274. H-Index

 

Efficiently Calculating H-Index Using Binary Search in JavaScript

Introduction

The H-Index is a crucial metric used to measure the productivity and citation impact of a researcher’s published work. It provides a balanced view of both the quantity and quality of publications by considering the number of citations received. In this blog post, we will explore an efficient method to calculate the H-Index using binary search in JavaScript.

Intuition

To determine the H-Index, we need to find the largest number h such that there are at least h papers with at least h citations each. This means that for a given number of citations, we want to ensure that this number is at least as large as the number of papers that have received this many citations.

Approach

To efficiently calculate the H-Index, we can use the following steps:

  1. Sort the Citations: First, we sort the array of citations in ascending order. This will help us easily determine the number of papers with at least a certain number of citations.

  2. Binary Search: We use binary search to find the largest possible value of h that satisfies the H-Index conditions. Binary search is chosen because it allows us to efficiently narrow down the search space.

  3. Determine Potential H-Index: For each midpoint in the binary search, we calculate a potential H-Index by taking the minimum of the citations at that midpoint and the number of papers from that midpoint to the end.

  4. Update and Adjust Search: We update the maximum H-Index found so far and adjust the search range based on whether the potential H-Index meets the conditions.

Complexity Analysis

  • Time Complexity: O(nlog⁡n)O(n \log n)

    • Sorting the citations array takes O(nlog⁡n)O(n \log n) time.

    • The binary search operates in O(log⁡n)O(\log n) time, making the overall time complexity dominated by the sorting step.

  • Space Complexity: O(1)O(1)

    • The algorithm uses constant extra space for the pointers and variables.

Code Implementation

Here is the JavaScript code to efficiently calculate the H-Index using binary search:

var hIndex = function(citations) {
    // size of array
    let n = citations.length;
    // sort the array
    citations.sort((a, b) => a - b);
    // go for binary search
    let low = 0;
    let high = citations.length - 1;
    let h = 0;
    while (low <= high) {
        // find mid
        let mid = Math.floor((high + low) / 2);
        // find the h-index value
        h = Math.max(h, Math.min(citations[mid], n - mid));
        // move the search right or left
        if(n - mid >= citations[mid]) {
            low = mid + 1;
        }else {
            high = mid - 1;
        }
    }
    return h;
};

Conclusion

The H-Index provides a meaningful measure of a researcher’s impact through their publications. By leveraging sorting and binary search, we can efficiently calculate the H-Index with optimal performance. This approach not only ensures accuracy but also minimizes the computational resources needed.

For more insights and detailed discussions, you can check out the related LeetCode solution: H-Index - LeetCode

Feel free to use this solution and share your thoughts. If you have any questions or suggestions, drop them in the comments below! Happy coding! šŸ˜Š

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