# Bucket Sort Java Beispiel Essay

Radix Sortis a non-comparative sorting algorithm with asymptotic complexityO(nd). It is one of the most efficient and fastest linear sorting algorithms. Radix sort was developed to sort large integers. As integer is treated as a string of digits so we can also call it as string sorting algorithm.

The lower bound for comparison based sorting algorithm is O(n*log n) like merge sort, quick sort, heap sort. So radix sort is efficient than comparison sorting algorithm until the number of digits (key) is less than log n. Counting sort can’t be used if a range of key value is large (suppose range is 1 to n^{2}) so radix sort is the best choice to sort in linear time.

In radix sort, we first sort the elements based on last digit (least significant digit). Then the result is again sorted by second digit, continue this process for all digits until we reach most significant digit. We use counting sort to sort elements of every digit, so time complexity is O(nd).

**Here are some key points of radix sort algorithm –**

- Radix Sort is a linear sorting algorithm.
- Time complexity of Radix Sort is O(nd), where
**n**is the size of array and**d**is the number of digits in the largest number. - It is
**not an in-place sorting**algorithm as it requires extra additional space. - Radix Sort is
**stable sort**as relative order of elements with equal values is maintained. - Radix sort
**can be slower**than other sorting algorithms like merge sort and quick sort, if the operations are not efficient enough. These operations include inset and delete functions of the sub-list and the process of isolating the digits we want. - Radix sort is less flexible than other sorts as it depends on the digits or letter. Radix sort needs to be rewritten if the type of data is changed.

**Let’s understand it with an example –**

Observe the image given below carefully and try to visualize the concept of this algorithm.

In the above example:**For 1 ^{st} pass:** we sort the array on basis of least significant digit (1s place) using counting sort. Notice that 43

__5__is below 83

__5,__because 43

__5__occurred below 83

__5__in the original list.

**For 2**we sort the array on basis of next digit (10s place) using counting sort. Notice that here 6

^{nd}pass:__0__8 is below 7

__0__4, because 6

__0__8 occurred below 7

__0__4 in the previous list, and similarly for (8

__3__5, 4

__3__5) and (7

__5__1, 4

__5__3).

**For 3**we sort the array on basis of most significant digit (100s place) using counting sort. Notice that here

^{rd}pass:__4__35 is below

__4__53, because

__4__35 occurred below

__4__53 in the previous list, and similarly for (

__6__08,

__6__90) and (

__7__04,

__7__51).

### Pseudocode of Radix Sort

Radix-Sort(A, d) //It works same as counting sort for d number of passes. //Each key in A[1..n] is a d-digit integer. //(Digits are numbered 1 to d from right to left.) for j = 1 to d do //A[]-- Initial Array to Sort int count[10] = {0}; //Store the count of "keys" in count[] //key- it is number at digit place j for i = 0 to n do count[key of(A[i]) in pass j]++ for k = 1 to 10 do count[k] = count[k] + count[k-1] //Build the resulting array by checking //new position of A[i] from count[k] for i = n-1 downto 0 do result[ count[key of(A[i])] ] = A[j] count[key of(A[i])]-- //Now main array A[] contains sorted numbers //according to current digit place for i=0 to n do A[i] = result[i] end for(j) end func### Asymptotic Analysis of Radix Sort

In this algorithm running time depends on intermediate sorting algorithm which is counting sort. If the range of digits is from 1 to k, then counting sort time complexity is O(n+k). There are d passes i.e counting sort is called d time, so total time complexity is O(nd+nk) =O(nd). As k=O(n) and d is constant, so radix sort runs in linear time.

*Worst Case Time complexity: O (nd)**Average Case Time complexity: O(nd)**Best Case Time complexity: O(nd)**Space Complexity: O(n+k) **Data Structure: Array**Sorting In Place: No**Stable: Yes*

### Implementation of Radix Sort in C and Java programming language

## C

## JAVA

**Output:-**Unsorted array: 209,3,48,91,66,101,30,795 Sorted array: 3,30,48,66,91,101,209,795

Radix Sort is one of the most efficient and fastest linear sorting algorithms. It is simple to understand and easy to implement. Radix Sort is a good choice for many programs which need a fast sort.

Radix Sort can handle larger keys more efficiently as compare to Counting Sort. Radix sort is most equally efficient as the best comparison-based sorts (and worse if keys are much longer than log n).

Another linear sorting algorithm is bucket sort which we will discuss in the future post.

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Tags:Algorithm pseudocode, algorithms, Algorithms Analysis, algorithms and data structure, algorithms complexity, algorithms examples, algorithms implementation in c, algorithms implementation in java, Interview Algorithm Problems

#### About The Author

##### PriyanshMangal

Here is the source code of the Java Program to Implement Bucket Sort. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

Output:

**Sanfoundry Global Education & Learning Series – 1000 Java Programs.**

Here’s the list of Best Reference Books in Java Programming, Data Structures and Algorithms.

- //This is a java program to sort numbers using bucket sort
- importjava.util.Random;
- publicclass Bucket_Sort
- {
- staticint[] sort(int[] sequence, int maxValue)
- {
- // Bucket Sort
- int[] Bucket =newint[maxValue +1];
- int[] sorted_sequence =newint[sequence.length];
- for(int i =0; i < sequence.length; i++)
- Bucket[sequence[i]]++;
- int outPos =0;
- for(int i =0; i < Bucket.length; i++)
- for(int j =0; j < Bucket[i]; j++)
- sorted_sequence[outPos++]= i;
- return sorted_sequence;
- }
- staticvoid printSequence(int[] sorted_sequence)
- {
- for(int i =0; i < sorted_sequence.length; i++)
- System.out.print(sorted_sequence[i]+" ");
- }
- staticint maxValue(int[] sequence)
- {
- int maxValue =0;
- for(int i =0; i < sequence.length; i++)
- if(sequence[i]> maxValue)
- maxValue = sequence[i];
- return maxValue;
- }
- publicstaticvoid main(String args[])
- {
- System.out
- .println("Sorting of randomly generated numbers using BUCKET SORT");
- Random random =newRandom();
- int N =20;
- int[] sequence =newint[N];
- for(int i =0; i < N; i++)
- sequence[i]=Math.abs(random.nextInt(100));
- int maxValue = maxValue(sequence);
- System.out.println("\nOriginal Sequence: ");
- printSequence(sequence);
- System.out.println("\nSorted Sequence: ");
- printSequence(sort(sequence, maxValue));
- }
- }

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