Leetcode: H-Index

Given an array of citations (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."

For example, given citations = [3, 0, 6, 1, 5], which 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, his h-index is 3.

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

Hint:

1. An easy approach is to sort the array first.
2. What are the possible values of h-index?
3. A faster approach is to use extra space.

Sort first then scan: O(NlogN) time, O(1)space

use another array: O(N) time, O(N) space（有点像counting sort）

我们额外使用一个大小为N+1的数组stats。stats[i]表示有多少文章被引用了i次，这里如果一篇文章引用大于N次，我们就将其当为N次，因为H指数不会超过文章的总数。为了构建这个数组，我们需要先将整个文献引用数组遍历一遍，对相应的格子加一。统计完后，我们从N向1开始遍历这个统计数组。如果遍历到某一个引用次数时，大于或等于该引用次数的文章数量，大于等于引用次数本身时，我们可以认为这个引用次数是H指数。这里引用次数是连续的，而书本数量不连续，所以用引用次数来表示H指数（如底下code中的j）

 we can then easily locate his h-index by scanning from right (L) to left (0). By definition, index k is his h-index if the summation of all elements fromcounts[k] to counts[L] is no less than k.  

(重要思路)Think in this way, the summation is the number of books with citatations at least k each, summation>=k means we are guaranteed to have k books with citation at least k each, the other books won't have k citations, so index k is 

之所以不用再向下找，因为我们要取最大的H指数。那如何求大于或等于某个引用次数的文章数量呢？我们可以用一个变量，从高引用次的文章数累加下来。因为我们知道，如果有x篇文章的引用大于等于3次，那引用大于等于2次的文章数量一定是x加上引用次数等于2次的文章数量。

public class Solution {
    public int hIndex(int[] citations) {
        int N = citations.length;
        int[] summary = new int[N+1];
        for (int m : citations) {
            if (m <= N) summary[m]++;
            else summary[N]++;
        }
        int sum = 0;
        for (int j=summary.length-1; j>=0; j--) {
            sum += summary[j]; //sum means # of papers that has citation greater than or equal to j
            if (sum >= j) return j;
        }
        return 0;
    }
}