Bucket sort is mainly useful when input is uniformly distributed over a range. For example, consider the following problem.
Sort a large set of floating point numbers which are in range from 0.0 to 1.0 and are uniformly distributed across the range. How do we sort the numbers efficiently?
A simple way is to apply a comparison based sorting algorithm. The lower bound for Comparison based sorting algorithm (Merge Sort, Heap Sort, Quick-Sort .. etc) is Ω(n Log n), i.e., they cannot do better than nLogn.
Can we sort the array in linear time? Counting sort can not be applied here as we use keys as index in counting sort. Here keys are floating point numbers.
The idea is to use bucket sort. Following is bucket algorithm.
bucketSort(arr[], n) 1) Create n empty buckets (Or lists). 2) Do following for every array element arr[i]. .......a) Insert arr[i] into bucket[n*array[i]] 3) Sort individual buckets using insertion sort. 4) Concatenate all sorted buckets.
Time Complexity: If we assume that insertion in a bucket takes O(1) time then steps 1 and 2 of the above algorithm clearly take O(n) time. The O(1) is easily possible if we use a linked list to represent a bucket (In the following code, C++ vector is used for simplicity). Step 4 also takes O(n) time as there will be n items in all buckets.
The main step to analyze is step 3. This step also takes O(n) time on average if all numbers are uniformly distributed (please refer CLRS book for more details)
Following is the implementation of the above algorithm.
C/C++
// C++ program to sort an array using bucket sort #include <algorithm> #include <iostream> #include <vector> using namespace std; // Function to sort arr[] of size n using bucket sort void bucketSort(float arr[], int n) { // 1) Create n empty buckets vector<float> b[n]; // 2) Put array elements in different buckets for (int i = 0; i < n; i++) { int bi = n * arr[i]; // Index in bucket b[bi].push_back(arr[i]); } // 3) Sort individual buckets for (int i = 0; i < n; i++) sort(b[i].begin(), b[i].end()); // 4) Concatenate all buckets into arr[] int index = 0; for (int i = 0; i < n; i++) for (int j = 0; j < b[i].size(); j++) arr[index++] = b[i][j]; } /* Driver program to test above function */int main() { float arr[] = { 0.897, 0.565, 0.656, 0.1234, 0.665, 0.3434 }; int n = sizeof(arr) / sizeof(arr[0]); bucketSort(arr, n); cout << "Sorted array is \n"; for (int i = 0; i < n; i++) cout << arr[i] << " "; return 0; } |
Java
// Java program to sort an array // using bucket sort import java.util.*; import java.util.Collections; class GFG { // Function to sort arr[] of size n // using bucket sort static void bucketSort(float arr[], int n) { if (n <= 0) return; // 1) Create n empty buckets @SuppressWarnings("unchecked") Vector<Float>[] buckets = new Vector[n]; for (int i = 0; i < n; i++) { buckets[i] = new Vector<Float>(); } // 2) Put array elements in different buckets for (int i = 0; i < n; i++) { float idx = arr[i] * n; buckets[(int)idx].add(arr[i]); } // 3) Sort individual buckets for (int i = 0; i < n; i++) { Collections.sort(buckets[i]); } // 4) Concatenate all buckets into arr[] int index = 0; for (int i = 0; i < n; i++) { for (int j = 0; j < buckets[i].size(); j++) { arr[index++] = buckets[i].get(j); } } } // Driver code public static void main(String args[]) { float arr[] = { (float)0.897, (float)0.565, (float)0.656, (float)0.1234, (float)0.665, (float)0.3434 }; int n = arr.length; bucketSort(arr, n); System.out.println("Sorted array is "); for (float el : arr) { System.out.print(el + " "); } } } // This code is contributed by Himangshu Shekhar Jha |
Python3
# Python3 program to sort an array # using bucket sort def insertionSort(b): for i in range(1, len(b)): up = b[i] j = i - 1 while j >= 0 and b[j] > up: b[j + 1] = b[j] j -= 1 b[j + 1] = up return b def bucketSort(x): arr = [] slot_num = 10 # 10 means 10 slots, each # slot's size is 0.1 for i in range(slot_num): arr.append([]) # Put array elements in different buckets for j in x: index_b = int(slot_num * j) arr[index_b].append(j) # Sort individual buckets for i in range(slot_num): arr[i] = insertionSort(arr[i]) # concatenate the result k = 0 for i in range(slot_num): for j in range(len(arr[i])): x[k] = arr[i][j] k += 1 return x # Driver Code x = [0.897, 0.565, 0.656, 0.1234, 0.665, 0.3434] print("Sorted Array is") print(bucketSort(x)) # This code is contributed by # Oneil Hsiao |
Output:
Sorted array is 0.1234 0.3434 0.565 0.656 0.665 0.897
Bucket Sort To Sort an Array with Negative Numbers
References:
Introduction to Algorithms 3rd Edition by Clifford Stein, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
http://en.wikipedia.org/wiki/Bucket_sort
Snapshots:
Quiz on Bucket Sort
Other Sorting Algorithms on GeeksforGeeks/GeeksQuiz:
- Selection Sort
- Bubble Sort
- Insertion Sort
- Merge Sort
- Heap Sort
- QuickSort
- Radix Sort
- Counting Sort
- ShellSort
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
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