Design a Queue data structure to get minimum or maximum in O(1) time

Problem: Design a Data Structure a SpecialQueue which supports following operations enque, deque, getMin() or getMax() where getMin() operation takes O(1) time.


Let the data to be inserted in queue be -
4, 2, 1, 6

Operation     Queue       Output
push(4)         4           -
push(2)        4, 2         -
push(1)       4, 2, 1       -
getMin()      4, 2, 1       1
push(6)      4, 2, 1, 6     -
pop()         2, 1, 6       4
pop()          1, 6         2
pop()            6          1
getMin()         6          6

// Notice the getMin() function call
// It returns the minimum element 
// of all the values present in the queue

Approach: The idea is to use Doubly ended Queue to store in increasing order if the structure is to return the minimum element and store in decreasing order if the structure is to return the maximum element. The operations of the Data Struture is defined as follows:


  • Insert the element into the queue structure.
  • If the size of the Deque structure is empty that is the size of the Deque is 0. Then, Insert the element from the back.
  • Otherwise, If there are some elements in the Deque structure then pop the elements out from the Deque until the back of the Deque is greater than the current element and then finally insert the element from back.


  • If the first element of the Deque is equal to the front element of the queue then pop the elements out from the Queue and the Deque at the same time.
  • Otherwise, Pop the element from the front of the queue to maintain the order of the elements.

Get Minimum

Return the front element of the Deque to get the minimum element of the current element of the queue.

Below is the implementation of the above approach:






// C++ implementation to design 
// a queue data structure to get 
// minimum element in O(1) time
#include <bits/stdc++.h>
using namespace std;
template <typename T>
// Structure of the queue
class MinMaxQueue {
    // Queue to store the 
    // element to maintain the 
    // order of insertion
    queue<T> Q;
    // Doubly ended queue to
    // get the minimum element 
    // in the O(1) time
    deque<T> D;
    // Function to push a element
    // into the queue
    void enque_element(T element)
        // If there is no element
        // in the queue
        if (Q.size() == 0) {
        else {
            // Pop the elements out
            // until the element at 
            // back is greater than 
            // current element
            while (!D.empty() && 
               D.back() > element) {
    // Function to pop the element
    // out from the queue
    void deque_element()
        // Condition when the Minimum
        // element is the element at 
        // the front of the Deque
        if (Q.front() == D.front()) {
        else {
    // Function to get the
    // minimum element from 
    // the queue
    T getMin()
        return D.front();
// Driver Code
int main()
    MinMaxQueue<int> k;
    int example[3] = { 1, 2, 4 };
    // Loop to enque element
    for (int i = 0; i < 3; i++) {
    cout << k.getMin() << "\n";
    cout << k.getMin() << "\n";




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