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前缀表达式计算与中缀表达式转换

一、前缀表达式计算方法

前缀表达式（Prefix Expression）是一种无需括号的表达式形式，计算时从右到左扫描，数字直接入栈，运算符则弹出栈顶两个数进行计算。具体步骤如下：

二、中缀表达式转换为前缀表达式

中缀表达式（Infix Expression）通常需要括号来明确运算优先级。将中缀表达式转换为前缀表达式的方法如下：

三、代码实现

package fighting;import java.util.Scanner;import java.util.Stack;import java.util.HashSet;public class Fighting {    private static HashSet
   
     oper = new HashSet<>();    private static void initOper() {        oper.add('+');        oper.add('-');        oper.add('*');        oper.add('/');    }    private static boolean isOper(char c) {        return oper.contains(c);    }    private static boolean isNum(char c) {        return c >= '0' && c <= '9';    }    private static int priority(char c) {        switch (c) {            case '*':            case '/':                return 3;            case '+':            case '-':                return 2;            case ')':                return 1;            default:                System.out.println("输入错误！");                return 0;        }    }    public static int calculate(String str) {        Stack
    
      numStack = new Stack<>();        char c;        for (int i = str.length() - 1; i >= 0; i--) {            if (isNum(c = str.charAt(i))) {                numStack.push(c - '0');            } else {                int num1 = numStack.pop();                int num2 = numStack.pop();                switch (c) {                    case '+':                        numStack.push(num1 + num2);                        break;                    case '-':                        numStack.push(num1 - num2);                        break;                    case '*':                        numStack.push(num1 * num2);                        break;                    case '/':                        if (num2 != 0) {                            numStack.push(num1 / num2);                        } else {                            throw new RuntimeException("除数不能为零！");                        }                        break;                }            }        }        return numStack.pop();    }    public static void main(String[] args) {        initOper();        System.out.println("请输入表达式：");        Scanner sc = new Scanner(System.in());        String expression = sc.nextLine();        StringBuilder preExpression = new StringBuilder();        Stack
     
       operStack = new Stack<>();        for (int i = expression.length() - 1; i >= 0; i--) {            char c = expression.charAt(i);            if (isNum(c)) {                preExpression.append(c);            } else if (isOper(c)) {                if (operStack.isEmpty()) {                    operStack.push(c);                } else {                    while (true) {                        if (operStack.isEmpty() || priority(operStack.peek()) <= priority(c)) {                            break;                        }                        char pop = operStack.pop();                        preExpression.append(pop);                    }                    operStack.push(c);                }            } else if (c == ')') {                operStack.push(c);            } else if (c == '(') {                while ((pop = operStack.pop()) != ')') {                    preExpression.append(pop);                }            } else {                System.out.println("输入表达式有误！");            }        }        while (!operStack.isEmpty()) {            char pop = operStack.pop();            preExpression.append(pop);        }        preExpression = preExpression.reverse();        System.out.println("转换后的前缀表达式为：" + preExpression.toString());        System.out.println("前缀表达式计算的结果为：" + calculate(preExpression.toString()));    }}
     
    
   

运行结果

转换后的前缀表达式为：( 3 1 + 2 * ) ( ( 5 3 - ) 4 / )

计算结果：38

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