学习JavaScript数据结构与算法（二）——栈

栈是一种遵从后进先出（LIFO）原则的有序集合。
新添加的或待删除的元素都保存在栈的末尾，称作栈顶，另一端叫做栈底。
在栈里，新元素靠近栈顶，旧元素接近栈底。
在现实生活中也有很多栈的例子，比如餐厅里堆放的盘子，最先放的盘子在最底下，最后放的盘子在最上面。

一、栈的创建

function Stack () {    //创建一个数组，保存栈里的元素    var items = [];    /*声明一些方法*/    /*    push(element(s))    添加一个或几个新元素到栈顶     */    this.push = function(element){        items.push(element);    };    /*    pop()    移除栈顶的元素，同时返回被移除的元素     */    this.pop = function(){        return items.pop();    };    /*    peek()    返回栈顶的元素，不对栈做任何修改    不会移除栈顶的元素，仅仅返回它     */    this.peek = function(){        return items[items.length-1];    };    /*    isEmpty()    如果栈里没有任何元素就返回true，否则返回false     */    this.isEmpty = function(){        return items.length == 0;    };    /*    size()    返回栈里的元素个数    和数组的length属性类似     */    this.size = function(){        return items.length;    };    /*    clear()    移除栈里的所有元素     */    this.clear = function(){        items = [];    };    /*    print()    辅助方法，将栈里的元素输出到控制台     */    this.print = function(){        console.log(items.toString());    };}

二、使用Stack类

//初始化Stack类var stack = new Stack();//验证栈是否为空console.log(stack.isEmpty());  //输出为true//向栈里添加元素stack.push(5);stack.push(6);console.log(stack.peek());  //输出6stack.push(11);console.log(stack.size());  //输出3console.log(stack.isEmpty());  //输出为false//从栈里移除两个元素stack.pop();stack.pop();console.log(stack.size());  //输出1stack.print();  //输出5

三、应用实例

1、进制转换

1）从十进制到二进制

function divideBy2 (decNumber) {    var remStack = new Stack(),        rem,        binaryString = '';    while (decNumber > 0) {        rem = Math.floor(decNumber % 2);        remStack.push(rem);        decNumber = Math.floor(decNumber / 2);    }    while (!remStack.isEmpty()) {        binaryString += remStack.pop().toString();    }    return binaryString;}

2）从十进制到任意进制

function baseConverter (decNumber, base) {    var remStack = new Stack(),        rem,        baseString = '',        digits = '0123456789ABCDEF';    while (decNumber > 0) {        rem = Math.floor(decNumber % base);        remStack.push(rem);        decNumber = Math.floor(decNumber / base);    }    while (!remStack.isEmpty()) {        baseString += digits[remStack.pop()];    }    return baseString;}

2、平衡圆括号

function parenthesesChecker (symbols) {    let stack = new Stack(),        balanced = true,        index = 0,        symbol, top,        opens = "([{",        closers = ")]}";    while (index < symbols.length && balanced){        symbol = symbols.charAt(index);        if (opens.indexOf(symbol) >= 0){            stack.push(symbol);            console.log(`open symbol - stacking ${symbol}`);        } else {            console.log(`close symbol ${symbol}`);            if (stack.isEmpty()){                balanced = false;                console.log('Stack is empty, no more symbols to pop and compare');            } else {                top = stack.pop();                if (!(opens.indexOf(top) === closers.indexOf(symbol))) {                    balanced = false;                    console.log(`poping symbol ${top} - is not a match compared to ${symbol}`);                } else {                    console.log(`poping symbol ${top} - is is a match compared to ${symbol}`);                }            }        }        index++;    }    if (balanced && stack.isEmpty()){        return true;    }    return false;}

3、汉诺塔

function towerOfHanoi(n, from, to, helper){    if (n > 0){        towerOfHanoi(n-1, from, helper, to);        to.push(from.pop());        console.log('-----');        console.log('Disk: ' + n);        console.log('Source: ');        from.print();        console.log('Destination: ');        to.print();        console.log('Helper: ');        helper.print();        towerOfHanoi(n-1, helper, to, from);    }}var source = new Stack();source.push(3);source.push(2);source.push(1);var dest = new Stack();var helper = new Stack();towerOfHanoi(source.size(), source, dest, helper);

【注】关于print()方法需要注意一点，该方法中已经包含了console.log()方法，直接使用就可以在控制台上打印输出。

【补充】

function towerOfHanoi(n, from, to, helper){    if (n > 0){        towerOfHanoi(n-1, from, helper, to);        console.log('移动盘子 ' + n + ' 从 ' + from + ' 到 ' + to);        towerOfHanoi(n-1, helper, to, from);    }}towerOfHanoi(3, 'A', 'B', 'C');