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    "### Problem 1. Fibonacci Sequence\n",
    "在课程里，讨论过如果去找到第N个Fibonacci number。在这里，我们来试着求一下它的Closed-form解。 \n",
    "\n",
    "Fibonacci数列为 1,1,2,3,5,8,13,21,.... 也就第一个数为1，第二个数为1，以此类推...\n",
    "我们用f(n)来数列里的第n个数，比如n=3时 f(3)=2。\n",
    "\n",
    "下面，来证明一下fibonacci数列的closed-form, 如下：\n",
    "\n",
    "$f(n)=\\frac{1}{\\sqrt{5}}(\\frac{1+\\sqrt{5}}{2})^n-\\frac{1}{\\sqrt{5}}(\\frac{1-\\sqrt{5}}{2})^n$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "// your proof is here ....\n",
    "\n",
    "见图片problem1.jpg\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem2. Algorithmic Complexity\n",
    "对于下面的复杂度，从小大排一下顺序：\n",
    "\n",
    "$O(N),  O(N^2),  O(2^N),  O(N\\log N),  O(N!),  O(1),  O(\\log N),  O(3^N),  O(N^2\\log N), O(N^{2.1})$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "// your answer....\n",
    "\n",
    "$O(N!),O(3^N),  O(2^N), O(N^{2.1}),O(N^2\\log N),  O(N^2), O(N\\log N), O(N),O(\\log N)$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem 3  Dynamic Programming Problem"
   ]
  },
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   "metadata": {},
   "source": [
    "#### Edit Distance (编辑距离）\n",
    "编辑距离用来计算两个字符串之间的最短距离，这里涉及到三个不通过的操作，add, delete和replace. 每一个操作我们假定需要1各单位的cost. \n",
    "\n",
    "例子： \"apple\", \"appl\" 之间的编辑距离为1 （需要1个删除的操作）\n",
    "\"machine\", \"macaide\" dist = 2\n",
    "\"mach\", \"aaach\"  dist=2"
   ]
  },
  {
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   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 1, 1, 1, 1, 1, 1, 1], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0]]\n",
      "[[0, 1, 1, 1, 1, 1, 1, 0], [1, 0, 1, 2, 2, 2, 2, 1], [1, 1, 0, 1, 2, 3, 3, 2], [1, 2, 1, 0, 1, 2, 3, 3], [1, 2, 2, 1, 1, 2, 3, 4], [1, 2, 3, 2, 2, 1, 2, 3], [1, 2, 3, 3, 3, 2, 2, 3], [1, 2, 3, 4, 4, 3, 3, 2]]\n",
      "2\n"
     ]
    }
   ],
   "source": [
    "# 基于动态规划的解法\n",
    "import math\n",
    "def edit_dist(str1, str2):\n",
    "    # 两个string 输入\n",
    "    # your code here\n",
    "    len1 = len(str1)\n",
    "    len2 = len(str2)\n",
    "    dist = [ [0] * (len2+1) for i in range((len1+1))]\n",
    "    for j in range(1,len2+1,1):\n",
    "        dist[0][j] =1 \n",
    "    for i in range(1,len1+1,1):\n",
    "        dist[i][0] =1\n",
    "    \n",
    "    print(dist)\n",
    "    for i in range(0,len1+1,1):\n",
    "        for j in range(1,len2+1,1):\n",
    "            if str1[i-1] == str2[j-1]:\n",
    "                dist[i][j] = dist[i-1][j-1]\n",
    "            else:\n",
    "                dist[i][j] = min(dist[i-1][j-1]+1,dist[i-1][j]+1,dist[i][j-1]+1)\n",
    "    print(dist)\n",
    "    return dist[len1][len2]\n",
    "    \n",
    "if __name__ == \"__main__\":\n",
    "    str1='machine'\n",
    "    str2 = 'macaide'\n",
    "\n",
    "    dist = edit_dist(str1,str2)\n",
    "    print(dist)\n",
    "  \n",
    "    \n",
    "    \n",
    "    \n",
    "    "
   ]
  },
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   "metadata": {},
   "source": [
    "### Problem 4 非技术问题\n",
    "本题目的目的是想再深入了解背景，之后课程的内容也会根据感兴趣的点来做适当会调整。 \n",
    "\n",
    "\n",
    "Q1: 之前或者现在，做过哪些AI项目/NLP项目？可以适当说一下采用的解决方案，如果目前还没有想出合适的解决方案，也可以说明一下大致的想法。 请列举几个点。\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "Q2: 未来想往哪个行业发展？ 或者想做哪方面的项目？ 请列举几个点。\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "Q3: 参加训练营，最想获得的是什么？可以列举几个点。\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "//your answer...\n",
    "\n",
    "Q1:\n",
    "之前做过恶意作弊账号分类，主要是建立用户画像然后采用xgboost模型融合的方式进行分类预测。\n",
    "\n",
    "Q2:\n",
    "未来主要是希望可以往金融等领域发展，主要希望可以做文本分类等方面的工作。\n",
    "\n",
    "Q3:\n",
    "希望能够巩固自己的知识体系，为将来面试新的工作做好铺垫。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
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