The H-Index is a crucial metric used to quantify the productivity and citation impact of a researcher. It measures how many papers (h) have received at least h citations. Solving this problem programmatically can help us quickly compute the H-Index for a given dataset.
In this article, we'll explore two different Java approaches for solving the H-Index problem: a simple approach involving sorting and a more efficient approach utilizing bucket sorting.
Problem Statement:
Given an array of integers where each integer represents the number of citations a researcher has received for each paper, the task is to compute the H-Index.
For example: int[] arr = {3, 0, 6, 1, 5};
In this case, the expected H-Index is 3, since there are three papers with at least three citations.
Simple Approach (Sorting)
This approach relies on sorting the array in descending order and then iterating to find the H-Index. Here’s how the logic works:
Steps:
- Sort the Array: Use bubble sort to arrange the elements in descending order.
- Find the H-Index: Traverse the sorted array and return the first element where the number of citations is less than or equal to the index (i + 1).
Code:
public static int simpleApproach(int[] arr) {
if (arr.length==0) {
return 0;
}
if (arr.length==1) {
return arr[0];
}
//bubble sort the array in descending order
for (int i = 0; i < arr.length-1; i++) {
boolean swapped = false;
for (int j = 0; j < arr.length-i-1; j++) {
if (arr[j+1]>arr[j]) {
int temp = arr[j];
arr[j] = arr[j+1];
arr[j+1] = temp;
swapped = true;
}
}
if (!swapped) {
break;
}
}
for (int i = 0; i < arr.length; i++) {
if (arr[i] <= i+1) {
return arr[i];
}
}
return 0;
}
Time Complexity:
- Sorting the array takes O(n²) due to bubble sort.
- Traversing the sorted array is O(n).
Drawbacks:
While this method is easy to understand, its time complexity makes it inefficient for large arrays, as bubble sort has a poor performance with O(n²).
Efficient Approach (Bucket Sort)
To improve efficiency, we can use a bucket sorting technique that reduces the time complexity to O(n). Instead of sorting the array, we use a counting approach to group papers by their citation count.
Steps:
- Create Buckets: Create an array of size
n + 1(wherenis the length of the input array) to count how many papers have a certain number of citations. - Count Citations: For each paper, increment the appropriate bucket based on its citation count. Papers with citations greater than or equal to
ngo into the last bucket. - Find the H-Index: Iterate through the buckets and compute the cumulative sum to find the H-Index.
Code:
public static int effecientApproach(int[] arr) {
if (arr.length==0) {
return 0;
}
if (arr.length==1) {
return arr[0];
}
int n = arr.length;
int[] bucket = new int[n+1];
for (int i = 0; i < arr.length; i++) {
if (arr[i]<n) {
bucket[i]=1;
}
else {
bucket[n] +=1;
}
}
int sum = 0;
for (int i = bucket.length-1; i >=0; i--) {
sum +=bucket[i];
if (sum>=i+1) {
return sum;
}
}
return sum;
}
Time Complexity:
- The time complexity of this approach is O(n), which is significantly better than the simple approach. We only need to iterate through the array and the bucket once.
Benefits:
- Faster: No need to sort the array.
- Space-Efficient: The bucket array has a fixed size of
n + 1.
Conclusion
Both the simple and efficient approaches solve the H-Index problem, but the efficient approach is clearly better for large datasets due to its O(n) time complexity. If performance is critical, the bucket sort method is the way to go.
Code Implementation:
public static void main(String[] args) {
int[] arr = {3, 0, 6, 1, 5};
//System.out.println("H-Index is: "+simpleApproach(arr));
System.out.println("H-Index is: "+effecientApproach(arr));
}
In summary, while the simple approach is a good starting point for understanding the problem, the efficient approach is the ideal solution for handling larger arrays. Understanding both methods provides insight into optimization strategies, which are crucial for tackling complex coding challenges in real-world scenarios.
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#LeetCode #Java #DSA #CodingChallenges #HIndex #Sorting #BucketSort #InterviewPrep #TechInterview #LearnToCode