我們常用的1+1, 2 * 4 / 2 - 3等運算表達式為中綴表達式，運算符在數據中間，而計算機運算時需要轉成后綴表達式也就是逆波蘭表達式。逆波蘭表達式將運算的順序從左往右依次排序輸出進行運算，運算時遇到操作符就將操作符前兩位進行順序運算，最終得到結果。
中綴表達式轉后綴表達式主要用到了棧進行運算符處理，隊列進行排序輸出，規則為：
1.數字直接入隊列
2.運算符要與棧頂元素比較
-棧為空直接入棧
-運算符優先級大於棧頂元素優先級則直接入棧
-小於或等於則出棧入列，再與棧頂元素進行比較，直到運算符優先級小於棧頂元素優先級后，操作符再入棧
3.操作符是 ( 則無條件入棧
4.操作符為 )，則依次出棧入列，直到匹配到第一個(為止，此操作符直接舍棄，棧頂)直接出棧舍棄
package calc;
import java.util.*;
import java.util.regex.Pattern;
public class MultiCalc {
/**
* 匹配 + - * / ( ) 運算符
*/
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;
/**
* 括號
*/
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、換頁符等等, 等價於[ \f\n\r\t\v]
return s.replaceAll("\\s+","");
}
/**
* 判斷是不是數字 int double long float
* @param s
* @return
*/
public static boolean isNumber(String s){
Pattern pattern = Pattern.compile("^[-\\+]?[.\\d]*$");
return pattern.matcher(s).matches();
}
/**
* 判斷是不是運算符
* @param s
* @return
*/
public static boolean isSymbol(String s){
return s.matches(SYMBOL);
}
/**
* 匹配運算等級
* @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)+"";
//棧為空，(操作符，或者 操作符優先級大於棧頂優先級 && 操作符優先級不是( )的優先級 及是 ) 不能直接入棧
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())){
//棧非空，操作符優先級小於等於棧頂優先級時出棧入列，直到棧為空，或者遇到了(，最后操作符入棧
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，依次出棧入列直到空棧或者遇到了第一個)操作符，此時)出棧
while (!stack.isEmpty() && LEVEL_HIGH >= calcLevel(stack.peek())){
if(LEVEL_HIGH == calcLevel(stack.peek())){
stack.pop();
break;
}
data.add(stack.pop());
}
}
start = i ; //前一個運算符的位置
}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");
}
}
//如果棧里還有元素，此時元素需要依次出棧入列，可以想象棧里剩下棧頂為/，棧底為+，應該依次出棧入列，可以直接翻轉整個stack 添加到隊列
Collections.reverse(stack);
data.addAll(new ArrayList<>(stack));
System.out.println(data);
return data;
}
/**
* 算出結果
* @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;
}
/**
* 運算
* @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();
}
}
}