Comb Sort is mainly an improvement over Bubble Sort. Bubble sort always compares adjacent values. So all inversions are removed one by one. Comb Sort improves on Bubble Sort by using a gap of the size of more than 1. The gap starts with a large value and shrinks by a factor of 1.3 in every iteration until it reaches the value 1. Thus Comb Sort removes more than one inversion count with one swap and performs better than Bubble Sort.
The shrink factor has been empirically found to be 1.3 (by testing Combsort on over 200,000 random lists) [Source: Wiki]
Although it works better than Bubble Sort on average, worst-case remains O(n2).
Flowchart
Flowchart
Below is the implementation.
C++
// C++ implementation of Comb Sort
#include<bits/stdc++.h>
using namespace std;
// To find gap between elements
int getNextGap(int gap)
{
// Shrink gap by Shrink factor
gap = (gap*10)/13;
if (gap < 1)
return 1;
return gap;
}
// Function to sort a[0..n-1] using Comb Sort
void combSort(int a[], int n)
{
// Initialize gap
int gap = n;
// Initialize swapped as true to make sure that
// loop runs
bool swapped = true;
// Keep running while gap is more than 1 and last
// iteration caused a swap
while (gap != 1 || swapped == true)
{
// Find next gap
gap = getNextGap(gap);
// Initialize swapped as false so that we can
// check if swap happened or not
swapped = false;
// Compare all elements with current gap
for (int i=0; i<n-gap; i++)
{
if (a[i] > a[i+gap])
{
swap(a[i], a[i+gap]);
swapped = true;
}
}
}
}
// Driver program
int main()
{
int a[] = {8, 4, 1, 56, 3, -44, 23, -6, 28, 0};
int n = sizeof(a)/sizeof(a[0]);
combSort(a, n);
printf("Sorted array: \n");
for (int i=0; i<n; i++)
printf("%d ", a[i]);
return 0;
}
// Java program for implementation of Comb Sort
import java.io.*;
public class CombSort
{
// To find gap between elements
int getNextGap(int gap)
{
// Shrink gap by Shrink factor
gap = (gap*10)/13;
if (gap < 1)
return 1;
return gap;
}
// Function to sort arr[] using Comb Sort
void sort(int arr[])
{
int n = arr.length;
// initialize gap
int gap = n;
// Initialize swapped as true to make sure that
// loop runs
boolean swapped = true;
// Keep running while gap is more than 1 and last
// iteration caused a swap
while (gap != 1 || swapped == true)
{
// Find next gap
gap = getNextGap(gap);
// Initialize swapped as false so that we can
// check if swap happened or not
swapped = false;
// Compare all elements with current gap
for (int i=0; i<n-gap; i++)
{
if (arr[i] > arr[i+gap])
{
// Swap arr[i] and arr[i+gap]
int temp = arr[i];
arr[i] = arr[i+gap];
arr[i+gap] = temp;
// Set swapped
swapped = true;
}
}
}
}
// Driver method
public static void main(String args[])
{
CombSort ob = new CombSort();
int arr[] = {8, 4, 1, 56, 3, -44, 23, -6, 28, 0};
ob.sort(arr);
System.out.println("sorted array");
for (int i=0; i<arr.length; ++i)
System.out.print(arr[i] + " ");
}
}
/* This code is contributed by Rajat Mishra */
# Python program for implementation of CombSort
# To find next gap from current
def getNextGap(gap):
# Shrink gap by Shrink factor
gap = (gap * 10)//13
if gap < 1:
return 1
return gap
# Function to sort arr[] using Comb Sort
def combSort(arr):
n = len(arr)
# Initialize gap
gap = n
# Initialize swapped as true to make sure that
# loop runs
swapped = True
# Keep running while gap is more than 1 and last
# iteration caused a swap
while gap !=1 or swapped == 1:
# Find next gap
gap = getNextGap(gap)
# Initialize swapped as false so that we can
# check if swap happened or not
swapped = False
# Compare all elements with current gap
for i in range(0, n-gap):
if arr[i] > arr[i + gap]:
arr[i], arr[i + gap]=arr[i + gap], arr[i]
swapped = True
# Driver code to test above
arr = [8, 4, 1, 56, 3, -44, 23, -6, 28, 0]
combSort(arr)
print ("Sorted array:")
for i in range(len(arr)):
print (arr[i],end=" ")
# This code is contributed by Mohit Kumra
// C# program for implementation of Comb Sort
using System;
class GFG
{
// To find gap between elements
static int getNextGap(int gap)
{
// Shrink gap by Shrink factor
gap = (gap*10)/13;
if (gap < 1)
return 1;
return gap;
}
// Function to sort arr[] using Comb Sort
static void sort(int []arr)
{
int n = arr.Length;
// initialize gap
int gap = n;
// Initialize swapped as true to
// make sure that loop runs
bool swapped = true;
// Keep running while gap is more than
// 1 and last iteration caused a swap
while (gap != 1 || swapped == true)
{
// Find next gap
gap = getNextGap(gap);
// Initialize swapped as false so that we can
// check if swap happened or not
swapped = false;
// Compare all elements with current gap
for (int i=0; i<n-gap; i++)
{
if (arr[i] > arr[i+gap])
{
// Swap arr[i] and arr[i+gap]
int temp = arr[i];
arr[i] = arr[i+gap];
arr[i+gap] = temp;
// Set swapped
swapped = true;
}
}
}
}
// Driver method
public static void Main()
{
int []arr = {8, 4, 1, 56, 3, -44, 23, -6, 28, 0};
sort(arr);
Console.WriteLine("sorted array");
for (int i=0; i<arr.Length; ++i)
Console.Write(arr[i] + " ");
}
}
// This code is contributed by Sam007
<script>
// Javascript program for implementation of Comb Sort
// To find gap between elements
function getNextGap(gap)
{
// Shrink gap by Shrink factor
gap = parseInt((gap*10)/13, 10);
if (gap < 1)
return 1;
return gap;
}
// Function to sort arr[] using Comb Sort
function sort(arr)
{
let n = arr.length;
// initialize gap
let gap = n;
// Initialize swapped as true to
// make sure that loop runs
let swapped = true;
// Keep running while gap is more than
// 1 and last iteration caused a swap
while (gap != 1 || swapped == true)
{
// Find next gap
gap = getNextGap(gap);
// Initialize swapped as false so that we can
// check if swap happened or not
swapped = false;
// Compare all elements with current gap
for (let i=0; i<n-gap; i++)
{
if (arr[i] > arr[i+gap])
{
// Swap arr[i] and arr[i+gap]
let temp = arr[i];
arr[i] = arr[i+gap];
arr[i+gap] = temp;
// Set swapped
swapped = true;
}
}
}
}
let arr = [8, 4, 1, 56, 3, -44, 23, -6, 28, 0];
sort(arr);
document.write("sorted array" + "</br>");
for (let i=0; i<arr.length; ++i)
document.write(arr[i] + " ");
// This code is contributed by decode2207
</script>
OutputSorted array:
-44 -6 0 1 3 4 8 23 28 56
Illustration:
Let the array elements be
8, 4, 1, 56, 3, -44, 23, -6, 28, 0
Initially gap value = 10
After shrinking gap value => 10/1.3 = 7;
8 4 1 56 3 -44 23 -6 28 0
-6 4 1 56 3 -44 23 8 28 0
-6 4 0 56 3 -44 23 8 28 1
New gap value => 7/1.3 = 5;
-44 4 0 56 3 -6 23 8 28 1
-44 4 0 28 3 -6 23 8 56 1
-44 4 0 28 1 -6 23 8 56 3
New gap value => 5/1.3 = 3;
-44 1 0 28 4 -6 23 8 56 3
-44 1 -6 28 4 0 23 8 56 3
-44 1 -6 23 4 0 28 8 56 3
-44 1 -6 23 4 0 3 8 56 28
New gap value => 3/1.3 = 2;
-44 1 -6 0 4 23 3 8 56 28
-44 1 -6 0 3 23 4 8 56 28
-44 1 -6 0 3 8 4 23 56 28
New gap value => 2/1.3 = 1;
-44 -6 1 0 3 8 4 23 56 28
-44 -6 0 1 3 8 4 23 56 28
-44 -6 0 1 3 4 8 23 56 28
-44 -6 0 1 3 4 8 23 28 56
no more swaps required (Array sorted)
Time Complexity: Average case time complexity of the algorithm is Ω(N2/2p), where p is the number of increments. The worst-case complexity of this algorithm is O(n2) and the Best Case complexity is O(nlogn).
Auxiliary Space : O(1).
Snapshots:
Other Sorting Algorithms on GeeksforGeeks/GeeksQuiz
Selection Sort, Bubble Sort, Insertion Sort, Merge Sort, Heap Sort, QuickSort, Radix Sort, Counting Sort, Bucket Sort, ShellSort, Pigeonhole Sort
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem