275.H-Index II

Tags: Medium Binary Search

Links: https://leetcode.com/problems/h-index-ii/

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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?

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下标i	0	1	2	3	4
citations[i]	0	1	3	5	6
n - i	5	4	3	2	1

根据上面的表格，很容易知道去寻找第一个满足citations[i] >= n - i的下标i，然后结果就是n-i，数组内全是0的情况单独考虑，常数空间，时间复杂度$O(\log n)$。

class Solution {
public:
    int hIndex(vector<int>& citations) {
        int n = citations.size();
        if(n == 0 || citations[n - 1] == 0) return 0;
        int left = 0,right = n - 1;
        while(left < right)
        {
            int mid = (left + right) / 2;
            if(citations[mid] >= n - mid) right = mid;
            else left = mid + 1;
        }
        return n - left;
    }
};