数据结构（背包、队列和栈）

一.背包

　　背包是一种不支持从中删除元素的集合数据类型，目的是帮助用例收集元素并迭代所有收集到的元素，也可以检查背包是否为空，或者获取背包中元素的数量。背包里面的元素的顺序不确定。

　　要理解背包的概念，可以想象一个喜欢收集弹珠球的人。他将所有的弹珠球都放在一个背包里，一次一个，并且会不时在所有的弹珠球中寻找某一颗；

　　

 1.用链表实现

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
import java.util.Iterator;
import java.util.NoSuchElementException;

public class Bag<Item> implements Iterable<Item> {
    private Node<Item> first;    
    private int n;               

    private static class Node<Item> {
        private Item item;
        private Node<Item> next;
    }

    /**
     * Initializes an empty bag.
     */
    public Bag() {
        first = null;
        n = 0;
    }

    public boolean isEmpty() {
        return first == null;
    }

    public int size() {
        return n;
    }

    public void add(Item item) {
        Node<Item> oldfirst = first;
        first = new Node<Item>();
        first.item = item;
        first.next = oldfirst;
        n++;
    }

    public Iterator<Item> iterator()  {
        return new ListIterator(first);
    }

    private class ListIterator implements Iterator<Item> {
        private Node<Item> current;

        public ListIterator(Node<Item> first) {
            current = first;
        }

        public boolean hasNext()  { return current != null;                     }
        public void remove()      { throw new UnsupportedOperationException();  }

        public Item next() {
            if (!hasNext()) throw new NoSuchElementException();
            Item item = current.item;
            current = current.next;
            return item;
        }
    }

    public static void main(String[] args) {
        Bag<String> bag = new Bag<String>();
        while (!StdIn.isEmpty()) {
            String item = StdIn.readString();
            bag.add(item);
        }

        StdOut.println("size of bag = " + bag.size());
        for (String s : bag) {
            StdOut.println(s);
        }
    }

}

二.队列

队列的特性：

• 在队尾插入元素，在队首删除元素。

• FIFO（先进先出），就向排队取票一样。

 1.用链表实现

package structure;

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
import java.util.Iterator;
import java.util.NoSuchElementException;

public class Queue<Item> implements Iterable<Item> {
    private Node<Item> first;    
    private Node<Item> last;     
    private int n;               

    private static class Node<Item> {
        private Item item;
        private Node<Item> next;
    }

    public Queue() {
        first = null;
        last  = null;
        n = 0;
    }

    public boolean isEmpty() {
        return first == null;
    }

    public int size() {
        return n;
    }

    public Item peek() {
        if (isEmpty()) throw new NoSuchElementException("Queue underflow");
        return first.item;
    }

    //增加元素
    public void enqueue(Item item) {
        Node<Item> oldlast = last;
        last = new Node<Item>();
        last.item = item;
        last.next = null;
        if (isEmpty()) first = last;
        else           oldlast.next = last;
        n++;
    }

    //删除元素
    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
        return item;
    }

    public String toString() {
        StringBuilder s = new StringBuilder();
        for (Item item : this) {
            s.append(item);
            s.append(' ');
        }
        return s.toString();
    }

    public Iterator<Item> iterator()  {
        return new ListIterator(first);
    }

    private class ListIterator implements Iterator<Item> {
        private Node<Item> current;

        public ListIterator(Node<Item> first) {
            current = first;
        }

        public boolean hasNext()  { return current != null;                     }
        public void remove()      { throw new UnsupportedOperationException();  }

        public Item next() {
            if (!hasNext()) throw new NoSuchElementException();
            Item item = current.item;
            current = current.next;
            return item;
        }
    }


    public static void main(String[] args) {
        Queue<String> queue = new Queue<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)");
    }
}

三.栈

（1）栈是一种线性结构，栈中的元素遵循先入后出的原则，最先进入的元素所在位置叫做栈底，最后放入的元素所在位置叫做栈顶。

这种结构类似于盛放羽毛球的圆筒，一端封闭，另一端开口，先放入的羽毛球位于筒的底部（即栈底），后放入的羽毛球位于筒的入口（即栈顶）。

（2）栈也是一种抽象的逻辑结构，依赖于物理结构（如数组、链表）而存在。既可以使用数组实现，也可以使用链表实现。

（3）出栈、入栈的时间复杂都是O(1)。

1.用数组实现

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
import java.util.Iterator;
import java.util.NoSuchElementException;

public class ResizingArrayStack<Item> implements Iterable<Item> {
    private Item[] a;
    private int n;

    public ResizingArrayStack() {
        a = (Item[]) new Object[2];
        n = 0;
    }

    public boolean isEmpty() {
        return n == 0;
    }

    public int size() {
        return n;
    }

    //重置数组大小
    private void resize(int capacity) {
        assert capacity >= n;

        // textbook implementation
        Item[] temp = (Item[]) new Object[capacity];
        for (int i = 0; i < n; i++) {
            temp[i] = a[i];
        }
        a = temp;
        // alternative implementation
        // a = java.util.Arrays.copyOf(a, capacity);
    }

    public void push(Item item) {
        if (n == a.length) resize(2*a.length);
        a[n++] = item;
    }

    public Item pop() {
        if (isEmpty()) throw new NoSuchElementException("Stack underflow");
        Item item = a[n-1];
        a[n-1] = null;
        n--;
        if (n > 0 && n == a.length/4) resize(a.length/2);
        return item;
    }

    // 返回栈顶部数据，但不移除
    public Item peek() {
        if (isEmpty()) throw new NoSuchElementException("Stack underflow");
        return a[n-1];
    }

    public Iterator<Item> iterator() {
        return new ReverseArrayIterator();
    }

    private class ReverseArrayIterator implements Iterator<Item> {
        private int i;

        public ReverseArrayIterator() {
            i = n-1;
        }

        public boolean hasNext() {
            return i >= 0;
        }

        public void remove() {
            throw new UnsupportedOperationException();
        }

        public Item next() {
            if (!hasNext()) throw new NoSuchElementException();
            return a[i--];
        }
    }

    public static void main(String[] args) {
        ResizingArrayStack<String> stack = new ResizingArrayStack<String>();
        while (!StdIn.isEmpty()) {
            String item = StdIn.readString();
            if (!item.equals("-")) stack.push(item);
            else if (!stack.isEmpty()) StdOut.print(stack.pop() + " ");
        }
        StdOut.println("(" + stack.size() + " left on stack)");
    }
}

2.用链表实现

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
import java.util.Iterator;
import java.util.NoSuchElementException;

public class Stack<Item> implements Iterable<Item> {
    private Node<Item> first;
    private int n;

    private static class Node<Item> {
        private Item item;
        private Node<Item> next;
    }

    public Stack() {
        first = null;
        n = 0;
    }

    public boolean isEmpty() {
        return first == null;
    }

    public int size() {
        return n;
    }

    public void push(Item item) {
        Node<Item> oldfirst = first;
        first = new Node<Item>();
        first.item = item;
        first.next = oldfirst;
        n++;
    }

    public Item pop() {
        if (isEmpty()) throw new NoSuchElementException("Stack underflow");
        Item item = first.item;        // save item to return
        first = first.next;            // delete first node
        n--;
        return item;                   // return the saved item
    }

    //返回栈顶部数据，但不移除
    public Item peek() {
        if (isEmpty()) throw new NoSuchElementException("Stack underflow");
        return first.item;
    }

    public String toString() {
        StringBuilder s = new StringBuilder();
        for (Item item : this) {
            s.append(item);
            s.append(' ');
        }
        return s.toString();
    }

    public Iterator<Item> iterator() {
        return new ListIterator(first);
    }

    private class ListIterator implements Iterator<Item> {
        private Node<Item> current;

        public ListIterator(Node<Item> first) {
            current = first;
        }

        public boolean hasNext() {
            return current != null;
        }

        public void remove() {
            throw new UnsupportedOperationException();
        }

        public Item next() {
            if (!hasNext()) throw new NoSuchElementException();
            Item item = current.item;
            current = current.next;
            return item;
        }
    }

    public static void main(String[] args) {
        Stack<String> stack = new Stack<String>();
        while (!StdIn.isEmpty()) {
            String item = StdIn.readString();
            if (!item.equals("-"))
                stack.push(item);
            else if (!stack.isEmpty())
                StdOut.print(stack.pop() + " ");
        }
        StdOut.println("(" + stack.size() + " left on stack)");
    }
}