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: 3
Explanation:
There are atleast 3 papers (5, 3, 3) with atleast 3 citationsInput: arr[] = {5, 4, 2, 1, 1}
Output: 2
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++
// 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); } |
Java
// 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 |
Python3
# 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 = 5citations = [ 5, 3, 3, 2, 2 ] # Function Call hIndex(citations, n) # This code is contributed by Shivam Singh |
C#
// 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 |
3
Time Complexity: O(logN)
Auxiliary Space: O(1)
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