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Question

Formatted question description: https://leetcode.ca/all/275.html

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.

Algorithm

First initialize left and right to 0 and len-1, then take the middle value mid, compare citations[mid] with len-mid,

• If the former is big, right moves before mid
• On the contrary, right moves after mid The loop condition is left<=right, and finally returns len-left.

Code

• Java
• C++
• Python
• Go
• TypeScript

• 
  public class H_Index_II {
      class Solution {
          public int hIndex(int[] citations) {
              int len = citations.length, left = 0, right = len - 1;
              while (left <= right) {
                  int mid = (left + right) / 2;
                  if (citations[mid] == len - mid) {
                      return len - mid;
                  }
                  else if (citations[mid] > len - mid) { // cites > h`, try next round
                      right = mid - 1;
                  }
                  else {
                      left = mid + 1;
                  }
              }
  
              return len - left;
          }
      }
  }
  
  
  ############
  
  class Solution {
      public int hIndex(int[] citations) {
          int n = citations.length;
          int left = 0, right = n;
          while (left < right) {
              int mid = (left + right + 1) >> 1;
              if (citations[n - mid] >= mid) {
                  left = mid;
              } else {
                  right = mid - 1;
              }
          }
          return left;
      }
  }
  

• // OJ: https://leetcode.com/problems/h-index-ii/
  // Time: O(logN)
  // Space: O(1)
  class Solution {
  public:
      int hIndex(vector<int>& A) {
          int N = A.size(), L = 0, R = N - 1;
          while (L <= R) {
              int M = (L + R) / 2;
              if (A[M] >= N - M) R = M - 1;
              else L = M + 1;
          }
          return N - L;
      }
  };
  

• class Solution:
      def hIndex(self, citations: List[int]) -> int:
          n = len(citations)
          left, right = 0, n
          while left < right:
              mid = (left + right + 1) >> 1
              if citations[n - mid] >= mid:
                  left = mid
              else:
                  right = mid - 1
          return left
  
  ############
  
  class Solution(object):
    def hIndex(self, citations):
      """
      :type citations: List[int]
      :rtype: int
      """
      if not citations:
        return 0
      n = len(citations)
      start, end = 0, n - 1
      while start < end:
        mid = start + (end - start) / 2
        if citations[mid] >= n - mid:
          end = mid
        else:
          start = mid + 1
      return n - start if citations[start] != 0 else 0
  
  

• func hIndex(citations []int) int {
  	n := len(citations)
  	left, right := 0, n
  	for left < right {
  		mid := (left + right + 1) >> 1
  		if citations[n-mid] >= mid {
  			left = mid
  		} else {
  			right = mid - 1
  		}
  	}
  	return left
  }
  

• function hIndex(citations: number[]): number {
      const n = citations.length;
      let left = 0,
          right = n;
      while (left < right) {
          const mid = (left + right + 1) >> 1;
          if (citations[n - mid] >= mid) {
              left = mid;
          } else {
              right = mid - 1;
          }
      }
      return left;
  }
  
  

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