逆波兰表达式计算器
逆波兰表达式计算器
先看效果
实现过程
- 将算式解析为中缀表达式
- 将中缀表达式转换为后缀表达式
- 计算
中缀表达式
什么是中缀表达式？
中缀表达式是一种数学表达式的书写方式，指的是运算符位于操作数之间的表达式。
直白一点讲,例如:"(3+4)*5",这个就是中缀表达式
后缀表达式
什么是后缀表达式？
后缀表达式（也叫做逆波兰式）：运算符位于操作数之后，例如"3 4 +"表示加法运算3和4， 计算结果为7。
中缀表达式转后缀表达式
[(, (, 100, +, 101, ), +, (, 102, +, 103, ), ), *, 104, +, 105]
算式转中缀表达式咱们就不细说怎么做了，这个太基础了。
中缀表达式转后缀表达式。
使用一个list，stack和map。
list用于存放最终的表达式的元素，
stack用于临时存放运算符和数值，
map中初始化四个运算符，key为运算符，value为优先级，“*”,“/“的优先级为2，”+”,"-"的优先级为1
接下来直接看代码吧
转换结果：
[100, 101, +, 102, 103, +, +, 104, *, 105, +]
List<String> infixExpression = Arrays.asList("(", "(", "100", "+", "101", ")", "+", "(", "102", "+", "103", ")", ")", "*", "104","+","105");
List<String> rpnExpression = convertToRPN(infixExpression);
public static List<String> convertToRPN(List<String> infixExpression) {
Map<String, Integer> precedence = new HashMap<>(); // 初始化四个运算符，并配置优先级
precedence.put("+", 1);
precedence.put("-", 1);
precedence.put("*", 2);
precedence.put("/", 2);
Stack<String> operatorStack = new Stack<>();
List<String> output = new ArrayList<>();
for (String token : infixExpression) {
if (isNumber(token)) {
output.add(token);
} else if (token.equals("(")) {
operatorStack.push(token);
} else if (token.equals(")")) {
while (!operatorStack.isEmpty() && !operatorStack.peek().equals("(")) {
output.add(operatorStack.pop());
}
operatorStack.pop(); // 弹出左括号
} else if (isOperator(token)) {
while (!operatorStack.isEmpty() && precedence.getOrDefault(operatorStack.peek(), 0) >= precedence.get(token)) {
output.add(operatorStack.pop());
}
operatorStack.push(token);
}
}
while (!operatorStack.isEmpty()) {
output.add(operatorStack.pop());
}
return output;
}
public static boolean isNumber(String token) {
return token.matches("\\d+");
}
public static boolean isOperator(String token) {
return token.equals("+") || token.equals("-") || token.equals("*") || token.equals("/");
}
使用后缀表达式计算出结果
List<String> rpnExpression = convertToRPN(infixExpression);
int result = evaluateRPN(rpnExpression);
public static int evaluateRPN(List<String> rpnExpression) {
Stack<Integer> stack = new Stack<>();
for (String token : rpnExpression) {
if (isNumber(token)) {
stack.push(Integer.parseInt(token));
} else if (isOperator(token)) {
int operand2 = stack.pop();
int operand1 = stack.pop();
int result = evaluate(operand1, operand2, token);
stack.push(result);
}
}
return stack.pop();
}
public static int evaluate(int operand1, int operand2, String operator) {
switch (operator) {
case "+":
return operand1 + operand2;
case "-":
return operand1 - operand2;
case "*":
return operand1 * operand2;
case "/":
return operand1 / operand2;
default:
throw new IllegalArgumentException("Unknown operator: " + operator);
}
}
完整代码
package com.tfxing.persondaily;
import java.util.*;
public class Main {
public static void main(String[] args) {
List<String> infixExpression = Arrays.asList("(", "(", "100", "+", "101", ")", "+", "(", "102", "+", "103", ")", ")", "*", "104","+","105");
System.out.println(infixExpression);
List<String> rpnExpression = convertToRPN(infixExpression);
System.out.println(rpnExpression);
int result = evaluateRPN(rpnExpression);
System.out.println(result);
}
public static List<String> convertToRPN(List<String> infixExpression) {
Map<String, Integer> precedence = new HashMap<>();
precedence.put("+", 1);
precedence.put("-", 1);
precedence.put("*", 2);
precedence.put("/", 2);
Stack<String> operatorStack = new Stack<>();
List<String> output = new ArrayList<>();
for (String token : infixExpression) {
if (isNumber(token)) {
output.add(token);
} else if (token.equals("(")) {
operatorStack.push(token);
} else if (token.equals(")")) {
while (!operatorStack.isEmpty() && !operatorStack.peek().equals("(")) {
output.add(operatorStack.pop());
}
operatorStack.pop(); // 弹出左括号
} else if (isOperator(token)) {
while (!operatorStack.isEmpty() && precedence.getOrDefault(operatorStack.peek(), 0) >= precedence.get(token)) {
output.add(operatorStack.pop());
}
operatorStack.push(token);
}
}
while (!operatorStack.isEmpty()) {
output.add(operatorStack.pop());
}
return output;
}
public static boolean isNumber(String token) {
return token.matches("\\d+");
}
public static boolean isOperator(String token) {
return token.equals("+") || token.equals("-") || token.equals("*") || token.equals("/");
}
public static int evaluateRPN(List<String> rpnExpression) {
Stack<Integer> stack = new Stack<>();
for (String token : rpnExpression) {
if (isNumber(token)) {
stack.push(Integer.parseInt(token));
} else if (isOperator(token)) {
int operand2 = stack.pop();
int operand1 = stack.pop();
int result = evaluate(operand1, operand2, token);
stack.push(result);
}
}
return stack.pop();
}
public static int evaluate(int operand1, int operand2, String operator) {
switch (operator) {
case "+":
return operand1 + operand2;
case "-":
return operand1 - operand2;
case "*":
return operand1 * operand2;
case "/":
return operand1 / operand2;
default:
throw new IllegalArgumentException("Unknown operator: " + operator);
}
}
}