1.什么是棧
先進后出，元素的刪除和插入只能在同一端的一種線性表

2.棧的實現(xiàn)方式
數(shù)組和鏈表都可以，本次使用數(shù)組

3.什么是中綴表達式
3+2-1*6+10

4.代碼：

/**
 * @author shengjk1
 * @date 2020/2/13
 */
public class Calcaulator {
    public static void main(String[] args) {
        // 中綴表達式
        String expression = "5-1*6+2";
        //創(chuàng)建兩個棧 數(shù)棧、符號棧
        ArrayStack1 numStack = new ArrayStack1(10);
        ArrayStack1 operStack = new ArrayStack1(10);
        
        //用于遍歷
        int index = 0;
        int num1, num2 = 0;
        int oper = 0;
        int res = 0;
        //每次掃描得到的char
        char ch = ' ';
        //用來拼接多位數(shù)
        String keepNum = "";
        
        while (true) {
            ch = expression.substring(index, index + 1).charAt(0);
            //判斷 ch 是什么，然后做相應的處理
            if (operStack.isOper(ch)) {
                //判斷當前的符號棧是否為空
                if (!operStack.isEmpty()) {
                    //如果當前的操作符的優(yōu)先級小于等于棧中符號的優(yōu)先級，就需要從數(shù)棧中 pop  兩個數(shù)
                    //在從符號棧中 pop 出一個符號，進行運算，將得到結果，入數(shù)棧，然后將當前的操作符入符號棧
                    if (operStack.priority(ch) <= operStack.priority(operStack.peek())) {
                        num1 = numStack.pop();
                        num2 = numStack.pop();
                        oper = operStack.pop();
                        res = numStack.cal(num1, num2, oper);
                        //運算的結果入數(shù)棧
                        numStack.push(res);
                        //然后將當前的操作符入符號棧
                        operStack.push(ch);
                    } else {
                        //如果當前的操作符大于棧中的操作符，就直接入符號棧
                        operStack.push(ch);
                    }
                } else {
                    //如果為空，直接入符號棧
                    operStack.push(ch);
                }
            } else {
                // 如果是數(shù)字則直接入數(shù)棧
//              numStack.push(ch - 48);
                //看 index 后一位，如果是數(shù)則繼續(xù)進行掃描，如果不是則入棧
                keepNum += ch;
                if (index == expression.length() - 1) {
                    numStack.push(Integer.parseInt(keepNum));
                } else {
                    if (operStack.isOper(expression.substring(index + 1, index + 2).charAt(0))) {
                        numStack.push(Integer.parseInt(keepNum));
                        keepNum = "";
                    }
                }
            }
            //讓 index +1，并判斷是否掃描到 exoression 最后
            index++;
            if (index >= expression.length()) {
                break;
            }
        }
        
        //當表達式掃描完畢，就順序的從數(shù)棧和符號棧中pop出相應的數(shù)和符號，并運行
        while (true) {
            if (operStack.isEmpty()) {
                break;
            }
            num1 = numStack.pop();
            num2 = numStack.pop();
            oper = operStack.pop();
            res = numStack.cal(num1, num2, oper);
            //運算的結果入數(shù)棧
            numStack.push(res);
        }
        System.out.printf("表達式 %s = %d ", expression, numStack.pop());
    }
}

class ArrayStack1 {
    private int maxSize;
    private int[] stack;
    private int top = -1;
    
    public ArrayStack1(int maxSize) {
        this.maxSize = maxSize;
        stack = new int[maxSize];
    }
    
    
    // 棧滿
    public boolean isFull() {
        return top == maxSize - 1;
    }
    
    //?？?    public boolean isEmpty() {
        return top == -1;
    }
    
    //查看當前棧頂?shù)闹?    public int peek() {
        return stack[top];
    }
    
    //入棧
    public void push(int element) {
        if (isFull()) {
            System.out.println("棧滿");
            return;
        }
        top++;
        stack[top] = element;
    }
    
    //出棧
    public int pop() {
        if (isEmpty()) {
            throw new RuntimeException("stack is empty!");
        }
        int temp = stack[top];
//      stack[top]=null; 防止內存泄露
        top--;
        return temp;
    }
    
    //
    public void list() {
        if (isEmpty()) {
            System.out.println("stack is empty");
            return;
        }
        for (int i = top; i >= 0; i--) {
            System.out.printf("stack[%d]=%d\n", i, stack[i]);
        }
    }
    
    //返回運算符的優(yōu)先級 假設優(yōu)先級越高返回的數(shù)字越大
    public int priority(int oper) {
        if (oper == '*' || oper == '/') {
            return 1;
        } else if (oper == '+' || oper == '-') {
            return 0;
        } else {
            //假設目前表達式只有 + - * /
            return -1;
        }
    }
    
    /**
     * @param val
     * @return
     */
    public boolean isOper(char val) {
        return val == '+' || val == '-' || val == '*' || val == '/';
    }
    
    /**
     * 計算
     *
     * @param num1
     * @param num2
     * @param oper
     * @return
     */
    public int cal(int num1, int num2, int oper) {
        int res = 0;
        switch (oper) {
            case '+':
                res = num1 + num2;
                break;
            case '-':
                //注意順序
                res = num2 - num1;
                break;
            case '*':
                res = num1 * num2;
                break;
            case '/':
                res = num2 / num1;
                break;
            default:
                break;
        }
        return res;
    }
}

5.棧的使用場景：
1.遞歸
2.方法調用
3.表達式的轉化和求值
4.二叉樹遍歷
5.圖的深度優(yōu)先遍歷
6.逆序輸出 如 單鏈表的反轉

6.面試題
如何用兩個棧達到一個隊列的效果