java中缀表达式转后缀表达式

四则运算是栈的重要应用之一

中缀表达式转后缀表达式（逆波兰算法）过程

1. 从左到右遍历中缀表达式
2. 数字直接输出为后缀表达式一部分
3. 如果是符号，则判断与栈顶元素的优先级
4. 高于栈顶元素优先级直接入栈
5. 低于或等于栈顶优先级栈顶元素出栈并输出为后缀表达式一部分（注意这里是递归比较栈顶元素的优先级并出栈），最后将当前元素入栈
   直到遍历完中缀表达式，最终输出后缀表达式

下面是自己的实现源码

package com.yhq.demospringboot;
import org.apache.commons.lang3.StringUtils;
import java.util.*;
import java.util.concurrent.LinkedBlockingQueue;
/**
 * yanghq
 * 2018/3/12
 */
public class PreToAfterUtil {

private static String leftChar = "(";
private static String rightChar = ")";
private static Map<String, Integer> operationSymbolMap = new HashMap<>();

static {
        //初始化符号和优先级
        operationSymbolMap.put(")",00); //右括号需匹配左括号，故优先级最低
        operationSymbolMap.put("+",10);
        operationSymbolMap.put("-",10);
        operationSymbolMap.put("*",20);
        operationSymbolMap.put("/",20);
        operationSymbolMap.put("(",30);
}

/**
 * 中缀表达式转化为后缀表达式
 * @param strings
 * @return
 */
public Queue parsePre(String[] strings) {
        Stack<String> preStack = new Stack<String>();
        Queue<String> queue = new LinkedBlockingQueue();
        int i = 0;
        while(i<strings.length && Objects.nonNull(strings[i])) {
                if(StringUtils.isNumeric(strings[i])) {
                        queue.add(strings[i]);
                }else if(StringUtils.isNotEmpty(strings[i])) {
                        if(preStack.isEmpty()) {
                                preStack.push(strings[i]);
                        } else {
                                String top = preStack.pop();
                                if(comparePriority(strings[i], top) < 0) {
                                        if(top.equals(leftChar)) {
                                                preStack.push(top);
                                                preStack.push(strings[i]);
                                        }else if(strings[i].equals(rightChar)) {
                                                appendTo(queue, top);
                                                preStack.pop();
                                        } else{
                                                appendTo(queue, top);
                                                popPre(preStack, strings[i], queue);
                                                preStack.push(strings[i]); //当前元素入栈
                                        }
                                } else {
                                        preStack.push(top);
                                        preStack.push(strings[i]);
                                }
                        }
                }
                i++;
        }
        while (!preStack.isEmpty()) {
                queue.add(preStack.pop());
        }
        return queue;
}

/**
 * 递归比较当前元素与栈顶元素优先级
 * @param preStatck
 * @param charTemp
 * @param queue
 */
public void popPre(Stack<String> preStatck, String charTemp, Queue queue) {
        if(!preStatck.isEmpty()) {
                String top = preStatck.pop();
                if(comparePriority(charTemp, top) <= 0) {
                        //低于栈顶元素，成为后缀表达式一部分
                        appendTo(queue, top);
                        popPre(preStatck, charTemp, queue);
                } else {
                        preStatck.push(top);
                }
        }
}

private void appendTo(Queue queue, String s) {
        if(!s.equals(leftChar) && !s.equals(rightChar)) {
                queue.add(s);
        }
}

/**
 * 比较优先级
 * @param start
 * @param to
 * @return
 */
private int comparePriority(String start, String to) {
        return operationSymbolMap.get(start).compareTo(operationSymbolMap.get(to));
}

/**
 * 计算后缀表达式结果
 * @param queue
 * @return
 */
public int computeResult(Queue<String> queue) {
        int result = 0;
        if(Objects.isNull(queue)) {
                return result;
        }
        String s = queue.poll();
        Stack<Integer> stack = new Stack();
        while(Objects.nonNull(s)) {
                if(StringUtils.isNumeric(s)) {
                        stack.push(Integer.valueOf(s));
                }else if(!StringUtils.isEmpty(s)) {
                        int first = 0;
                        int second = 0;
                        switch (s) {
                                case "+" :
                                        first = stack.pop();
                                        second = stack.pop();
                                        result = first + second;
                                        stack.push(result);
                                        break;
                                case "-" :
                                        first = stack.pop();
                                        second = stack.pop();
                                        result = second - first;
                                        stack.push(result);
                                        break;
                                case "*" :
                                        first = stack.pop();
                                        second = stack.pop();
                                        result = first * second;
                                        stack.push(result);
                                        break;
                                case "/" :
                                        first = stack.pop();
                                        second = stack.pop();
                                        result = second/first;
                                        stack.push(result);
                                        break;
                        }
                }
                s = queue.poll();
        }
        return result;
}

/**
 * 测试
 * @param args
 */
public static void main(String[] args) {
        String[] pre = new String[]{"8","+","(","6","-","1",")","*","2","+","10","/","2"};
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < pre.length; i++) {
                sb.append(pre[i]);
        }
        System.out.println("前缀表达式：" + sb.toString());
        Queue queue = new PreToAfterUtil().parsePre(pre);
        System.out.println("后缀表达式：" + queue.toString());
        System.out.println("后缀表达式计算结果：" + new PreToAfterUtil().computeResult(queue));
}

}

输出结果展示
前缀表达式：8+(6-1)2+10/2
后缀表达式：[8, 6, 1, -, 2, , +, 10, 2, /, +]
后缀表达式计算结果：23

原文地址：http://blog.51cto.com/11290909/2085571