# Bucket Sort Algorithm

In this tutorial, you will learn how bucket sort works. Likewise, you will discover working instances of bucket sort in C, C++, Java and Python.

Contents

## What is Bucket Sort?

Bucket Sort is a sorting method that places items in buckets or categories. These items are then prioritized or ranked arranged by significance, first by category and afterward by specific items inside every category.

Bucket Sort is a sorting method that sorts the elements by first dividing the elements into a few groups called buckets. The elements inside each bucket are sorted using any of the appropriate sorting algorithms or recursively calling a similar algorithm.

A few buckets are created. Each bucket is loaded up with a particular range of elements. The elements inside the bucket are sorted using some other algorithm. At long last, the elements of the bucket are gathered to get the sorted array.

The process of bucket sort can be perceived as a scatter-gather approach. The elements are initially scattered into buckets then the elements of buckets are sorted. At long last, the elements are gathered in order.

## How does Bucket Sort work?

1. Assume, the input array is:

Create an array of size 10. Each slot of this array is used as a bucket for storing elements.

2. Insert elements into the buckets from the array. The elements are inserted by the range of the bucket.

In our example code, we have buckets every one of reaches from 0 to 1, 1 to 2, 2 to 3,…… (n-1) to n.

Assume, an input element is .23 is taken. It is multiplied by size = 10 (ie. .23*10=2.3). At that point, it is changed over into an integer (ie. 2.3≈2). At last, .23 is inserted into bucket-2.

Essentially, .25 is additionally inserted into a similar bucket. Every time, the floor value of the floating-point number is taken.

On the off chance that we take integer numbers as input, we need to divide it by the interval (10 here) to get the floor value.

Additionally, different elements are inserted into their respective buckets.

3. The elements of each bucket are sorted using any of the stable sorting algorithms. Here, we have used quicksort (inbuilt function).

4. The elements from each bucket are gathered.

It is finished by iterating through the bucket and inserting an individual element into the first array in each cycle. The element from the bucket is deleted whenever it is duplicated into the first array.

## Bucket Sort Algorithm

```bucketSort()
create N buckets each of which can hold a range of values
for all the buckets
initialize each bucket with 0 values
for all the buckets
put elements into buckets matching the range
for all the buckets
sort elements in each bucket
gather elements from each bucket
end bucketSort
```

## Python, Java, and C/C++ Examples

```# Bucket Sort in Python

def bucketSort(array):
bucket = []

# Create empty buckets
for i in range(len(array)):
bucket.append([])

# Insert elements into their respective buckets
for j in array:
index_b = int(10 * j)
bucket[index_b].append(j)

# Sort the elements of each bucket
for i in range(len(array)):
bucket[i] = sorted(bucket[i])

# Get the sorted elements
k = 0
for i in range(len(array)):
for j in range(len(bucket[i])):
array[k] = bucket[i][j]
k += 1
return array

array = [.42, .32, .33, .52, .37, .47, .51]
print("Sorted Array in descending order is")
print(bucketSort(array))```

Java

```// Bucket sort in Java

import java.util.ArrayList;
import java.util.Collections;

public class BucketSort {
public void bucketSort(float[] arr, int n) {
if (n <= 0)
return;
@SuppressWarnings("unchecked")
ArrayList<Float>[] bucket = new ArrayList[n];

// Create empty buckets
for (int i = 0; i < n; i++)
bucket[i] = new ArrayList<Float>();

// Add elements into the buckets
for (int i = 0; i < n; i++) {
int bucketIndex = (int) arr[i] * n;
}

// Sort the elements of each bucket
for (int i = 0; i < n; i++) {
Collections.sort((bucket[i]));
}

// Get the sorted array
int index = 0;
for (int i = 0; i < n; i++) {
for (int j = 0, size = bucket[i].size(); j < size; j++) {
arr[index++] = bucket[i].get(j);
}
}
}

// Driver code
public static void main(String[] args) {
BucketSort b = new BucketSort();
float[] arr = { (float) 0.42, (float) 0.32, (float) 0.33, (float) 0.52, (float) 0.37, (float) 0.47,
(float) 0.51 };
b.bucketSort(arr, 7);

for (float i : arr)
System.out.print(i + "  ");
}
}```

C

```// Bucket sort in C

#include <stdio.h>
#include <stdlib.h>

#define NARRAY 7   // Array size
#define NBUCKET 6  // Number of buckets
#define INTERVAL 10  // Each bucket capacity

struct Node {
int data;
struct Node *next;
};

void BucketSort(int arr[]);
struct Node *InsertionSort(struct Node *list);
void print(int arr[]);
void printBuckets(struct Node *list);
int getBucketIndex(int value);

// Sorting function
void BucketSort(int arr[]) {
int i, j;
struct Node **buckets;

// Create buckets and allocate memory size
buckets = (struct Node **)malloc(sizeof(struct Node *) * NBUCKET);

// Initialize empty buckets
for (i = 0; i < NBUCKET; ++i) {
buckets[i] = NULL;
}

// Fill the buckets with respective elements
for (i = 0; i < NARRAY; ++i) {
struct Node *current;
int pos = getBucketIndex(arr[i]);
current = (struct Node *)malloc(sizeof(struct Node));
current->data = arr[i];
current->next = buckets[pos];
buckets[pos] = current;
}

// Print the buckets along with their elements
for (i = 0; i < NBUCKET; i++) {
printf("Bucket[%d]: ", i);
printBuckets(buckets[i]);
printf("\n");
}

// Sort the elements of each bucket
for (i = 0; i < NBUCKET; ++i) {
buckets[i] = InsertionSort(buckets[i]);
}

printf("-------------\n");
printf("Bucktets after sorting\n");
for (i = 0; i < NBUCKET; i++) {
printf("Bucket[%d]: ", i);
printBuckets(buckets[i]);
printf("\n");
}

// Put sorted elements on arr
for (j = 0, i = 0; i < NBUCKET; ++i) {
struct Node *node;
node = buckets[i];
while (node) {
arr[j++] = node->data;
node = node->next;
}
}

return;
}

// Function to sort the elements of each bucket
struct Node *InsertionSort(struct Node *list) {
struct Node *k, *nodeList;
if (list == 0 || list->next == 0) {
return list;
}

nodeList = list;
k = list->next;
nodeList->next = 0;
while (k != 0) {
struct Node *ptr;
if (nodeList->data > k->data) {
struct Node *tmp;
tmp = k;
k = k->next;
tmp->next = nodeList;
nodeList = tmp;
continue;
}

for (ptr = nodeList; ptr->next != 0; ptr = ptr->next) {
if (ptr->next->data > k->data)
break;
}

if (ptr->next != 0) {
struct Node *tmp;
tmp = k;
k = k->next;
tmp->next = ptr->next;
ptr->next = tmp;
continue;
} else {
ptr->next = k;
k = k->next;
ptr->next->next = 0;
continue;
}
}
return nodeList;
}

int getBucketIndex(int value) {
return value / INTERVAL;
}

void print(int ar[]) {
int i;
for (i = 0; i < NARRAY; ++i) {
printf("%d ", ar[i]);
}
printf("\n");
}

// Print buckets
void printBuckets(struct Node *list) {
struct Node *cur = list;
while (cur) {
printf("%d ", cur->data);
cur = cur->next;
}
}

// Driver code
int main(void) {
int array[NARRAY] = {42, 32, 33, 52, 37, 47, 51};

printf("Initial array: ");
print(array);
printf("-------------\n");

BucketSort(array);
printf("-------------\n");
printf("Sorted array: ");
print(array);
return 0;
}```

C++

```// Bucket sort in C++

#include <iomanip>
#include <iostream>
using namespace std;

#define NARRAY 7   // Array size
#define NBUCKET 6  // Number of buckets
#define INTERVAL 10  // Each bucket capacity

struct Node {
int data;
struct Node *next;
};

void BucketSort(int arr[]);
struct Node *InsertionSort(struct Node *list);
void print(int arr[]);
void printBuckets(struct Node *list);
int getBucketIndex(int value);

// Sorting function
void BucketSort(int arr[]) {
int i, j;
struct Node **buckets;

// Create buckets and allocate memory size
buckets = (struct Node **)malloc(sizeof(struct Node *) * NBUCKET);

// Initialize empty buckets
for (i = 0; i < NBUCKET; ++i) {
buckets[i] = NULL;
}

// Fill the buckets with respective elements
for (i = 0; i < NARRAY; ++i) {
struct Node *current;
int pos = getBucketIndex(arr[i]);
current = (struct Node *)malloc(sizeof(struct Node));
current->data = arr[i];
current->next = buckets[pos];
buckets[pos] = current;
}

// Print the buckets along with their elements
for (i = 0; i < NBUCKET; i++) {
cout << "Bucket[" << i << "] : ";
printBuckets(buckets[i]);
cout << endl;
}

// Sort the elements of each bucket
for (i = 0; i < NBUCKET; ++i) {
buckets[i] = InsertionSort(buckets[i]);
}

cout << "-------------" << endl;
cout << "Bucktets after sorted" << endl;
for (i = 0; i < NBUCKET; i++) {
cout << "Bucket[" << i << "] : ";
printBuckets(buckets[i]);
cout << endl;
}

// Put sorted elements on arr
for (j = 0, i = 0; i < NBUCKET; ++i) {
struct Node *node;
node = buckets[i];
while (node) {
arr[j++] = node->data;
node = node->next;
}
}

for (i = 0; i < NBUCKET; ++i) {
struct Node *node;
node = buckets[i];
while (node) {
struct Node *tmp;
tmp = node;
node = node->next;
free(tmp);
}
}
free(buckets);
return;
}

// Function to sort the elements of each bucket
struct Node *InsertionSort(struct Node *list) {
struct Node *k, *nodeList;
if (list == 0 || list->next == 0) {
return list;
}

nodeList = list;
k = list->next;
nodeList->next = 0;
while (k != 0) {
struct Node *ptr;
if (nodeList->data > k->data) {
struct Node *tmp;
tmp = k;
k = k->next;
tmp->next = nodeList;
nodeList = tmp;
continue;
}

for (ptr = nodeList; ptr->next != 0; ptr = ptr->next) {
if (ptr->next->data > k->data)
break;
}

if (ptr->next != 0) {
struct Node *tmp;
tmp = k;
k = k->next;
tmp->next = ptr->next;
ptr->next = tmp;
continue;
} else {
ptr->next = k;
k = k->next;
ptr->next->next = 0;
continue;
}
}
return nodeList;
}

int getBucketIndex(int value) {
return value / INTERVAL;
}

// Print buckets
void print(int ar[]) {
int i;
for (i = 0; i < NARRAY; ++i) {
cout << setw(3) << ar[i];
}
cout << endl;
}

void printBuckets(struct Node *list) {
struct Node *cur = list;
while (cur) {
cout << setw(3) << cur->data;
cur = cur->next;
}
}

// Driver code
int main(void) {
int array[NARRAY] = {42, 32, 33, 52, 37, 47, 51};

cout << "Initial array: " << endl;
print(array);
cout << "-------------" << endl;

BucketSort(array);
cout << "-------------" << endl;
cout << "Sorted array: " << endl;
print(array);
}```

## Complexity

• Worst Case Complexity: O(n2)

When there are elements of close range in the array, they are probably going to be set in a similar bucket. This may bring about certain containers having more elements than others.

It causes the complexity to rely upon the sorting algorithm used to sort the elements of the bucket.

The complexity turns out to be worse when the elements are in backward order. In the event that insertion sort is used to sort elements of the bucket, the time complexity becomes O(n2).

• Best Case Complexity: O(n+k)

It happens when the elements are consistently dispersed in the bucket with an almost equivalent number of elements in each bucket.

The complexity turns out to be even better if the elements inside the buckets are now sorted.

On the off chance that insertion sort is used to sort elements of a bucket, the general complexity in the best case will be linear ie. O(n+k). O(n) is the complexity for making the buckets and O(k) is the complexity for sorting the elements of the bucket using algorithms having linear time complexity at the best case.

• Average Case Complexity: O(n)

It happens when the elements are dispersed randomly in the array. Even if the elements are not disseminated consistently, bucket sort runs in linear time. It remains constant until the amount of the squares of the bucket sizes is linear in the complete number of elements.

## Bucket Sort Applications

Bucket sort is used when:

• input is consistently appropriated over a range.
• there are floating-point values

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