逆波兰表达式

Posted 2020-11-07 sansamh

我们常用的1+1, 2 * 4 / 2 - 3等运算表达式为中缀表达式，运算符在数据中间，而计算机运算时需要转成后缀表达式也就是逆波兰表达式。逆波兰表达式将运算的顺序从左往右依次排序输出进行运算，运算时遇到操作符就将操作符前两位进行顺序运算，最终得到结果。

中缀表达式转后缀表达式主要用到了栈进行运算符处理，队列进行排序输出，规则为：

1.数字直接入队列
2.运算符要与栈顶元素比较
-栈为空直接入栈
-运算符优先级大于栈顶元素优先级则直接入栈
-小于或等于则出栈入列，再与栈顶元素进行比较，直到运算符优先级小于栈顶元素优先级后，操作符再入栈
3.操作符是 ( 则无条件入栈
4.操作符为 )，则依次出栈入列，直到匹配到第一个(为止，此操作符直接舍弃，栈顶)直接出栈舍弃

package calc;

import java.util.*;
import java.util.regex.Pattern;

public class MultiCalc {
    /**
     * 匹配 + - * / ( ) 运算符
     */
    static final String SYMBOL = "\\+|-|\\*|/|\\(|\\)";

    static final String LEFT = "(";
    static final String RIGHT = ")";
    static final String ADD = "+";
    static final String MINUS= "-";
    static final String TIMES = "*";
    static final String DIVISION = "/";

    /**
     * 加減 + -
     */
    static final int LEVEL_01 = 1;
    /**
     * 乘除 * /
     */
    static final int LEVEL_02 = 2;

    /**
     * 括号
     */
    static final int LEVEL_HIGH = Integer.MAX_VALUE;


    static Stack<String> stack = new Stack<>();
    static List<String> data = Collections.synchronizedList(new ArrayList<String>());

    /**
     * 去除所有空白符
     * @param s
     * @return
     */
    public static String replaceAllBlank(String s ){
        // \\s+ 匹配任何空白字符，包括空格、制表符、换页符等等, 等价于[ \f\n\r\t\v]
        return s.replaceAll("\\s+","");
    }

    /**
     * 判断是不是数字 int double long float
     * @param s
     * @return
     */
    public static boolean isNumber(String s){
        Pattern pattern = Pattern.compile("^[-\\+]?[.\\d]*$");
        return pattern.matcher(s).matches();
    }

    /**
     * 判断是不是运算符
     * @param s
     * @return
     */
    public static boolean isSymbol(String s){
        return s.matches(SYMBOL);
    }

    /**
     * 匹配运算等级
     * @param s
     * @return
     */
    public static int calcLevel(String s){
        if("+".equals(s) || "-".equals(s)){
            return LEVEL_01;
        } else if("*".equals(s) || "/".equals(s)){
            return LEVEL_02;
        }
        return LEVEL_HIGH;
    }

    /**
     * 匹配
     * @param s
     * @throws Exception
     */
    public static List<String> doMatch (String s) throws Exception{
        if(s == null || "".equals(s.trim())) throw new RuntimeException("data is empty");
        if(!isNumber(s.charAt(0)+"")) throw new RuntimeException("data illeagle,start not with a number");

        s = replaceAllBlank(s);

        String each;
        int start = 0;

        for (int i = 0; i < s.length(); i++) {
            if(isSymbol(s.charAt(i)+"")){
                each = s.charAt(i)+"";
                //栈为空，(操作符，或者 操作符优先级大于栈顶优先级 && 操作符优先级不是( )的优先级 及是 ) 不能直接入栈
                if(stack.isEmpty() || LEFT.equals(each)
                        || ((calcLevel(each) > calcLevel(stack.peek())) && calcLevel(each) < LEVEL_HIGH)){
                    stack.push(each);
                }else if( !stack.isEmpty() && calcLevel(each) <= calcLevel(stack.peek())){
                    //栈非空，操作符优先级小于等于栈顶优先级时出栈入列，直到栈为空，或者遇到了(，最后操作符入栈
                    while (!stack.isEmpty() && calcLevel(each) <= calcLevel(stack.peek()) ){
                        if(calcLevel(stack.peek()) == LEVEL_HIGH){
                            break;
                        }
                        data.add(stack.pop());
                    }
                    stack.push(each);
                }else if(RIGHT.equals(each)){
                    // ) 操作符，依次出栈入列直到空栈或者遇到了第一个)操作符，此时)出栈
                    while (!stack.isEmpty() && LEVEL_HIGH >= calcLevel(stack.peek())){
                        if(LEVEL_HIGH == calcLevel(stack.peek())){
                            stack.pop();
                            break;
                        }
                        data.add(stack.pop());
                    }
                }
                start = i ;    //前一个运算符的位置
            }else if( i == s.length()-1 || isSymbol(s.charAt(i+1)+"") ){
                each = start == 0 ? s.substring(start,i+1) : s.substring(start+1,i+1);
                if(isNumber(each)) {
                    data.add(each);
                    continue;
                }
                throw new RuntimeException("data not match number");
            }
        }
        //如果栈里还有元素，此时元素需要依次出栈入列，可以想象栈里剩下栈顶为/，栈底为+，应该依次出栈入列，可以直接翻转整个stack 添加到队列
        Collections.reverse(stack);
        data.addAll(new ArrayList<>(stack));

        System.out.println(data);
        return data;
    }

    /**
     * 算出结果
     * @param list
     * @return
     */
    public static Double doCalc(List<String> list){
        Double d = 0d;
        if(list == null || list.isEmpty()){
            return null;
        }
        if (list.size() == 1){
            System.out.println(list);
            d = Double.valueOf(list.get(0));
            return d;
        }
        ArrayList<String> list1 = new ArrayList<>();
        for (int i = 0; i < list.size(); i++) {
            list1.add(list.get(i));
            if(isSymbol(list.get(i))){
                Double d1 = doTheMath(list.get(i - 2), list.get(i - 1), list.get(i));
                list1.remove(i);
                list1.remove(i-1);
                list1.set(i-2,d1+"");
                list1.addAll(list.subList(i+1,list.size()));
                break;
            }
        }
        doCalc(list1);
        return d;
    }

    /**
     * 运算
     * @param s1
     * @param s2
     * @param symbol
     * @return
     */
    public static Double doTheMath(String s1,String s2,String symbol){
        Double result ;
        switch (symbol){
            case ADD : result = Double.valueOf(s1) + Double.valueOf(s2); break;
            case MINUS : result = Double.valueOf(s1) - Double.valueOf(s2); break;
            case TIMES : result = Double.valueOf(s1) * Double.valueOf(s2); break;
            case DIVISION : result = Double.valueOf(s1) / Double.valueOf(s2); break;
            default : result = null;
        }
        return result;

    }

    public static void main(String[] args) {
        String math = "9+(3-1)*3+10/2";
//        String math = "1.8+(2-3.5)*4+10/5.0";
        try {
            long start = System.currentTimeMillis();
            doCalc(doMatch(math));
            long end = System.currentTimeMillis();
            System.out.println(end - start);
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
}