一、基本介绍
二、应用实例
package stack;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
public class InffixToSuffixExpression {
public static void main(String[] args) {
String inffixExpression = "1+((2+3)*4)-5";
List<String> inffiExpression_list = toList(inffixExpression); // 获得中缀表达式对应的List集合
List<String> suffixExpression_list = toParseSuffixExpression(inffiExpression_list);
Collections.reverse(suffixExpression_list); // 将list集合逆序，即为对应的后缀表达式
String suffixExpression = String.join("", suffixExpression_list); // 将list集合转为字符串
System.out.println("中缀表达式：" + inffixExpression);
System.out.println("后缀表达式：" + suffixExpression);
System.out.println("后缀表达式(逆波兰表达式)求值：" + calculate(suffixExpression_list));
}
// inffixExpression = "1+((2+3)*4)-5";
public static List<String> toList(String inffixExpression) {
List<String> list = new ArrayList<>();
char ch = ' ';
int index = 0;
String temp;
while (index != inffixExpression.length()) {
// 如果该字符是非数字，则将其直接放入list数组
if ((ch = inffixExpression.charAt(index)) < 48 || (ch = inffixExpression.charAt(index)) > 57) {
list.add(ch + "");
index++;
} else {
// 如果该字符是数字，则需要考虑多位数的情况
temp = ""; // 每循环一轮，都需将字符串置为空
while (index < inffixExpression.length() && (((ch = inffixExpression.charAt(index)) >= 48) && ((ch = inffixExpression.charAt(index)) <= 57))) {
temp += ch;
index++;
}
list.add(temp);
}
}
return list;
}
private static List<String> toParseSuffixExpression(List<String> list) {
Stack operStack = new Stack(32);
Stack tempStack = new Stack(32);
String op = "";
// 2、从左至右扫描中缀表达式
for (String item : list) {
// 3、遇到是数字时
if (item.matches("\\d+")) { // 匹配多位数
tempStack.push(item);
// 3.1、遇到左括号
} else if (item.equals("(")) {
operStack.push(item);
// 3.2、遇到右括号
} else if (item.equals(")")) {
while (!operStack.peek().equals("(")) {
tempStack.push(operStack.pop());
}
operStack.pop(); // 将左括号出栈
// 4、遇到运算符时
} else {
// 4.1、operStack栈为空 或 栈顶元素为（ 时，直接将元素入栈
if (operStack.isEmpty() || operStack.peek().equals("(")) {
operStack.push(item);
// 4.2、该字符元素优先级比栈顶元素优先级高，则直接入栈
} else if (operStack.priority(item) > operStack.priority(operStack.peek())) {
operStack.push(item);
} else {
// 4.3、该字符元素的优先级 <= 栈顶元素的优先级
while(!operStack.isEmpty() && operStack.priority(item) <= operStack.priority(operStack.peek())) {
tempStack.push(operStack.pop());
}
// 退出while循环时，一般为当前元素的优先级高于栈顶元素的优先级，所以要将该元素直接入栈
operStack.push(item);
}
}
}
// 5、将operStack剩余的运算符弹出并压入tempStack
while (!operStack.isEmpty()) {
tempStack.push(operStack.pop());
}
// 6、弹出tempStack的元素放入List数组中返回，结果的逆序即为对应的后缀表达式
List<String> resultList = new ArrayList();
while(!tempStack.isEmpty()) {
resultList.add(tempStack.pop());
}
return resultList;
}
private static String calculate(List<String> list) {
Stack stack = new Stack(16);
int num1 = 0;
int num2 = 0;
int res = 0;
for (String item : list) {
if (item.matches("\\d+")) { // 匹配多位数字
stack.push(item);
} else {
num1 = Integer.parseInt(stack.pop());
num2 = Integer.parseInt(stack.pop());
if (item.equals("+")) {
res = num1 + num2;
} else if (item.equals("-")) {
res = num2 - num1;
} else if (item.equals("*")) {
res = num1 * num2;
} else if (item.equals("/")) {
res = num2 / num1;
} else {
System.out.println("无效运算符！");
}
stack.push(res+"");
}
}
// 栈中最后的值即为表达式的结果
return stack.pop();
}
}
class Stack {
private String[] arr;
private int maxSize;
private int top;
public Stack(int maxSize) {
this.maxSize = maxSize;
this.arr = new String[maxSize];
this.top = -1;
}
public String peek() {
return arr[top];
}
public void push(String val) {
if (isFull()) {
throw new RuntimeException("栈满，入栈失败！");
}
arr[++top] = val;
}
public String pop() {
if (isEmpty()) {
throw new RuntimeException("栈空，出栈失败！");
}
return arr[top--];
}
public void print() {
if (isEmpty()) {
throw new RuntimeException("栈空，出栈失败！");
}
System.out.print("栈元素：");
for (int i = top; i >= 0 ; i--) {
System.out.print(arr[i] + " ");
}
System.out.println();
}
public boolean isEmpty() {
if (top == -1) {
return true;
}
return false;
}
public boolean isFull() {
if (top == maxSize - 1) {
return true;
}
return false;
}
public int priority(String ch) {
if (ch == "x" || ch == "/") {
return 1;
} else if (ch == "+" || ch == "-") {
return 0;
} else {
return -1;
}
}
}
