数据结构-栈、队列、堆(java)

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Studying-swz 发表于 2022/10/24 19:56:04 2022/10/24
【摘要】 栈栈(Stack)又名堆栈–先进后出,它是一种重要的数据结构。从数据结构角度看,栈也是线性表,其特殊性在于栈的基本操作是线性表操作的子集,它是操作受限的线性表,因此,可称为限定性的数据结构。限定它仅在表尾进行插入或删除操作。表尾称为栈顶,相应地,表头称为栈底。栈的基本操作除了在栈顶进行插入和删除外,还有栈的初始化,判空以及取栈顶元素等。import java.util.Stack;publ...

栈(Stack)又名堆栈–先进后出,它是一种重要的数据结构。从数据结构角度看,栈也是线性表,其特殊性在于栈的基本操作是线性表操作的子集,它是操作受限的线性表,因此,可称为限定性的数据结构。限定它仅在表尾进行插入或删除操作。表尾称为栈顶,相应地,表头称为栈底。栈的基本操作除了在栈顶进行插入和删除外,还有栈的初始化,判空以及取栈顶元素等。

import java.util.Stack;
public class ReStack {
    public static void main(String[] args) {
    	//可见stack是继承Vector的,所以是同步的--线程安全的
	    Stack<Integer>stack = new Stack<>();
	    stack.push(1);
	    stack.push(13);
        stack.push(123);
        stack.push(1234);
        stack.push(1231);
        //返回最先匹配的索引,栈顶默认索引为1
        System.out.println(stack.search(123));
	    int peek = stack.peek();
	    int pop = stack.pop();
	    stack.isEmpty();
	}
}
//源码部分
package java.util;
public class Stack<E> extends Vector<E> {
    /**
     * Creates an empty Stack.
     */
    public Stack() {
    }

    public E push(E item) {
        addElement(item);

        return item;
    }

    public synchronized E pop() {
        E       obj;
        int     len = size();

        obj = peek();
        removeElementAt(len - 1);

        return obj;
    }

   
    public synchronized E peek() {
        int     len = size();

        if (len == 0)
            throw new EmptyStackException();
        return elementAt(len - 1);
    }

 
    public boolean empty() {
        return size() == 0;
    }

   
    public synchronized int search(Object o) {
        int i = lastIndexOf(o);

        if (i >= 0) {
            return size() - i;
        }
        return -1;
    }

    /** use serialVersionUID from JDK 1.0.2 for interoperability */
    private static final long serialVersionUID = 1224463164541339165L;
}

队列

队列(Queue)是一种先进先出(FIFO,First-In-First-Out)的线性表。
在具体应用中通常用链表或者数组来实现。队列只允许在后端(称为 rear)进行插入操作,在前端(称为 front)进行删除操作。
队列的操作方式和堆栈类似,唯一的区别在于队列只允许新数据在后端进行添加。
队列常用的方法有:add、remove、element、offer、poll、peek、put、take。

import java.util.Queue;

public class ReStack {
    public static void main(String[] args) {
    	//可见队列是接
	    Queue<Integer>queue= new LinkedList<>();
	    //add和offer一样
	    queue.add(123);
        queue.add(512);
        queue.add(5124);
        queue.add(5112);
        queue.offer(5122);
        System.out.println(queue.poll());
        queue.remove(123);
        //peek和element一样
        System.out.println(queue.peek());
        System.out.println(queue.element());
	}
}

//源码部分
package java.util;
public interface Queue<E> extends Collection<E> {
   
    boolean add(E e);
    boolean offer(E e);
    E remove();
    E poll();
    E element();
    E peek();
}
//源码部分u
package java.util;
import java.util.function.Consumer;

public class LinkedList<E>
    extends AbstractSequentialList<E>
    implements List<E>, Deque<E>, Cloneable, java.io.Serializable
{
    transient int size = 0;

    transient Node<E> first;
    transient Node<E> last;
    public LinkedList() {
    }
    public LinkedList(Collection<? extends E> c) {
        this();
        addAll(c);
    }

    private void linkFirst(E e) {
        final Node<E> f = first;
        final Node<E> newNode = new Node<>(null, e, f);
        first = newNode;
        if (f == null)
            last = newNode;
        else
            f.prev = newNode;
        size++;
        modCount++;
    }

    /**
     * Links e as last element.
     */
    void linkLast(E e) {
        final Node<E> l = last;
        final Node<E> newNode = new Node<>(l, e, null);
        last = newNode;
        if (l == null)
            first = newNode;
        else
            l.next = newNode;
        size++;
        modCount++;
    }

    /**
     * Inserts element e before non-null Node succ.
     */
    void linkBefore(E e, Node<E> succ) {
        // assert succ != null;
        final Node<E> pred = succ.prev;
        final Node<E> newNode = new Node<>(pred, e, succ);
        succ.prev = newNode;
        if (pred == null)
            first = newNode;
        else
            pred.next = newNode;
        size++;
        modCount++;
    }

    /**
     * Unlinks non-null first node f.
     */
    private E unlinkFirst(Node<E> f) {
        // assert f == first && f != null;
        final E element = f.item;
        final Node<E> next = f.next;
        f.item = null;
        f.next = null; // help GC
        first = next;
        if (next == null)
            last = null;
        else
            next.prev = null;
        size--;
        modCount++;
        return element;
    }

    /**
     * Unlinks non-null last node l.
     */
    private E unlinkLast(Node<E> l) {
        // assert l == last && l != null;
        final E element = l.item;
        final Node<E> prev = l.prev;
        l.item = null;
        l.prev = null; // help GC
        last = prev;
        if (prev == null)
            first = null;
        else
            prev.next = null;
        size--;
        modCount++;
        return element;
    }

    /**
     * Unlinks non-null node x.
     */
    E unlink(Node<E> x) {
        // assert x != null;
        final E element = x.item;
        final Node<E> next = x.next;
        final Node<E> prev = x.prev;

        if (prev == null) {
            first = next;
        } else {
            prev.next = next;
            x.prev = null;
        }

        if (next == null) {
            last = prev;
        } else {
            next.prev = prev;
            x.next = null;
        }

        x.item = null;
        size--;
        modCount++;
        return element;
    }

  
    public E getFirst() {
        final Node<E> f = first;
        if (f == null)
            throw new NoSuchElementException();
        return f.item;
    }

    public E getLast() {
        final Node<E> l = last;
        if (l == null)
            throw new NoSuchElementException();
        return l.item;
    }

    public E removeFirst() {
        final Node<E> f = first;
        if (f == null)
            throw new NoSuchElementException();
        return unlinkFirst(f);
    }

    public E removeLast() {
        final Node<E> l = last;
        if (l == null)
            throw new NoSuchElementException();
        return unlinkLast(l);
    }

    public void addFirst(E e) {
        linkFirst(e);
    }

    public void addLast(E e) {
        linkLast(e);
    }


    public boolean contains(Object o) {
        return indexOf(o) != -1;
    }


    public int size() {
        return size;
    }

    public boolean add(E e) {
        linkLast(e);
        return true;
    }


    public boolean remove(Object o) {
        if (o == null) {
            for (Node<E> x = first; x != null; x = x.next) {
                if (x.item == null) {
                    unlink(x);
                    return true;
                }
            }
        } else {
            for (Node<E> x = first; x != null; x = x.next) {
                if (o.equals(x.item)) {
                    unlink(x);
                    return true;
                }
            }
        }
        return false;
    }

    
    public void add(int index, E element) {
        checkPositionIndex(index);

        if (index == size)
            linkLast(element);
        else
            linkBefore(element, node(index));
    }


    public E remove(int index) {
        checkElementIndex(index);
        return unlink(node(index));
    }

    /**
     * Tells if the argument is the index of an existing element.
     */
    private boolean isElementIndex(int index) {
        return index >= 0 && index < size;
    }


    private boolean isPositionIndex(int index) {
        return index >= 0 && index <= size;
    }

    private String outOfBoundsMsg(int index) {
        return "Index: "+index+", Size: "+size;
    }

    private void checkElementIndex(int index) {
        if (!isElementIndex(index))
            throw new IndexOutOfBoundsException(outOfBoundsMsg(index));
    }

    private void checkPositionIndex(int index) {
        if (!isPositionIndex(index))
            throw new IndexOutOfBoundsException(outOfBoundsMsg(index));
    }

    /**
     * Returns the (non-null) Node at the specified element index.
     */
    Node<E> node(int index) {
        // assert isElementIndex(index);

        if (index < (size >> 1)) {
            Node<E> x = first;
            for (int i = 0; i < index; i++)
                x = x.next;
            return x;
        } else {
            Node<E> x = last;
            for (int i = size - 1; i > index; i--)
                x = x.prev;
            return x;
        }
    }


    public int indexOf(Object o) {
        int index = 0;
        if (o == null) {
            for (Node<E> x = first; x != null; x = x.next) {
                if (x.item == null)
                    return index;
                index++;
            }
        } else {
            for (Node<E> x = first; x != null; x = x.next) {
                if (o.equals(x.item))
                    return index;
                index++;
            }
        }
        return -1;
    }

    
    public int lastIndexOf(Object o) {
        int index = size;
        if (o == null) {
            for (Node<E> x = last; x != null; x = x.prev) {
                index--;
                if (x.item == null)
                    return index;
            }
        } else {
            for (Node<E> x = last; x != null; x = x.prev) {
                index--;
                if (o.equals(x.item))
                    return index;
            }
        }
        return -1;
    }

    public E peek() {
        final Node<E> f = first;
        return (f == null) ? null : f.item;
    }

    public E element() {
        return getFirst();
    }

    public E poll() {
        final Node<E> f = first;
        return (f == null) ? null : unlinkFirst(f);
    }

    public E remove() {
        return removeFirst();
    }

    public boolean offer(E e) {
        return add(e);
    }

    public boolean offerFirst(E e) {
        addFirst(e);
        return true;
    }

    public boolean offerLast(E e) {
        addLast(e);
        return true;
    }

    public E peekLast() {
        final Node<E> l = last;
        return (l == null) ? null : l.item;
    }
    public E pollFirst() {
        final Node<E> f = first;
        return (f == null) ? null : unlinkFirst(f);
    }

    public E pollLast() {
        final Node<E> l = last;
        return (l == null) ? null : unlinkLast(l);
    }


    public void push(E e) {
        addFirst(e);
    }

    public E pop() {
        return removeFirst();
    }


    public boolean removeFirstOccurrence(Object o) {
        return remove(o);
    }

    public boolean removeLastOccurrence(Object o) {
        if (o == null) {
            for (Node<E> x = last; x != null; x = x.prev) {
                if (x.item == null) {
                    unlink(x);
                    return true;
                }
            }
        } else {
            for (Node<E> x = last; x != null; x = x.prev) {
                if (o.equals(x.item)) {
                    unlink(x);
                    return true;
                }
            }
        }
        return false;
    }

			...................................................
}

什么是最大堆和最小堆?最大(小)堆是指在树中,存在一个结点而且该结点有儿子结点,该结点的data域值都不小于(大于)其儿子结点的data域值,并且它是一个完全二叉树(不是满二叉树)。最大堆的根结点是树中元素最大的;最小堆的根结点是树中元素最小的。

在这里插入图片描述

大小为 k 的堆中添加元素的时间复杂度为 O ( log ⁡ k ),我们将重复该操作 N 次,故总时间复杂度为O ( N log ⁡ k )。
Java中的堆是用优先队列PriorityQueue实现的。默认创建一个最小堆,可以接受一个Comparator比较器,来创建最大堆。由于Comparator是一个函数接口,这里我们可以直接传入一个lambda表达式就能够自动创建Comparator对象。

import java.util.PriorityQueue;
public class ReStack {
    public static void main(String[] args) {
		Queue<Integer> minheap =new PriorityQueue<Integer>();//默认为最小堆
		Queue<Integer> maxheap =new PriorityQueue<Integer>((n1, n2) -> n2-n1);//创建最大堆
		minheap.add(12);
        minheap.add(124);
        minheap.add(122);
        minheap.add(128);
        System.out.println(minheap.peek());
        minheap.poll();
        System.out.println(minheap.peek());
        minheap.size();
	}
}

//源码
package java.util;

import java.util.function.Consumer;

public class PriorityQueue<E> extends AbstractQueue<E>
    implements java.io.Serializable {

    private static final long serialVersionUID = -7720805057305804111L;

    private static final int DEFAULT_INITIAL_CAPACITY = 11;

    /**
     * Priority queue represented as a balanced binary heap: the two
     * children of queue[n] are queue[2*n+1] and queue[2*(n+1)].  The
     * priority queue is ordered by comparator, or by the elements'
     * natural ordering, if comparator is null: For each node n in the
     * heap and each descendant d of n, n <= d.  The element with the
     * lowest value is in queue[0], assuming the queue is nonempty.
     */
    transient Object[] queue; // non-private to simplify nested class access

    /**
     * The number of elements in the priority queue.
     */
    private int size = 0;

    /**
     * The comparator, or null if priority queue uses elements'
     * natural ordering.
     */
    private final Comparator<? super E> comparator;

    /**
     * The number of times this priority queue has been
     * <i>structurally modified</i>.  See AbstractList for gory details.
     */
    transient int modCount = 0; // non-private to simplify nested class access

    /**
     * Creates a {@code PriorityQueue} with the default initial
     * capacity (11) that orders its elements according to their
     * {@linkplain Comparable natural ordering}.
     */
    public PriorityQueue() {
        this(DEFAULT_INITIAL_CAPACITY, null);
    }

    public PriorityQueue(int initialCapacity) {
        this(initialCapacity, null);
    }


    public PriorityQueue(Comparator<? super E> comparator) {
        this(DEFAULT_INITIAL_CAPACITY, comparator);
    }

    public PriorityQueue(int initialCapacity,
                         Comparator<? super E> comparator) {
        // Note: This restriction of at least one is not actually needed,
        // but continues for 1.5 compatibility
        if (initialCapacity < 1)
            throw new IllegalArgumentException();
        this.queue = new Object[initialCapacity];
        this.comparator = comparator;
    }


    @SuppressWarnings("unchecked")
    public PriorityQueue(Collection<? extends E> c) {
        if (c instanceof SortedSet<?>) {
            SortedSet<? extends E> ss = (SortedSet<? extends E>) c;
            this.comparator = (Comparator<? super E>) ss.comparator();
            initElementsFromCollection(ss);
        }
        else if (c instanceof PriorityQueue<?>) {
            PriorityQueue<? extends E> pq = (PriorityQueue<? extends E>) c;
            this.comparator = (Comparator<? super E>) pq.comparator();
            initFromPriorityQueue(pq);
        }
        else {
            this.comparator = null;
            initFromCollection(c);
        }
    }

   
    @SuppressWarnings("unchecked")
    public PriorityQueue(PriorityQueue<? extends E> c) {
        this.comparator = (Comparator<? super E>) c.comparator();
        initFromPriorityQueue(c);
    }

   
    @SuppressWarnings("unchecked")
    public PriorityQueue(SortedSet<? extends E> c) {
        this.comparator = (Comparator<? super E>) c.comparator();
        initElementsFromCollection(c);
    }

    private void initFromPriorityQueue(PriorityQueue<? extends E> c) {
        if (c.getClass() == PriorityQueue.class) {
            this.queue = c.toArray();
            this.size = c.size();
        } else {
            initFromCollection(c);
        }
    }

    private void initElementsFromCollection(Collection<? extends E> c) {
        Object[] a = c.toArray();
        // If c.toArray incorrectly doesn't return Object[], copy it.
        if (a.getClass() != Object[].class)
            a = Arrays.copyOf(a, a.length, Object[].class);
        int len = a.length;
        if (len == 1 || this.comparator != null)
            for (int i = 0; i < len; i++)
                if (a[i] == null)
                    throw new NullPointerException();
        this.queue = a;
        this.size = a.length;
    }
    .....................................
}

堆的操作:
1)创建堆–最大堆/最小堆
2)添加元素-add() ----O(logn)
3)删除元素-poll()-----O(logn)—删除堆顶
4)堆的长度----minheap.size();
5)堆得遍历—删除元素

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