Sort a nearly sorted array using STL - GeeksforGeeks

30 Jun, 2021
Given an array of n elements, where each element is at most k away from its target position, devise an algorithm that sorts in O(n log k) time. For example, let us consider k is 2, an element at index 7 in the sorted array, can be at indexes 5, 6, 7, 8, 9 in the given array. It may be assumed that k < n.
Example:  
Input: arr[] = {6, 5, 3, 2, 8, 10, 9}, 
       k = 3
Output: arr[] = {2, 3, 5, 6, 8, 9, 10}

Input: arr[] = {10, 9, 8, 7, 4, 70, 60, 50}, 
       k = 4
Output: arr[] = {4, 7, 8, 9, 10, 50, 60, 70}
Simple Approach: The basic solution is to sort the array using any standard sorting algorithm. 
CPP14
Java
Python3
C#
Javascript
// A STL based C++ program to// sort a nearly sorted array.#include <bits/stdc++.h>using namespace std; // Given an array of size n,// where every element// is k away from its target// position, sorts the// array in O(n Log n) time.int sortK(int arr[], int n, int k){    // Sort the array using    // inbuilt function    sort(arr, arr + n);} // An utility function to print// array elementsvoid printArray(    int arr[], int size){    for (int i = 0; i < size; i++)        cout << arr[i] << " ";    cout << endl;} // Driver program to test// above functionsint main(){    int k = 3;    int arr[] = { 2, 6, 3, 12, 56, 8 };    int n = sizeof(arr) / sizeof(arr[0]);    sortK(arr, n, k);     cout << "Following is sorted array\n";    printArray(arr, n);     return 0;}
// A STL based Java program to// sort a nearly sorted array.import java.util.*;public class GFG{   // Given an array of size n,  // where every element  // is k away from its target  // position, sorts the  // array in O(n Log n) time.  static void sortK(int[] arr, int n, int k)  {     // Sort the array using    // inbuilt function    Arrays.sort(arr);  }   // An utility function to print  // array elements  static void printArray(    int[] arr, int size)  {    for (int i = 0; i < size; i++)      System.out.print(arr[i] + " ");    System.out.println();  }   // Driver code  public static void main(String[] args)  {    int k = 3;    int[] arr = { 2, 6, 3, 12, 56, 8 };    int n = arr.length;    sortK(arr, n, k);     System.out.println("Following is sorted array");    printArray(arr, n);  }} // This code is contributed by divyesh072019.
# A STL based Java program to# sort a nearly sorted array. # Given an array of size n,# where every element# is k away from its target# position, sorts the# array in O(n Log n) time.def sortK(arr, n, k):       # Sort the array using    # inbuilt function    arr.sort() # An utility function to print# array elementsdef printArray(arr, size):    for i in range(size):        print(arr[i], end = " ")    print() # Driver codek = 3arr = [ 2, 6, 3, 12, 56, 8]n = len(arr)sortK(arr, n, k)print("Following is sorted array")printArray(arr, n) # This code is contributed by avanitrachhadiya2155
// A STL based C# program to// sort a nearly sorted array.using System;class GFG{         // Given an array of size n,    // where every element    // is k away from its target    // position, sorts the    // array in O(n Log n) time.    static void sortK(int[] arr, int n, int k)    {               // Sort the array using        // inbuilt function        Array.Sort(arr);    }           // An utility function to print    // array elements    static void printArray(        int[] arr, int size)    {        for (int i = 0; i < size; i++)            Console.Write(arr[i] + " ");        Console.WriteLine();    }   // Driver code  static void Main()  {    int k = 3;    int[] arr = { 2, 6, 3, 12, 56, 8 };    int n = arr.Length;    sortK(arr, n, k);       Console.WriteLine("Following is sorted array");    printArray(arr, n);  }} // This code is contributed by divyeshrabadiya07.
<script>// A STL based Javascript program to// sort a nearly sorted array. // Given an array of size n,// where every element// is k away from its target// position, sorts the// array in O(n Log n) time.function sortK(arr,n,k){    // Sort the array using    // inbuilt function    (arr).sort(function(a,b){return a-b;});} // An utility function to print// array elementsfunction printArray(arr,size){    for (let i = 0; i < size; i++)      document.write(arr[i] + " ");    document.write("<br>");} // Driver codelet k = 3;let arr=[ 2, 6, 3, 12, 56, 8 ];let n = arr.length;sortK(arr, n, k);document.write("Following is sorted array<br>");printArray(arr, n);  // This code is contributed by ab2127</script>
Following is sorted arrayn2 3 6 8 12 56
 
Complexity Analysis: 
Time complexity: O(n log n), where n is the size of the array. The sorting algorithm takes log n time. Since the size of the array is n, the whole program takes O(n log n) time.
Space Complexity: O(1). As no extra space is required.
 
Efficient Solution: Sliding Window technique. Approach: A better solution is to use a priority queue(or heap data structure). Use sliding window technique to keep consecutive k elements of a window in heap. Then remove the top element(smallest element) and replace the first element of the window with it. As each element will be at most k distance apart, therefore keeping k consecutive elements in a window while replacing the i-th element with the smallest element from i to (i+k) will suffice(first i-1 elements are sorted).Algorithm: 
Build a priority queue pq of first (k+1) elements.Initialize index = 0 (For result array).Do the following for elements from k+1 to n-1. Pop an item from pq and put it at index, increment index.Push arr[i] to pq.While pq is not empty, Pop an item from pq and put it at index, increment index.
Build a priority queue pq of first (k+1) elements.
Initialize index = 0 (For result array).
Do the following for elements from k+1 to n-1. Pop an item from pq and put it at index, increment index.Push arr[i] to pq.
Pop an item from pq and put it at index, increment index.Push arr[i] to pq.
Pop an item from pq and put it at index, increment index.
Push arr[i] to pq.
While pq is not empty, Pop an item from pq and put it at index, increment index.
We have discussed a simple implementation in Sort a nearly sorted (or K sorted) array. In this post, an STL based implementation is done. 
CPP
// A STL based C++ program to sort// a nearly sorted array.#include <bits/stdc++.h>using namespace std; // Given an array of size n,// where every element// is k away from its target// position, sorts the// array in O(nLogk) time.int sortK(int arr[], int n, int k){    // Insert first k+1 items in a    // priority queue (or min heap)    // (A O(k) operation)    priority_queue<int, vector<int>,                   greater<int> >        pq(arr, arr + k + 1);     // i is index for remaining    // elements in arr[] and index    // is target index of for    // current minimum element in    // Min Heapm 'hp'.    int index = 0;    for (int i = k + 1; i < n; i++) {        arr[index++] = pq.top();        pq.pop();        pq.push(arr[i]);    }     while (pq.empty() == false) {        arr[index++] = pq.top();        pq.pop();    }} // A utility function to print// array elementsvoid printArray(int arr[], int size){    for (int i = 0; i < size; i++)        cout << arr[i] << " ";    cout << endl;} // Driver program to test above functionsint main(){    int k = 3;    int arr[] = { 2, 6, 3, 12, 56, 8 };    int n = sizeof(arr) / sizeof(arr[0]);    sortK(arr, n, k);     cout << "Following is sorted arrayn";    printArray(arr, n);     return 0;}
Following is sorted arrayn2 3 6 8 12 56
 
Complexity Analysis: 
Time Complexity: O(n Log k). For every element, it is pushed in the priority queue and the insertion and deletion needs O(log k) time as there are k elements in priority queue.
Auxiliary Space: O(k). To store k elements in the priority queue, O(k) space is required.
 
andrew1234
divyeshrabadiya07
divyesh072019
avanitrachhadiya2155
ab2127
cpp-priority-queue
STL
Arrays
Heap
Sorting
Arrays
Sorting
Heap
STL
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Count pairs with given sum
Chocolate Distribution Problem
Window Sliding Technique
Reversal algorithm for array rotation
Next Greater Element
HeapSort
Binary Heap
Huffman Coding | Greedy Algo-3
Insertion and Deletion in Heaps
Building Heap from Array