双向链表

双向链表和普通链表的区别在于，双向链表链接是双向的，一个链向上一个元素，一个链向下一个元素。
所以一个元素应该是:

node = function(element){
    this.element = element
    this.prev = null// 指向上一个
    this.next = null// 指向下一个
}

同时不仅包括head，还应该有tail，记录最后一个元素，

let head = null
let tail = null
let length = 0

2 方法实现

2.1在任意位置插入新元素和移除新元素

function DoublyLinkedList(){
  let Node = function(element){
    this.element = element
    this.prev = null
    this.next = null
  }
  let head = null
  let tail = null
  let length = 0
  this.insert = function (position,element){
    if(position>=0&&position<=length){// 考虑临界情况
      let node = new Node(element),
      current = head,
      prev,
      index = 0    
      if(position==0){
        if(!head){
          head = node
          tail = node
        }else{
          node.next = current //  node变成了head
          current.prev = node //  之前的head变成了node的下项 
          head = node // 赋值
        }
      }else if(position==length){
        current = tail //保存tail的值
        current.next = node //tail的next指向node
        node.prev = current //node的prev指向之前的tail
        tail = node  //将最后一个值保存为tail
      }else{
        while(index<position){
          prev = current //保存现任值
          current = current.next// 现任变前任，后任继位
          index++ //索引值增加
        }
        prev.next = node
        node.prev = prev
        node.next = current
        current.prev = node
        
      }
        length++
        return node
    }else{
      return null
    }
  }
//在任意位置移除元素
  this.remove = function(position){
      if(position>=0&&position<=length-1){
        let current = head,index =0,prev
        if(position==0){
        current = current.next
        head = current
        // 还需要改变prev 和 tail
          if(length ===1){
            tail = null
          }else{
            head.prev = null
          }
        }else if(position ==length-1){
        current = tail
        tail = current.prev
        tail.next =null
        }else{
          while(index<position){
            prev = current
            current = current.next
            index++
          }
          prev.next = current.next
          current.next.prev =prev
          
          
        }
        length --
          return current
      }else{
        return null
      }
}
//打印head
  this.print = function(){
    console.log(head)
  }
}