第四章栈（1）

一、Stack（）类

function Stack(){
	this.dataStore=[];
	this.top=0;
	this.push=push;
	this.pop=pop;
	this.peek=peek;
	this.clear=clear;
	this.length=length;
	this.isEmpty=isEmpty;
}

function push(element){
	this.dataStore[this.top++]=element;
	return this.top;
}

function pop(){
	return this.dataStore[--this.top];
}

function peek(){
	return this.dataStore[this.top-1];
}

function length(){
	return this.top;
}

function clear(){
	this.top=0;
}

function isEmpty(){
	if(this.length()<=0){
		return true;
	}else{
		return false;
	}
}


//测试Stack类的实现
let s=new Stack();
s.push("Tom");
s.push("Jack"); 
s.push("Bryan");
console.log("length: " + s.length());//3
console.log(s.peek());//Bryan
let popped = s.pop();
console.log("The popped element is: " + popped);//Bryan
console.log(s.peek());//Jack
s.push("Cynthia");
console.log(s.peek());//Cynthia
s.clear();
console.log("length: " + s.length());//0
console.log(s.peek());//undefined
s.push("Clayton");
console.log(s.peek());//Clayton

二、栈的应用

1.数制间的相互转换:假设想将数字n转换为以b为基数的数字，实现转换的算法如下
   (1) 最高位为 n % b,将此位压入栈
   (2) 使用 n/b代替n
   (3) 重复步骤1 和 2，直到 n 等于 0，且没有余数。
   (4) 持续将栈内元素弹出,直到栈为空,依次将这些元素排列,就得到转换后数字的字符串形式

function mulBase(num,base){
	let s=new Stack();
	do{
		s.push(num%base);
		num=Math.floor(num /= base);
	}while(num>0);

	let converted="";
	while(s.length()>0){
		converted +=s.pop();
	}

	return converted;
}


let num=31;
let base=2;
let newNum=mulBase(num,base);
console.log(num+" converted to base "+base+" is "+newNum);//11111

num =125;
base=8;
newNum=mulBase(num,base);
console.log(num+" converted to base "+base+" is "+newNum);//175

2.判断给定字符串是否是回文

function isPalindrome(word){
	let s=new Stack();
	for(let i=0;i<word.length;i++){
		s.push(word[i]);
	}
	let rword="";
	while(s.length()>0){
		rword +=s.pop();
	}
	if(word==rword){
		return true;
	}else{
		return false;
	}
}

let word="hello";
if(isPalindrome(word)){
	console.log(word+" is a palindrome");
}else{
	console.log(word+"is not a palindrome");
}
word='racecar';
if(isPalindrome(word)){
	console.log(word+" is a palindrome");
}else{
	console.log(word+"is not a palindrome");
}

3.递归

function factorial(n){
	if(n==0){
		return 1;
	}else{
		return n*factorial(n-1);
	}

}


function fact(n){
	let s=new Stack();
	while(n>1){
		s.push(n--);
	}
	let product=1;
	while(s.length()>0){
		product *=s.pop();
	}
	return product;
}

console.log(factorial(6));//720
console.log(fact(6));//720

三、习题

1.栈可以用来判断一个算术表达式中的括号是否匹配。编写一个函数，该函数接受一个算术表达式作为参数，返回括号缺失的位置。下面是一个括号不匹配的算术表达式的例子：2.3 + 23 / 12 + (3.14159×0.24。

function signUp(stack,ele){
	switch(ele){
		case "{":
		case "[":
		case "(":
			stack.push(ele);
			break;
		case "}":
		case "]":
		case ")":
	        let topEle=stack.pop();
	        console.log(stack.top);
	        if((topEle=='{'&& ele=='}')||(topEle=='['&& ele==']')||(topEle=='('&& ele==')')){
	        	console.log('ok');
	        }else{
	        	console.log("括号不匹配");
	        	return;
	        }
	        break;
	} 
}
let stack=new Stack();
let str="2.3 + 23 / 12 + ( 3.14159 × 0.24 ";
str=str.split(" ");

for(let i=0;i<str.length;i++){
	signUp(stack,str[i]);
}
if(!stack.isEmpty()){
	console.log("括号不匹配");
}