Find H-Index for sorted citations using Binary Search

Given an array arr[] consisting of N integers in non-increasing order, representing citations, the task is to find the H-index.

H-Index is usually assigned to the researcher denoting the contributions made in terms of no of papers and citations. H-index(H) is the largest value such that the researcher has at least H papers cited at least H times.

Examples:

Input: arr[] = {5, 3, 3, 0, 0} 
Output:
Explanation: 
There are atleast 3 papers (5, 3, 3) with atleast 3 citations

Input: arr[] = {5, 4, 2, 1, 1} 
Output:
Explanation: 
There are atleast 2 papers (5, 4, 2) with atleast 2 citations.



Naive Approach: A simple solution is to iterate through the papers from left to right and increment the H-index while citationsi is greater than or equal to index.

Time Complexity: O(N)

Efficient Approach: The idea is to use binary search to optimize the above approach. The H-index can lie in the range from 0 to N. To check if a given value is possible or not, check if citations[value] is greater than or equal to value.

  • Initialize the search range for the Binary search as 0 to N.
  • Find the middle element of the range.
  • Check if the middle element of the citation is less than the index. If so, then update the left range to middle element.
  • Otherwise, check if the middle element of the citation is greater than the index. If so, then update the right range to the middle element.
  • Otherwise, the given index is the H-index of the Citations.

Below is the implementation of the above approach:

C++

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// C++ implementation of the
// above approach
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the H-index
int hIndex(vector<int> citations,
           int n)
{
  
    int hindex = 0;
  
    // Set the range for binary search
    int low = 0, high = n - 1;
  
    while (low <= high) {
        int mid = (low + high) / 2;
  
        // Check if current citations is
        // possible
        if (citations[mid] >= (mid + 1)) {
  
            // Check to the right of mid
            low = mid + 1;
  
            // Update h-index
            hindex = mid + 1;
        }
        else {
  
            // Since current value is not
            // possible, check to the left
            // of mid
            high = mid - 1;
        }
    }
  
    // Print the h-index
    cout << hindex << endl;
  
    return hindex;
}
  
// Driver Code
int main()
{
  
    // citations
    int n = 5;
    vector<int> citations = { 5, 3, 3, 2, 2 };
  
    hIndex(citations, n);
}

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Java

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// Java implementation of the
// above approach
import java.io.*;
  
class GFG{
  
// Function to find the H-index
static int hIndex(int[] citations, int n)
{
    int hindex = 0;
  
    // Set the range for binary search
    int low = 0, high = n - 1;
  
    while (low <= high) 
    {
        int mid = (low + high) / 2;
  
        // Check if current citations is
        // possible
        if (citations[mid] >= (mid + 1))
        {
  
            // Check to the right of mid
            low = mid + 1;
  
            // Update h-index
            hindex = mid + 1;
        }
        else 
        {
  
            // Since current value is not
            // possible, check to the left
            // of mid
            high = mid - 1;
        }
    }
  
    // Print the h-index
    System.out.println(hindex);
  
    return hindex;
}
  
// Driver Code
public static void main (String[] args)
{
  
    // citations
    int n = 5;
    int[] citations = { 5, 3, 3, 2, 2 };
  
    hIndex(citations, n);
}
}
  
// This code is contributed by sanjoy_62

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Python3

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# Python3 implementation of the 
# above approach 
  
# Function to find the H-index 
def hIndex(citations, n):
  
    hindex = 0
  
    # Set the range for binary search
    low = 0
    high = n - 1
  
    while (low <= high):
        mid = (low + high) // 2
  
        # Check if current citations is
        # possible
        if (citations[mid] >= (mid + 1)):
  
            # Check to the right of mid
            low = mid + 1
  
            # Update h-index
            hindex = mid + 1
  
        else:
              
            # Since current value is not
            # possible, check to the left
            # of mid
            high = mid - 1
  
    # Print the h-index
    print(hindex)
  
    return hindex
  
# Driver Code
  
# citations
n = 5
citations = [ 5, 3, 3, 2, 2 ]
  
# Function Call
hIndex(citations, n)
  
# This code is contributed by Shivam Singh

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C#

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// C# implementation of the
// above approach
using System;
  
class GFG{
  
// Function to find the H-index
static int hIndex(int[] citations, int n)
{
    int hindex = 0;
  
    // Set the range for binary search
    int low = 0, high = n - 1;
  
    while (low <= high)
    {
        int mid = (low + high) / 2;
  
        // Check if current citations is
        // possible
        if (citations[mid] >= (mid + 1)) 
        {
              
            // Check to the right of mid
            low = mid + 1;
  
            // Update h-index
            hindex = mid + 1;
        }
        else
        {
              
            // Since current value is not
            // possible, check to the left
            // of mid
            high = mid - 1;
        }
    }
  
    // Print the h-index
    Console.WriteLine(hindex);
  
    return hindex;
}
  
// Driver Code
public static void Main ()
{
  
    // citations
    int n = 5;
    int[] citations = { 5, 3, 3, 2, 2 };
  
    hIndex(citations, n);
}
}
  
// This code is contributed by sanjoy_62

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Output: 

3

Time Complexity: O(logN) 
Auxiliary Space: O(1)

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Improved By : SHIVAMSINGH67, sanjoy_62