Sort the Queue using Recursion
Given a queue and the task is to sort it using recursion without using any loop. We can only use the following functions of queue:
empty(q): Tests whether the queue is empty or not.
push(q): Adds a new element to the queue.
pop(q): Removes front element from the queue.
size(q): Returns the number of elements in a queue.
front(q): Returns the value of the front element without removing it.
Examples:
Input: queue = {10, 7, 16, 9, 20, 5}
Output: 5 7 9 10 16 20
Input: queue = {0, -2, -1, 2, 3, 1}
Output: -2 -1 0 1 2 3
Approach: The idea of the solution is to hold all values in the function call stack until the queue becomes empty. When the queue becomes empty, insert all held items one by one in sorted order. Here sorted order is important.
How to manage sorted order?
Whenever you get the item from the function call stack, then first calculate the size of the queue and compare it with the elements of queue. Here, two cases arises:
- If the item (returned by function call stack) is greater than the front element of the queue then dequeue front element and enqueue this element into the same queue by decreasing the size.
- If the item is less than the front element from the queue then enqueue the element in the queue and dequeue the remaining element from the queue and enqueue by decreasing size repeat the case 1 and 2 unless size becomes zero. Take care of one thing, if size became zero and your element remains greater than all elements of the queue then push your element into the queue.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to push element in last by// popping from front until size becomes 0void FrontToLast(queue<int>& q, int qsize){ // Base condition if (qsize <= 0) return; // pop front element and push // this last in a queue q.push(q.front()); q.pop(); // Recursive call for pushing element FrontToLast(q, qsize - 1);}// Function to push an element in the queue// while maintaining the sorted ordervoid pushInQueue(queue<int>& q, int temp, int qsize){ // Base condition if (q.empty() || qsize == 0) { q.push(temp); return; } // If current element is less than // the element at the front else if (temp <= q.front()) { // Call stack with front of queue q.push(temp); // Recursive call for inserting a front // element of the queue to the last FrontToLast(q, qsize); } else { // Push front element into // last in a queue q.push(q.front()); q.pop(); // Recursive call for pushing // element in a queue pushInQueue(q, temp, qsize - 1); }}// Function to sort the given// queue using recursionvoid sortQueue(queue<int>& q){ // Return if queue is empty if (q.empty()) return; // Get the front element which will // be stored in this variable // throughout the recursion stack int temp = q.front(); // Remove the front element q.pop(); // Recursive call sortQueue(q); // Push the current element into the queue // according to the sorting order pushInQueue(q, temp, q.size());}// Driver codeint main(){ // Push elements to the queue queue<int> qu; qu.push(10); qu.push(7); qu.push(16); qu.push(9); qu.push(20); qu.push(5); // Sort the queue sortQueue(qu); // Print the elements of the // queue after sorting while (!qu.empty()) { cout << qu.front() << " "; qu.pop(); }} |
Java
// Java implementation of the approachimport java.util.*;class GFG {// Function to push element in last by// popping from front until size becomes 0static void FrontToLast(Queue<Integer> q, int qsize){ // Base condition if (qsize <= 0) return; // pop front element and push // this last in a queue q.add(q.peek()); q.remove(); // Recursive call for pushing element FrontToLast(q, qsize - 1);}// Function to push an element in the queue// while maintaining the sorted orderstatic void pushInQueue(Queue<Integer> q, int temp, int qsize){ // Base condition if (q.isEmpty() || qsize == 0) { q.add(temp); return; } // If current element is less than // the element at the front else if (temp <= q.peek()) { // Call stack with front of queue q.add(temp); // Recursive call for inserting a front // element of the queue to the last FrontToLast(q, qsize); } else { // Push front element into // last in a queue q.add(q.peek()); q.remove(); // Recursive call for pushing // element in a queue pushInQueue(q, temp, qsize - 1); }}// Function to sort the given// queue using recursionstatic void sortQueue(Queue<Integer> q){ // Return if queue is empty if (q.isEmpty()) return; // Get the front element which will // be stored in this variable // throughout the recursion stack int temp = q.peek(); // Remove the front element q.remove(); // Recursive call sortQueue(q); // Push the current element into the queue // according to the sorting order pushInQueue(q, temp, q.size());}// Driver codepublic static void main(String[] args) { // Push elements to the queue Queue<Integer> qu = new LinkedList<>(); qu.add(10); qu.add(7); qu.add(16); qu.add(9); qu.add(20); qu.add(5); // Sort the queue sortQueue(qu); // Print the elements of the // queue after sorting while (!qu.isEmpty()) { System.out.print(qu.peek() + " "); qu.remove(); }}} // This code is contributed by PrinciRaj1992 |
Python3
# defining a class Queueclass Queue: def __init__(self): self.queue = [] def put(self, item): self.queue.append(item) def get(self): if len(self.queue) < 1: return None return self.queue.pop(0) def front(self): return self.queue[0] def size(self): return len(self.queue) def empty(self): return not(len(self.queue))# Function to push element in last by # popping from front until size becomes 0 def FrontToLast(q, qsize) : # Base condition if qsize <= 0: return # pop front element and push # this last in a queue q.put(q.get()) # Recursive call for pushing element FrontToLast(q, qsize - 1) # Function to push an element in the queue # while maintaining the sorted order def pushInQueue(q, temp, qsize) : # Base condition if q.empty() or qsize == 0: q.put(temp) return # If current element is less than # the element at the front elif temp <= q.front() : # Call stack with front of queue q.put(temp) # Recursive call for inserting a front # element of the queue to the last FrontToLast(q, qsize) else : # Push front element into # last in a queue q.put(q.get()) # Recursive call for pushing # element in a queue pushInQueue(q, temp, qsize - 1) # Function to sort the given # queue using recursion def sortQueue(q): # Return if queue is empty if q.empty(): return # Get the front element which will # be stored in this variable # throughout the recursion stack temp = q.get() # Recursive call sortQueue(q) # Push the current element into the queue # according to the sorting order pushInQueue(q, temp, q.size())# Driver codequ = Queue()# Data is inserted into Queue # using put() Data is inserted # at the end qu.put(10) qu.put(7) qu.put(16) qu.put(9) qu.put(20) qu.put(5)# Sort the queue sortQueue(qu)# Print the elements of the # queue after sorting while not qu.empty(): print(qu.get(), end = ' ') # This code is contributed by Sadik Ali |
C#
// Program to print the given patternusing System;using System.Collections.Generic; class GFG {// Function to push element in last by// popping from front until size becomes 0static void FrontToLast(Queue<int> q, int qsize){ // Base condition if (qsize <= 0) return; // pop front element and push // this last in a queue q.Enqueue(q.Peek()); q.Dequeue(); // Recursive call for pushing element FrontToLast(q, qsize - 1);}// Function to push an element in the queue// while maintaining the sorted orderstatic void pushInQueue(Queue<int> q, int temp, int qsize){ // Base condition if (q.Count == 0 || qsize == 0) { q.Enqueue(temp); return; } // If current element is less than // the element at the front else if (temp <= q.Peek()) { // Call stack with front of queue q.Enqueue(temp); // Recursive call for inserting a front // element of the queue to the last FrontToLast(q, qsize); } else { // Push front element into // last in a queue q.Enqueue(q.Peek()); q.Dequeue(); // Recursive call for pushing // element in a queue pushInQueue(q, temp, qsize - 1); }}// Function to sort the given// queue using recursionstatic void sortQueue(Queue<int> q){ // Return if queue is empty if (q.Count==0) return; // Get the front element which will // be stored in this variable // throughout the recursion stack int temp = q.Peek(); // Remove the front element q.Dequeue(); // Recursive call sortQueue(q); // Push the current element into the queue // according to the sorting order pushInQueue(q, temp, q.Count);}// Driver codepublic static void Main(String[] args) { // Push elements to the queue Queue<int> qu = new Queue<int>(); qu.Enqueue(10); qu.Enqueue(7); qu.Enqueue(16); qu.Enqueue(9); qu.Enqueue(20); qu.Enqueue(5); // Sort the queue sortQueue(qu); // Print the elements of the // queue after sorting while (qu.Count != 0) { Console.Write(qu.Peek() + " "); qu.Dequeue(); }}}// This code is contributed by Princi Singh |
Javascript
<script> // Javascript implementation of the approach // Function to push element in last by // popping from front until size becomes 0 function FrontToLast(q, qsize) { // Base condition if (qsize <= 0) return; // pop front element and push // this last in a queue q.push(q[0]); q.shift(); // Recursive call for pushing element FrontToLast(q, qsize - 1); } // Function to push an element in the queue // while maintaining the sorted order function pushInQueue(q, temp, qsize) { // Base condition if (q.length == 0 || qsize == 0) { q.push(temp); return; } // If current element is less than // the element at the front else if (temp <= q[0]) { // Call stack with front of queue q.push(temp); // Recursive call for inserting a front // element of the queue to the last FrontToLast(q, qsize); } else { // Push front element into // last in a queue q.push(q[0]); q.shift(); // Recursive call for pushing // element in a queue pushInQueue(q, temp, qsize - 1); } } // Function to sort the given // queue using recursion function sortQueue(q) { // Return if queue is empty if (q.length==0) return; // Get the front element which will // be stored in this variable // throughout the recursion stack let temp = q[0]; // Remove the front element q.shift(); // Recursive call sortQueue(q); // Push the current element into the queue // according to the sorting order pushInQueue(q, temp, q.length); } // Push elements to the queue let qu = []; qu.push(10); qu.push(7); qu.push(16); qu.push(9); qu.push(20); qu.push(5); // Sort the queue sortQueue(qu); // Print the elements of the // queue after sorting while (qu.length != 0) { document.write(qu[0] + " "); qu.shift(); }// This code is contributed by mukesh07.</script> |
Output:
5 7 9 10 16 20
Time Complexity: The time complexity of this code is O(n^2), as the time taken to sort the queue is O(n^2) due to the use of recursion. The function pushInQueue() is called n times, and each time it calls the function FrontToLast() which takes O(n) time, resulting in a time complexity of O(n^2).
Auxiliary Space: The Auxiliary Space of this code is O(n), as the maximum size of the queue will be n, where n is the number of elements in the queue.
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