CS-Notes/docs/notes/算法 - 栈和队列.md

<!-- GFM-TOC -->
* [栈](#栈)
    * [1. 数组实现](#1-数组实现)
    * [2. 链表实现](#2-链表实现)
* [队列](#队列)
<!-- GFM-TOC -->


# 栈

```java
public interface MyStack<Item> extends Iterable<Item> {

    MyStack<Item> push(Item item);

    Item pop() throws Exception;

    boolean isEmpty();

    int size();

}
```

## 1. 数组实现

```java
public class ArrayStack<Item> implements MyStack<Item> {

    // 栈元素数组，只能通过转型来创建泛型数组
    private Item[] a = (Item[]) new Object[1];

    // 元素数量
    private int N = 0;


    @Override
    public MyStack<Item> push(Item item) {
        check();
        a[N++] = item;
        return this;
    }


    @Override
    public Item pop() throws Exception {

        if (isEmpty()) {
            throw new Exception("stack is empty");
        }

        Item item = a[--N];

        check();

        // 避免对象游离
        a[N] = null;

        return item;
    }


    private void check() {

        if (N >= a.length) {
            resize(2 * a.length);

        } else if (N > 0 && N <= a.length / 4) {
            resize(a.length / 2);
        }
    }


    /**
     * 调整数组大小，使得栈具有伸缩性
     */
    private void resize(int size) {

        Item[] tmp = (Item[]) new Object[size];

        for (int i = 0; i < N; i++) {
            tmp[i] = a[i];
        }

        a = tmp;
    }


    @Override
    public boolean isEmpty() {
        return N == 0;
    }


    @Override
    public int size() {
        return N;
    }


    @Override
    public Iterator<Item> iterator() {

        // 返回逆序遍历的迭代器
        return new Iterator<Item>() {

            private int i = N;

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

            @Override
            public Item next() {
                return a[--i];
            }
        };

    }
}
```

## 2. 链表实现

需要使用链表的头插法来实现，因为头插法中最后压入栈的元素在链表的开头，它的 next 指针指向前一个压入栈的元素，在弹出元素时就可以通过 next 指针遍历到前一个压入栈的元素从而让这个元素成为新的栈顶元素。

```java
public class ListStack<Item> implements MyStack<Item> {

    private Node top = null;
    private int N = 0;


    private class Node {
        Item item;
        Node next;
    }


    @Override
    public MyStack<Item> push(Item item) {

        Node newTop = new Node();

        newTop.item = item;
        newTop.next = top;

        top = newTop;

        N++;

        return this;
    }


    @Override
    public Item pop() throws Exception {

        if (isEmpty()) {
            throw new Exception("stack is empty");
        }

        Item item = top.item;

        top = top.next;
        N--;

        return item;
    }


    @Override
    public boolean isEmpty() {
        return N == 0;
    }


    @Override
    public int size() {
        return N;
    }


    @Override
    public Iterator<Item> iterator() {

        return new Iterator<Item>() {

            private Node cur = top;


            @Override
            public boolean hasNext() {
                return cur != null;
            }


            @Override
            public Item next() {
                Item item = cur.item;
                cur = cur.next;
                return item;
            }
        };

    }
}
```

# 队列

下面是队列的链表实现，需要维护 first 和 last 节点指针，分别指向队首和队尾。

这里需要考虑 first 和 last 指针哪个作为链表的开头。因为出队列操作需要让队首元素的下一个元素成为队首，所以需要容易获取下一个元素，而链表的头部节点的 next 指针指向下一个元素，因此可以让 first 指针链表的开头。

```java
public interface MyQueue<Item> extends Iterable<Item> {

    int size();

    boolean isEmpty();

    MyQueue<Item> add(Item item);

    Item remove() throws Exception;
}
```

```java
public class ListQueue<Item> implements MyQueue<Item> {

    private Node first;
    private Node last;
    int N = 0;


    private class Node {
        Item item;
        Node next;
    }


    @Override
    public boolean isEmpty() {
        return N == 0;
    }


    @Override
    public int size() {
        return N;
    }


    @Override
    public MyQueue<Item> add(Item item) {

        Node newNode = new Node();
        newNode.item = item;
        newNode.next = null;

        if (isEmpty()) {
            last = newNode;
            first = newNode;
        } else {
            last.next = newNode;
            last = newNode;
        }

        N++;
        return this;
    }


    @Override
    public Item remove() throws Exception {

        if (isEmpty()) {
            throw new Exception("queue is empty");
        }

        Node node = first;
        first = first.next;
        N--;

        if (isEmpty()) {
            last = null;
        }

        return node.item;
    }


    @Override
    public Iterator<Item> iterator() {

        return new Iterator<Item>() {

            Node cur = first;


            @Override
            public boolean hasNext() {
                return cur != null;
            }


            @Override
            public Item next() {
                Item item = cur.item;
                cur = cur.next;
                return item;
            }
        };
    }
}
```
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