usaco-guide/content/4_Silver/Stacks_Queues.md

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

Additional Reading

• CPH 4.5
• PAPS 3.2 3.3, 3.4, 6.2, 6.3, 6.5

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).

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

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

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

Queues

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

C++

• 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.

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

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:

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

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.

C++

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

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.

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]

Priority Queues

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++

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.

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]

Problems

(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