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Linked queue
Enqueue at the tail and dequeue at the head for FIFO order.
Overview
Enqueue at the tail and dequeue at the head for FIFO order. Maintaining both first and last avoids traversing the list on enqueue. Each update changes a fixed number of references.
Step-by-step walkthrough
- Save the old last reference.
- Create a new last node.
- If empty, also set first; otherwise link the old last to the new node.
- Dequeue from first and clear last when the queue becomes empty.
Complexity analysis
| Best case | Θ(1) |
|---|---|
| Average / aggregate | Θ(1) |
| Worst case | Θ(1) enqueue/dequeue |
| Space | Θ(n) |
Maintaining both first and last avoids traversing the list on enqueue. Each update changes a fixed number of references.
A worked example
enqueue(A), enqueue(B), dequeue() returns A and leaves B.
Common mistake / implementation note
Failing to reset last after removing the final item leaves an inconsistent empty-queue state.
Failing to reset last after removing the final item leaves an inconsistent empty-queue state.
Original course code
Source: code/LinkedQueue.java. Original logic, comments, variable names and attribution are retained.
Download LinkedQueue.javaLinkedQueue.javaJAVA
/****************************************************************************** * Compilation: javac LinkedQueue.java * Execution: java LinkedQueue < input.txt * Dependencies: StdIn.java StdOut.java * Data files: https://algs4.cs.princeton.edu/13stacks/tobe.txt * * A generic queue, implemented using a singly linked list. * * % java Queue < tobe.txt * to be or not to be (2 left on queue) * ******************************************************************************/ //package edu.princeton.cs.algs4; import java.util.Iterator;import java.util.NoSuchElementException; /** * The {@code LinkedQueue} class represents a first-in-first-out (FIFO) * queue of generic items. * It supports the usual <em>enqueue</em> and <em>dequeue</em> * operations, along with methods for peeking at the first item, * testing if the queue is empty, and iterating through * the items in FIFO order. * <p> * This implementation uses a singly linked list with a non-static nested class * for linked-list nodes. See {@link Queue} for a version that uses a static nested class. * The <em>enqueue</em>, <em>dequeue</em>, <em>peek</em>, <em>size</em>, and <em>is-empty</em> * operations all take constant time in the worst case. * <p> * For additional documentation, see <a href="https://algs4.cs.princeton.edu/13stacks">Section 1.3</a> of * <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne. * * @author Robert Sedgewick * @author Kevin Wayne */public class LinkedQueue<Item> implements Iterable<Item> { private int n; // number of elements on queue private Node first; // beginning of queue private Node last; // end of queue // helper linked list class private class Node { private Item item; private Node next; } /** * Initializes an empty queue. */ public LinkedQueue() { first = null; last = null; n = 0; assert check(); } /** * Is this queue empty? * @return true if this queue is empty; false otherwise */ public boolean isEmpty() { return first == null; } /** * Returns the number of items in this queue. * @return the number of items in this queue */ public int size() { return n; } /** * Returns the item least recently added to this queue. * @return the item least recently added to this queue * @throws java.util.NoSuchElementException if this queue is empty */ public Item peek() { if (isEmpty()) throw new NoSuchElementException("Queue underflow"); return first.item; } /** * Adds the item to this queue. * @param item the item to add */ public void enqueue(Item item) { Node oldlast = last; last = new Node(); last.item = item; last.next = null; if (isEmpty()) first = last; else oldlast.next = last; n++; assert check(); } /** * Removes and returns the item on this queue that was least recently added. * @return the item on this queue that was least recently added * @throws java.util.NoSuchElementException if this queue is empty */ public Item dequeue() { if (isEmpty()) throw new NoSuchElementException("Queue underflow"); Item item = first.item; first = first.next; n--; if (isEmpty()) last = null; // to avoid loitering assert check(); return item; } /** * Returns a string representation of this queue. * @return the sequence of items in FIFO order, separated by spaces */ public String toString() { StringBuilder s = new StringBuilder(); for (Item item : this) s.append(item + " "); return s.toString(); } // check internal invariants private boolean check() { if (n < 0) { return false; } else if (n == 0) { if (first != null) return false; if (last != null) return false; } else if (n == 1) { if (first == null || last == null) return false; if (first != last) return false; if (first.next != null) return false; } else { if (first == null || last == null) return false; if (first == last) return false; if (first.next == null) return false; if (last.next != null) return false; // check internal consistency of instance variable n int numberOfNodes = 0; for (Node x = first; x != null && numberOfNodes <= n; x = x.next) { numberOfNodes++; } if (numberOfNodes != n) return false; // check internal consistency of instance variable last Node lastNode = first; while (lastNode.next != null) { lastNode = lastNode.next; } if (last != lastNode) return false; } return true; } /** * Returns an iterator that iterates over the items in this queue in FIFO order. * @return an iterator that iterates over the items in this queue in FIFO order */ public Iterator<Item> iterator() { return new LinkedIterator(); } // a linked-list iterator private class LinkedIterator implements Iterator<Item> { private Node current = first; public boolean hasNext() { return current != null; } public Item next() { if (!hasNext()) throw new NoSuchElementException(); Item item = current.item; current = current.next; return item; } } /** * Unit tests the {@code LinkedQueue} data type. * * @param args the command-line arguments */ public static void main(String[] args) { LinkedQueue<String> queue = new LinkedQueue<String>(); while (!StdIn.isEmpty()) { String item = StdIn.readString(); if (!item.equals("-")) queue.enqueue(item); else if (!queue.isEmpty()) StdOut.print(queue.dequeue() + " "); } StdOut.println("(" + queue.size() + " left on queue)"); }} /****************************************************************************** * Copyright 2002-2022, Robert Sedgewick and Kevin Wayne. * * This file is part of algs4.jar, which accompanies the textbook * * Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne, * Addison-Wesley Professional, 2011, ISBN 0-321-57351-X. * http://algs4.cs.princeton.edu * * * algs4.jar is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * algs4.jar is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with algs4.jar. If not, see http://www.gnu.org/licenses. ******************************************************************************/