3 Explanation: [0,1,3,5,6] means the researcher has 5 papers in total and each of them had received 0, 1, 3, 5, 6 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 = [1,2,100] Output: 2
Constraints:
n == citations.length
1 <= n <= 105
0 <= citations[i] <= 1000
citations
is sorted in ascending order.
Solutions
Solution 1: Binary Search
We notice that if there are at least $x$ papers with citation counts greater than or equal to $x$, then for any $y \lt x$, its citation count must also be greater than or equal to $y$. This exhibits monotonicity.
Therefore, we use binary search to enumerate $h$ and obtain the maximum $h$ that satisfies the condition. Since we need to satisfy that $h$ papers are cited at least $h$ times, we have $citations[n - mid] \ge mid$.
The time complexity is $O(\log n)$, where $n$ is the length of the array $citations$. The space complexity is $O(1)$.
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