栈的使用-

计算中缀表达式

要点

①算式数组expressionArr=[num,symbol,num,symbol,...,num,"end"]

②算式数值最后一个元素会被设置为符号“end”，作为算式结束标志。

②symbol符号的权重：^>*=/>+=->end>empty。

③创建数字栈numStack、符号栈symbolStack。

④符号栈为空时，调用pop()返回符号“empty”。

⑤符号empty不会参与运算，是为了确保栈symbolStack为空时，可以把符号压入栈中。

⑥符号symbol入栈前，如果判断是end，标识运算结束，跳出循环。

过程

①算式字符串expressionStr拆分成算式数组expressionArr。

②读取expressionArr中的元素，数字num进出numStack，符号symbol进出symbolStack。

③得出结果

代码

public class Expression {
    public static void main(String[] args){
        Utils utils=new Utils();
        String expressionStr="1+12*3/2^2-6*2";
        String[] expressionArr=utils.getExpressionArr(expressionStr);
        System.out.println(utils.getResult(expressionArr));
    }
}

class Utils{
    private int point=0;
    private char[] symbolArr={'+','-','*','/','^'};
    private boolean isSymbol(char symbolOrNum){
        for(int i=0;i=getWeight(topSymbol);
        //return getWeight(toPushSymbol)>=getWeight(topSymbol) 也可以
    }
    public String getResult(String[] expressionArr){
        ArrayStack numStack=new ArrayStack(10);
        ArrayStack symbolStack=new ArrayStack(10);
        int index=0;
        while(true){
            String pushNum=expressionArr[index++];
            numStack.push(pushNum);
            String topushSymbol=expressionArr[index++];
            String topSymbol=symbolStack.getLast();
            while(canPush(topushSymbol,topSymbol)==false){
                topSymbol=symbolStack.pop();
                double toPushNum=0;
                double secondNum=Double.parseDouble(numStack.pop());
                double firstNum=Double.parseDouble(numStack.pop());
                switch (topSymbol){
                    case "+":toPushNum=firstNum+secondNum;break;
                    case "-":toPushNum=firstNum-secondNum;break;
                    case "*":toPushNum=firstNum*secondNum;break;
                    case "/":toPushNum=firstNum/secondNum;break;
                    case "^":toPushNum=Math.pow(firstNum,secondNum);break;
                }
                numStack.push(String.valueOf(toPushNum));
                topSymbol=symbolStack.getLast();
            }
            if(topushSymbol=="end"){
                break;
            }
            symbolStack.push(topushSymbol);
        }
        return numStack.pop();
    }
}
class ArrayStack{
    private int maxSize;
    private String[] stack;
    public int top=-1;

    public ArrayStack(int maxSize){
        this.maxSize=maxSize;
        stack=new String[this.maxSize];
    }
    public boolean isFull(){
        return this.top==this.maxSize-1;
    }
    public boolean isEmpty(){
        return this.top==-1;
    }
    public void push(String num){
        if(this.top==this.maxSize-1){
            System.out.println("栈已满");
            return;
        }
        top++;
        stack[top]=num;
    }
    public String pop(){
        if(this.top==-1){
            return "empty";
        }
        String value=stack[this.top];
        this.top--;
        return value;
    }
    public String getLast(){
        if(this.top==-1){
            return "empty";
        }
        String value=stack[this.top];
        return value;
    }
    public void showStack(){
        for(int i=0;i<=this.top;i++){
            System.out.print(this.stack[i]+" ");
        }
        System.out.println();
    }
}

运行结果

-2

中缀表达式转后缀表达式

要点

栈symbolStack弹出符号topSymbol后，不进行计算，而是把符号topSymbol压入栈numStack。

代码

public class Expression {
    public static void main(String[] args){
        Utils utils=new Utils();
        String expressionStr="1+12*3/2^2-6*2";
        String[] expressionArr=utils.getExpressionArr(expressionStr);
        ArrayStack numStack= utils.getResult(expressionArr);
        for(;numStack.top>=0;){
            System.out.print(numStack.pop()+" ");
        }
    }
}
class Utils{
    private int point=0;
    private char[] symbolArr={'+','-','*','/','^'};
    private boolean isSymbol(char symbolOrNum){
        for(int i=0;i=getWeight(topSymbol);
    }
    public ArrayStack getResult(String[] expressionArr){
        ArrayStack numStack=new ArrayStack(15);
        ArrayStack symbolStack=new ArrayStack(15);
        int index=0;
        while(true){
            String pushNum=expressionArr[index++];
            numStack.push(pushNum);
            String topushSymbol=expressionArr[index++];
            String topSymbol=symbolStack.getLast();
            while(canPush(topushSymbol,topSymbol)==false){
                topSymbol=symbolStack.pop();
                numStack.push(topSymbol);
                topSymbol=symbolStack.getLast();
            }
            if(topushSymbol=="end"){
                break;
            }
            symbolStack.push(topushSymbol);
        }
        return numStack;
    }
}
class ArrayStack{
    private int maxSize;
    private String[] stack;
    public int top=-1;

    public ArrayStack(int maxSize){
        this.maxSize=maxSize;
        stack=new String[this.maxSize];
    }
    public boolean isFull(){
        return this.top==this.maxSize-1;
    }
    public boolean isEmpty(){
        return this.top==-1;
    }
    public void push(String num){
        if(this.top==this.maxSize-1){
            System.out.println("栈已满");
            return;
        }
        top++;
        stack[top]=num;
    }
    public String pop(){
        if(this.top==-1){
            return "empty";
        }
        String value=stack[this.top];
        this.top--;
        return value;
    }
    public String getLast(){
        if(this.top==-1){
            return "empty";
        }
        String value=stack[this.top];
        return value;
    }
    public void showStack(){
        for(int i=0;i<=this.top;i++){
            System.out.print(this.stack[i]+" ");
        }
        System.out.println();
    }
}

运行结果

+ - * 2 6 * / ^ 2 2 3 12 1