# H-Index II

## June 18, 2020

## Introduction

Given an array of citations sorted in ascending order (each citation is a non-negative integer) of a researcher, write a function to compute the researcher’s h-index.

According to the definition of h-index on Wikipedia: “A scientist has index h if h of his/her N papers have at least h citations each, and the other N − h papers have no more than h citations each.”

Example:

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, her h-index is 3. Note:

If there are several possible values for h, the maximum one is taken as the h-index.

Follow up:

This is a follow up problem to H-Index, where citations is now guaranteed to be sorted in ascending order. Could you solve it in logarithmic time complexity?

## Solution

Let’s first solve this problem with for each loop

```
func hIndex(citations []int) int {
h := 0
n := len(citations)
for j := n-1; j >= 0; j-- {
pos := n - j
if citations[j] >= pos {
h = pos
}
}
return h
}
```

Performance of this solution is:

```
Runtime: 12 ms
Memory Usage: 6.3 MB
```

Another way to solve this problem is to use binary search

```
func hIndex(citations []int) int {
n := len(citations)
lo, hi := 0, n
for lo < hi {
mi := (hi - lo) / 2 + lo
pos := n - mi
if citations[mi] >= pos {
hi = mi
} else {
lo = mi+1
}
}
return n - lo
}
```

Performance of this solution is better, and complexity is just O(log(n)):

```
Runtime: 8 ms, faster than 100.00% of Go online submissions for H-Index II.
Memory Usage: 6.3 MB, less than 80.00% of Go online submissions for H-Index II.
```