【一起学数据结构与算法】深度学习栈

一、什么是栈？

栈（stack）又名堆栈，它是一种运算受限的线性表。限定仅在表尾进行插入和删除操作的线性表。这一端被称为栈顶，相对地，把另一端称为栈底。向一个栈插入新元素又称作进栈、入栈或压栈，它是把新元素放到栈顶元素的上面，使之成为新的栈顶元素；从一个栈删除元素又称作出栈或退栈，它是把栈顶元素删除掉，使其相邻的元素成为新的栈顶元素。

压栈：栈的插入操作叫做进栈/压栈/入栈，入数据在栈顶。
出栈：栈的删除操作叫做出栈。出数据在栈顶。

二、怎么使用栈？

栈的基本操作主要有：判空、判满、取栈顶元素、在栈顶进行插入和删除。在栈顶插入元素称为入栈，在栈顶删除元素称为出栈。

2.1 入栈 - push()

        Stack<Integer> s1 = new Stack<>();
        s1.push(1);
        s1.push(2);
        s1.push(3);
        s1.push(4);
        System.out.println(s1);

2.2 判空 - empty()

        Stack<Integer> s1 = new Stack<>();
        s1.push(1);
        s1.push(2);
        s1.push(3);
        s1.push(4);
        System.out.println(s1.empty());

2.3 出栈 - pop()

      Stack<Integer> s1 = new Stack<>();
	  s1.push(1);
      s1.push(2);
      s1.push(3);
      s1.push(4);
      System.out.println(s1);
      s1.pop();
      System.out.println(s1);

2.4 获取栈顶元素 - peek()

        Stack<Integer> s1 = new Stack<>();
        s1.push(1);
        s1.push(2);
        s1.push(3);
        s1.push(4);
        System.out.println(s1);
        s1.peek();
        System.out.println(s1);
        System.out.println(s1.peek());

2.5 获取栈中有效元素个数 - size()

        Stack<Integer> s1 = new Stack<>();
        s1.push(1);
        s1.push(2);
        s1.push(3);
        s1.push(4);
        System.out.println(s1.size());

三、栈的模拟实现

3.1 push

	public boolean isFull() {
        return this.usedSize == this.elem.length;
    }

    public void push(int val) {
        if (isFull()) {
            //扩容
            this.elem = Arrays.copyOf(this.elem,2*this.usedSize);
        }
        this.elem[this.usedSize] = val;
        this.usedSize++;
    }

3.2 isEmpty

	public boolean isEmpty() {
        return this.usedSize == 0;
    }

3.3 pop

	public int pop() {
        if (isEmpty()) {
            throw new RuntimeException("栈为空");
        }
        int oldVal = this.elem[usedSize-1];
        this.usedSize--;
        return oldVal;
    }

3.4 peek

	public int peek() {
        if (isEmpty()) {
            throw new RuntimeException("栈为空");
        }
        return this.elem[usedSize-1];
    }

3.5 MyStack.java

import java.lang.reflect.Array;
import java.util.Arrays;

@SuppressWarnings({"all"})
public class MyStack {
    public int[] elem;
    public int usedSize;

    public MyStack() {
        this.elem = new int[5];
    }

    public void push(int val) {
        if (isFull()) {
            //扩容
            this.elem = Arrays.copyOf(this.elem,2*this.usedSize);
        }
        this.elem[this.usedSize] = val;
        this.usedSize++;
    }

    public boolean isFull() {
        return this.usedSize == this.elem.length;
    }

    public int pop() {
        if (isEmpty()) {
            throw new RuntimeException("栈为空");
        }
        int oldVal = this.elem[usedSize-1];
        this.usedSize--;
        return oldVal;
    }

    public int peek() {
        if (isEmpty()) {
            throw new RuntimeException("栈为空");
        }
        return this.elem[usedSize-1];
    }

    public boolean isEmpty() {
        return this.usedSize == 0;
    }
}

四、经典题

4.1 有效的括号

class Solution {
    public boolean isValid(String s) {
        Stack<Character> stack = new Stack<>();

        for (int i = 0; i < s.length(); i++) {
            char ch = s.charAt(i);
            if (ch == '(' || ch == '[' || ch == '{') {
                //如果是左括号 直接入栈
                stack.push(ch);
            } else {
                //遇到了右括号
                if (stack.empty()) {
                    System.out.println("右括号多");
                    return false;
                } 
                char top = stack.peek();//哪个左括号
                if (top == '(' && ch ==')' || top == '[' && ch ==']' || top == '{' && ch =='}') {
                    stack.pop();
                } else {
                    System.out.println("左右括号不匹配");
                    return false;
                }
            }
        }
        if (!stack.empty()) {
            System.out.println("左括号多");
            return false;
        }
        return true;
    }
}

4.2 逆波兰表达式求值

class Solution {
    public int evalRPN(String[] tokens) {
        Stack<Integer> stack = new Stack<>();
        for (int i = 0; i < tokens.length; i++) {
            String val = tokens[i];
            if (!isOperation(val)) {
                stack.push(Integer.parseInt(val));
            } else {        
                int num2 = stack.pop();
                int num1 = stack.pop();
                switch (val) {
                    case "+":
                        stack.push(num1+num2);
                        break;
                    case "-":
                        stack.push(num1-num2);
                        break;
                    case "*":
                        stack.push(num1*num2);
                        break;
                    case "/":
                        stack.push(num1/num2);
                        break;
                }
            }
        }
        return stack.pop();
    }
    private boolean isOperation(String x) {
        if (x.equals("+") || x.equals("-") || x.equals("*") || x.equals("/")) {
            return true;
        }
        return false;
    }
}