Live Note

Remain optimistic

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公式: $$P{Q}R\ ({P}Q{R})$$

P 和 R 都是一阶公式, 如果前提条件 P 在执行 Q 前成立, 则执行后得到满足条件 R 的状态
部分正确性断言: 如果 P 在 Q 执行前为真, 那么, 如果 Q 的执行终止,则终止在使 R 为真的某个状态
终止性断言:如果 P 在 Q 执行前为真, 那么 Q 将终止在使 R 为真的某个状态
赋值公理: $$\vdash P_0 {x:=f} P$$

推理规则的表示

$$\frac{premise -> f_0, f_1, …, f_n}{conclusion -> f_0}$$

推理规则

  • Rules of Consequence:
    $$\frac{P{Q}R,\ R\rightarrow S}{P{Q}S}\ \ \ \ \ \frac{P{Q}R,\ S\rightarrow P}{S{Q}R}$$
  • Rule of Composition:
    $$\frac{P{Q_1}R_1,\ R_1{Q_2}R}{P{Q_1, Q_2}R}$$
  • Rules of Iteration:
    $$\frac{P\ &\ B{S}P}{P\ {while\ B\ do\ S}\ \neg B \ &\ P}$$

等式公理

  • 代换: $[N/x]M$ 表示表示 M 中的自由变元 x 用 N 代换的结果, N 中的自由变元代换后不能成为约束变元
  • 约束变元改名: $\lambda x:\sigma .M = \lambda y:\sigma.[y/x]M$ 例如:$\lambda x:\sigma.x + y = \lambda z:\sigma .z+y$
  • 等价公理: 计算函数实际就是在函数中使用实在变元替换形式变元, $(\lambda x:\sigma.M)N = [N/x]M$
  • 同余性规则: 相等的函数作用于相等的变元产生相等的结果, $\frac{M_1=M_2,\ N_1=N_2}{M_1N_1=M_2N_2}$

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状态模式

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let ResultState = (() => {
  let States = {
    state0: function () {
      console.log("state0")
    },
    state1: function () {
      console.log("state1")
    },
    state2: function () {
      console.log("state2")
    },
    state3: function () {
      console.log("state3")
    },
  }

  function show(result) {
    States["state" + result] && States["state" + result]()
  }

  return {
    show,
  }
})()

// for test
ResultState.show(3)

策略模式

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let Price = (() => {
  let obj = {
    return30: (price) => +price + parseInt(price / 100) * 30,
    return50: (price) => +price + parseInt(price / 100) * 50,
    percent90: (price) => (price * 100 * 90) / 10000,
    percent80: (price) => (price * 100 * 80) / 10000,
  }
  return (algorithm, price) => {
    return obj[algorithm] && obj[algorithm](price)
  }
})()

// for test
let price = Price("return50", 321.13)
console.log(price)

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class Node {
  constructor(data = -1, prev = null, next = null) {
    this.data = data
    this.prev = prev // 向前指针
    this.next = next // 向后指针
  }
}

class LinkList {
  constructor() {
    this.head = this.tail = null // 首、尾指针
    this.size = 0 // 元素个数
  }

  addHead(elem) {
    let elemNode = new Node(elem)
    if (this.size == 0) {
      this.head = this.tail = elemNode
      this.size++
    } else {
      this.head.prev = elemNode
      elemNode.next = this.head
      this.head = elemNode
      this.size++
    }
    return true
  }

  deleteHead() {
    if (this.size != 0) {
      let elem = this.head.data
      this.head.prev = null
      this.head = this.head.next
      this.size--
      return elem
    } else {
      console.log("list is empty")
      return
    }
  }

  addTail(elem) {
    let elemNode = new Node(elem)
    if (this.size == 0) {
      this.head = this.tail = elemNode
      this.size++
    } else {
      elemNode.prev = this.tail
      this.tail.next = elemNode
      this.tail = elemNode
      this.size++
    }
    return true
  }

  deleteTail() {
    if (this.size != 0) {
      let elem = this.tail.data
      this.tail.next = null
      this.tail = this.tail.prev
      this.size--
      return elem
    } else {
      console.log("list is empty")
      return
    }
  }

  display() {
    let current = this.head,
      count = this.size,
      str = ""
    while (count > 0) {
      str += current.data + " "
      current = current.next
      count--
    }
    console.log(str)
  }
}
let linklist = new LinkList()
linklist.addHead(1)
linklist.addHead(2)
linklist.addHead(3)
linklist.deleteHead()
linklist.addTail(4)
linklist.display()

结果

2 1 4

Posted on Edited on In

简单的 Array 实现

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class Array {
  constructor(size = 10) {
    this.arr = [] // 数组
    this.size = size // 最大长度
    this.elems = 0 // 成员数量
  }

  add(elem) {
    if (this.arr.length == this.size) {
      console.log("Array is full")
      return
    }
    this.arr[this.elems++] = elem
    return true
  }

  find(elem) {
    for (let i = 0, len = this.elems; i < len; i++) {
      if (this.arr[i] == elem) return i
    }
    return -1
  }

  delete(elem) {
    let index = this.find(elem)
    if (index == -1) {
      console.log("Element not found")
      return
    }
    for (let i = index, len = this.elems - 1; i < len; i++)
      this.arr[i] = this.arr[i + 1]
    this.elems--
    return true
  }

  update(oldVal, newVal) {
    // only use for unique element
    let index = this.find(oldVal)
    if (index == -1) {
      console.log("Element not found")
      return
    }
    this.arr[index] = newVal
    return true
  }

  display() {
    let srt = ""
    for (let i = 0, len = this.elems; i < len; i++) {
      srt += "" + this.arr[i] + " "
    }
    console.log(srt)
  }

  length() {
    return this.elems
  }
}
var arr = new Array()
arr.add(1)
arr.add(2)
arr.add(3)
arr.add(4)
arr.display()
console.log(arr.length())

结果

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1 2 3 4
4

Posted on Edited on In

简单的 Queue 实现

数组实现

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class Queue {
  constructor(size = 10) {
    this.size = size // 队列最大长度
    this.top = 0 // 首位置
    this.bottom = -1 // 尾位置
    this.elems = 0 // 成员个数
    this.arr = [] // 队列
  }

  add(elem) {
    if (this.elems == this.size) {
      console.log("Queue is full")
      return
    }
    if (this.bottom == this.size - 1) {
      // 循环队列
      this.bottom = -1
    }
    this.arr[++this.bottom] = elem
    this.elems++
    return true
  }

  out() {
    if (this.elems == 0) {
      console.log("Queue is empty")
      return
    }
    let elem = this.arr[this.top]
    this.arr[this.top] = null
    this.top++
    if (this.top == this.size) {
      this.top = 0
    }
    this.elems--
    return elem
  }
}
var queue = new Queue()
queue.add(3)
queue.add(2)
console.log(queue.out())
console.log(queue.out())
console.log(queue.out())
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