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).
### C++
- `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
```
### 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
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.
### C++
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]
```
### 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>();
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.
### C++
```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]
```
### Java
In Java, we delete and retrieve the element of **lowest** priority.
```java
PriorityQueue<Integer> pq = new PriorityQueue<Integer>();
> 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 problem, 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.