数据结构与算法JavaScript描述 第四章课后习题

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。下面是一个不匹配的算术表达式的例子：2.3+23/12+（3.14159*0.24。

 

// 栈的基本特性实现
function Stack(){
  this.dataStore =  [];
  this.top = 0;
  this.push = push;
  this.pop = pop;
  this.peek = peek;
  this.clear = clear;
  this.length = length;
  }

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

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

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

  function length(){
    return this.top;
  }

// 检查括号匹配
  function checkBracket(expression){
    var s = new Stack();
    for (var i = 0; i < expression.length; ++i){
      if (expression[i] == "("){
        s.push(i+1);
      }
      else if(expression[i] == ")"){
        s.pop();
      }
    }
    if (s.length() > 0){
      return s.pop();
    }
    else {
      return -1;
    }
  }

  var ans = checkBracket("2.3+((((23/12+(3.14)159*0.24");
  print("num:" + ans);

 

2.一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.dataStore =  [];
  this.top = 0;
  this.push = push;
  this.pop = pop;
  this.peek = peek;
  this.clear = clear;
  this.length = length;
  }

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

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

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

  function length(){
    return this.top;
  }
// 计算输入表达式
function cal(expression){
  var nums = new Stack();
  var opreators = new Stack();
  var exp = expression.split(" ");
  for (var i = 0; i < exp.length ; ++i){
    if (i < exp.length - 1){
      nums.push(exp[i]);
    }
    else{
      opreators.push(exp[i]);
    }
  }
  var num1 = nums.pop();
  // print(num1);
  var num2 = nums.pop();
  // print(num2);
  var op = opreators.pop();
  // print(op);
  var res = 0;
  switch (op){
    case "+":
      res = parseFloat(num1) + parseFloat(num2); 
      break;
    case "-":
      res = parseFloat(num1) - parseFloat(num2);  
      break;
    case "*":
      res = parseFloat(num1) * parseFloat(num2);  
      break;
    case "/":
      res = parseFloat(num1) / parseFloat(num2);  
      break;
      
  }
  return {
    expStr:num1 + op + num2 + "=" + res.toString(),
    res: res
  };

}
var expression = "12 15 +";
print(cal(expression).expStr);

3.现实生活中栈的一个例子是佩兹糖果盒。想象一下你有一盒佩兹糖果，里面塞满了红色、黄色和白色的糖果盒，但你不喜欢黄色的糖果。使用栈（优肯用到多个栈）写一段程序，在不改变盒内其他糖果叠放顺序的基础上，将黄色糖果移出。

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

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

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

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

  function length(){
    return this.top;
  }

var candies = new Stack();
candies.push("red");
candies.push("red1");
candies.push("yellow");
candies.push("yellow");
candies.push("blue");
candies.push("red");
candies.push("yellow");
candies.push("red");
var temp = new Stack();
while(candies.length()>0){
  var candle = candies.pop();
  if (candle != "yellow"){
    temp.push(candle);
  }
}
while(temp.length()>0){
  var candle = temp.pop();
  candies.push(candle);
}
while(candies.length()>0){
  var candle = candies.pop();
  print(candle);
}