---
id: stacks-queues
title: Introduction to Stacks & Queues
author: Darren Yao
description: 
prerequisites:
 - Bronze - Data Structures
---

import { Problem } from "../models";

export const metadata = {
  problems: {
    nearest: [
      new Problem("CSES", "Nearest Smaller Values", "1645", "Easy", false, [], ""),
    ],
    general: [
      new Problem("LC", "Max Histogram Area", "largest-rectangle-in-histogram", "Normal", false, [],""),
      new Problem("Old Gold", "Concurrently Balanced Strings", "194", "Normal", false, [],""),
      new Problem("YS","Persistent Queue","persistent_queue","Normal",false,["DFS"],"")
    ],
  }
};

## Additional Reading

<resources>
  <resource source="CPH" title="4.5 - Stacks, Queues, Priority Queues"></resource>
  <resource source="PAPS" title="3.2 to 3.4 - C++ STL"></resource>
  <resource source="PAPS" title="6.2, 6.3, 6.5 - Stacks, Queues, Priority Queues"></resource>
  <resource source="CP1" title="2.2 - Data Structures with Built-in Libraries"> </resource>
</resources>

## Stacks

A stack is a **Last In First Out** (LIFO) data structure that supports three operations, all in $O(1)$ time. Think of it like a real-world stack of papers (or cards).

<LanguageSection>

<CPPSection>

### [C++](http://www.cplusplus.com/reference/stack/stack/)

 - `push`: adds an element to the top of the stack
 - `pop`: removes an element from the top of the stack
 - `top`: retrieves the element at the top without removing it

```cpp
stack<int> s;
s.push(1); // [1]
s.push(13); // [1, 13]
s.push(7); // [1, 13, 7]
cout << s.top() << endl; // 7
s.pop(); // [1, 13]
cout << s.size() << endl; // 2
```

</CPPSection>

<JavaSection>

### Java

 - `push`: adds an element to the top of the stack
 - `pop`: removes an element from the top of the stack
 - `peek`: retrieves the element at the top without removing it

```java
Stack<Integer> s = new Stack<Integer>();
s.push(1); // [1]
s.push(13); // [1, 13]
s.push(7); // [1, 13, 7]
System.out.println(s.peek()); // 7
s.pop(); // [1, 13]
System.out.println(s.size()); // 2
```

</JavaSection>

</LanguageSection>

## Queues

A queue is a First In First Out (FIFO) data structure that supports three operations, all in $O(1)$ time. 

<LanguageSection>

<CPPSection>

### [C++](http://www.cplusplus.com/reference/queue/queue/)

 - `push`: insertion at the back of the queue
 - `pop`: deletion from the front of the queue 
 - `front`: which retrieves the element at the front without removing it.

```cpp
queue<int> q;
q.push(1); // [1]
q.push(3); // [3, 1]
q.push(4); // [4, 3, 1]
q.pop(); // [4, 3]
cout << q.front() << endl; // 3
```

</CPPSection>

<JavaSection>

### Java

 - `add`: insertion at the back of the queue
 - `poll`: deletion from the front of the queue
 - `peek`: which retrieves the element at the front without removing it

Java doesn't actually have a `Queue` class; it's only an interface. The most commonly used implementation is the `LinkedList`, declared as follows:

```java
Queue<Integer> q = new LinkedList<Integer>();
q.add(1); // [1]
q.add(3); // [3, 1]
q.add(4); // [4, 3, 1]
q.poll(); // [4, 3]
System.out.println(q.peek()); // 3
```

</JavaSection>

</LanguageSection>

## Deques

A **deque** (usually pronounced "deck") stands for double ended queue and is a combination of a stack and a queue, in that it supports $O(1)$ insertions and deletions from both the front and the back of the deque. Not very common in Bronze / Silver.

<LanguageSection>

<CPPSection>

### [C++](http://www.cplusplus.com/reference/deque/deque/)

The four methods for adding and removing are `push_back`, `pop_back`, `push_front`, and `pop_front`. 

```cpp
deque<int> d;
d.push_front(3); // [3]
d.push_front(4); // [4, 3]
d.push_back(7); // [4, 3, 7]
d.pop_front(); // [3, 7]
d.push_front(1); // [1, 3, 7]
d.pop_back(); // [1, 3]
```

</CPPSection>

<JavaSection>

### Java

In Java, the deque class is called `ArrayDeque`. The four methods for adding and removing are `addFirst` , `removeFirst`, `addLast`, and `removeLast`.

```java
ArrayDeque<Integer> deque = new ArrayDeque<Integer>();
deque.addFirst(3); // [3]
deque.addFirst(4); // [4, 3]
deque.addLast(7); // [4, 3, 7]
deque.removeFirst(); // [3, 7]
deque.addFirst(1); // [1, 3, 7]
deque.removeLast(); // [1, 3]
```

</JavaSection>

</LanguageSection>

## Priority Queues

<LanguageSection>

<CPPSection>

### [C++](http://www.cplusplus.com/reference/queue/priority_queue/)

A priority queue supports the following operations: insertion of elements, deletion of the element considered highest priority, and retrieval of the highest priority element, all in $O(\log n)$ time according to the number of elements in the priority queue. Priority is based on a comparator function. The priority queue is one of the most important data structures in competitive programming, so make sure you understand how and when to use it.

```cpp
priority_queue<int> pq;
pq.push(7); // [7]
pq.push(2); // [2, 7]
pq.push(1); // [1, 2, 7]
pq.push(5); // [1, 2, 5, 7]
cout << pq.top() << endl; // 7
pq.pop(); // [1, 2, 5]
pq.pop(); // [1, 2]
pq.push(6); // [1, 2, 6]
```


</CPPSection>

<JavaSection>

### Java

In Java, we delete and retrieve the element of **lowest** priority.

```java
PriorityQueue<Integer> pq = new PriorityQueue<Integer>();
pq.add(7); // [7]
pq.add(2); // [7, 2]
pq.add(1); // [7, 2, 1]
pq.add(5); // [7, 5, 2, 1]
System.out.println(pq.peek()); // 1
pq.poll(); // [7, 5, 2]
pq.poll(); // [7, 5]
pq.add(6); // [7, 6, 5]
```

</JavaSection>

</LanguageSection>



## Monotonic Stack

<problems-list problems={metadata.problems.nearest} />

Consider the following problem: 

> Given an array, $a$, of $N$ ($1 \le N \le 10^5$) integers, for every index $i$, find the rightmost index $j$ such that $j < i$ and $a_i > a_j$. 

To solve this, let's store a stack of pairs of `<value, index>` and iterate over the array from left to right.  For some index $i$, we will compute $ans_i$, the rightmost index for $i$, as follows:

- Keep popping the top element off the stack as long as $value \ge a_i$. This is because we know that the pair containing $value$ will never be the solution to any index $j > i$, since $a_i$ is less than or equal to than $value$ and has an index further to the right.
- If $value < a_i$, set $ans[i]$ to $index$, because a stack stores the most recently added values first (or in this case, the rightmost ones), $index$ will contain the rightmost value which is less than $a_i$. Then, pop the top element off the stack, because $index$ can't be the solution for two elements.

The stack we used is called a **monotonic stack** because we keep popping off the top element of the stack which maintains it's monotonicity (the same property needed for algorithms like binary search) because the elements in the stack are increasing. 

(add code)

<IncompleteSection />

### Further Reading

<resources>
  <resource source="CPH" title="8.2 - Nearest Smaller Element"></resource>
  <resource source="Medium" title="Monotonic Stack" url="https://medium.com/@vishnuvardhan623/monotonic-stack-e9dcc4fa8c3e"></resource>
</resources>

## Problems

<problems-list problems={metadata.problems.general} />

<!-- 

(actually go through these and check ...)

### Stack

  - UVa 00514 - Rails
  - UVa 00732 - Anagram by Stack
  - UVa 01062 - Containers

### Queue / Deque 

  - UVa 10172 - The Lonesome Cargo
  - UVa 10901 - Ferry Loading III
  - UVa 11034 - Ferry Loading IV
 -->