利用栈对表达式求值
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Title</title>
<script src="js.js"></script>
</head>
<body>
输入中缀表达式空格分隔 例如 2 + 3
<input type="text" id="input" value=""><input type="button" onclick="fun()" value="计算">
<div id="aa">
</div>
<script>
/*
*
* #Re:【js数据结构】栈解决括号不匹配问题
*
*一个算术表达式的后缀表达式形式如下: op1 op2 operator
*使用两个栈，一个用来存储操作数，另外一个用来存储操作符，设计并实现一个 JavaScript 函 数，该函数可以将中缀表达式转换为后缀表达式，然后利用栈对该表达式求值。
*/
function Stack()
{
this.top = 0;
this.arr = [];
this.push = push;
this.pop = pop;
this.peek = peek;
this.clear = clear;
this.len = len;
this.isEmpty = isEmpty;
}
function push(val)
{
this.arr[this.top++] = val;
}
function pop()
{
return this.arr[--this.top];
}
function peek(){
return this.arr[this.top-1];
}
function clear(){
delete this.arr;
this.top = 0;
this.arr = [];
}
function len(){
return this.top;
}
function isEmpty() {
if(this.len() <= 0)
return true;
else
return false;
}
function operatorFun(result, val, operator)
{
switch (operator)
{
case "+":
return parseInt(result) + parseInt(val);
break;
case "-":
return result - val;
break;
case "*":
return result * val;
break;
case "/":
return result / val;
break;
}
}
var numStack = new Stack();
var operatorStack = new Stack();
function fun() {
var Str = document.getElementById("input").value;
strline = Str.split(" ");
for(var i = 0; i<strline.length; i++)
{
if(i%2 == 0)
numStack.push(strline[i])
else
operatorStack.push(strline[i])
}
var op, operator, result;
if(numStack.len()>0)
result = numStack.pop()
while(numStack.len()>0 && operatorStack.len()>0)
{
operator = operatorStack.pop();
op = numStack.pop();
result = operatorFun(result, op, operator)
}
console.log(result)
}
</script>
</body>
</html>
展示如下：
顺序从右向左，无优先级顺序，图中顺序 4*5=20， 20+4=24，结果为24
考虑优先级的运算表达式求值
以上为不考虑优先级的表达式求值方法，那么接下来考虑优先级时，将考虑：
- 先乘除
- 后加减
- 有括号先算括号里
换成编程思路：
执行表达式运算时，总是将结果压入numStack栈
1. 遇到 “+”、“-” 操作符时，优先级最低，先计算栈内已存数据的加减乘除操作
2. 遇到 “*” 、“/” 操作符时，计算栈内已存数据的乘除操作
3. 遇到 “(” 直接入operatorStack
4. 遇到 “)” 运算栈内的数据，直到找到 “(”
代码如下：
function operatorFun(numStack, operatorStack)
{
var op1, op2, operator;
op1 = numStack.pop();
op2 = numStack.pop();
operator = operatorStack.pop();
switch (operator)
{
case "+":
numStack.push(parseInt(op2) + parseInt(op1));
break;
case "-":
numStack.push(op2 - op1);
break;
case "*":
numStack.push(op2 * op1);
break;
case "/":
numStack.push(op2 / op1);
break;
}
}
function fun() {
var Str = document.getElementById("input").value;
strline = Str.split(" ");
for(var i = 0; i<strline.length; i++)
{
if(strline[i] == "")
{
continue;
}
else if(strline[i] == "+" ||strline[i] == "-")
{
while((operatorStack.len() !=0 ) && (operatorStack.peek() == "+" || operatorStack.peek() == "-"|| operatorStack.peek() == "*" ||operatorStack.peek() == "/"))
{
operatorFun(numStack,operatorStack);
}
operatorStack.push(strline[i])
}
else if(strline[i] == "*" ||strline[i] == "/")
{
while((operatorStack.len() !=0 ) && (operatorStack.peek() == "*" ||operatorStack.peek() == "/"))
{
operatorFun(numStack,operatorStack);
}
operatorStack.push(strline[i])
}
else if(strline[i] == "(" )
{
operatorStack.push('(')
}
else if(strline[i] == ")" )
{
while(operatorStack.peek() != "(")
{
operatorFun(numStack,operatorStack);
}
operatorStack.pop();
}
else
{
numStack.push(strline[i])
}
}
while(operatorStack.len() != 0)
{
operatorFun(numStack,operatorStack);
}
console.log(numStack.pop()) ;
}
例如：计算 3 * 3 - ( 12 + 3 * 2 ) / 3
欢迎补充。
