algorithms/119-pascals-triangle-ii.ipynb

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    "### [杨辉三角 II](https://leetcode-cn.com/problems/pascals-triangle-ii/)\n",
    "\n",
    "给定一个非负索引`k`，其中`k ≤ 33`，返回杨辉三角的第`k`行。\n",
    "\n",
    "在杨辉三角中，每个数是它左上方和右上方的数的和。\n",
    "\n",
    "#### 示例:\n",
    "```\n",
    "输入: 3\n",
    "输出: [1,3,3,1]\n",
    "```\n",
    "\n",
    "#### 进阶：\n",
    "- 你可以优化你的算法到`O(k)`空间复杂度吗？"
   ]
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   "cell_type": "markdown",
   "id": "western-authentication",
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   "source": [
    "杨辉三角第n行满足：$ 𝐶^0_{𝑛−1}, 𝐶^1_{𝑛−1},⋯,𝐶^{𝑛−1}_{𝑛−1} $"
   ]
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  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "restricted-wireless",
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   "outputs": [],
   "source": [
    "from typing import List\n",
    "\n",
    "def permutation(n: int, m: int):\n",
    "    ans = 1\n",
    "    for i in range(m, n):\n",
    "        ans *= (i + 1)\n",
    "    return ans\n",
    "    \n",
    "def combination(n, m):\n",
    "    return permutation(n, m) // permutation(n - m, 1)\n",
    "\n",
    "def getRow(rowIndex: int) -> List[int]:\n",
    "    ans = [1 for _ in range(rowIndex + 1)]\n",
    "    for i in range(rowIndex):\n",
    "        ans[i] = combination(rowIndex, i)\n",
    "    return ans"
   ]
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   "cell_type": "code",
   "execution_count": 18,
   "id": "romance-special",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1]"
      ]
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     "execution_count": 18,
     "metadata": {},
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   "source": [
    "getRow(0)"
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   "cell_type": "code",
   "execution_count": 19,
   "id": "cooperative-parent",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 1]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "getRow(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "green-moldova",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 1]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "getRow(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "architectural-weekly",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 3, 1]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "getRow(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "chinese-verification",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 5, 10, 10, 5, 1]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "getRow(5)"
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