ipynb_files/096_Unique_Binary_Search_Trees.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-06T13:49:35.630086Z",
     "start_time": "2020-04-06T13:49:35.627086Z"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import display, Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question\n",
    "(https://leetcode.com/problems/unique-binary-search-trees/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-06T13:50:15.459437Z",
     "start_time": "2020-04-06T13:50:15.446142Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(Image('../images/096_Q.PNG'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution 1: DP"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "G(n) = F(1, n) + F(2, n) + ... + F(n, n)  # F(i, n), number i at root\n",
    "\n",
    "G(0) = 1, G(1) = 1\n",
    "\n",
    "F(i, n) = G(i - 1) * G(n - i) # left, right"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-06T14:08:51.913503Z",
     "start_time": "2020-04-06T14:08:51.910502Z"
    }
   },
   "outputs": [],
   "source": [
    "class Solution:\n",
    "    def numTrees(self, n):\n",
    "        if n == 0 or n == 1:\n",
    "            return 1\n",
    "        res = 0\n",
    "        for i in range(1, n+1):\n",
    "            res += self.numAtSpecPoint(i, n)\n",
    "        return res\n",
    "    \n",
    "    def numAtSpecPoint(self, i, n):\n",
    "        return self.numTrees(i - 1) * self.numTrees(n - i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### submit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-06T14:10:28.894390Z",
     "start_time": "2020-04-06T14:10:28.890391Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(Image('../images/096_S1.PNG'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution 2: DP+"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-06T14:14:13.171622Z",
     "start_time": "2020-04-06T14:14:13.168618Z"
    }
   },
   "outputs": [],
   "source": [
    "class Solution:\n",
    "    def numTrees(self, n):\n",
    "        res = [0] * (n + 1)\n",
    "        res[0] = 1\n",
    "        res[1] = 1\n",
    "        for i in range(2, n + 1):\n",
    "            for j in range(1, i+1):\n",
    "                res[i] += res[j - 1] * res[i - j]\n",
    "        return res[n]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### submit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-06T14:15:01.257164Z",
     "start_time": "2020-04-06T14:15:01.252167Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(Image('../images/096_S2.PNG'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution 3: Recursive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-06T14:22:38.429102Z",
     "start_time": "2020-04-06T14:22:38.425102Z"
    }
   },
   "outputs": [],
   "source": [
    "class Solution:\n",
    "    def numTrees(self, n):\n",
    "        return self.subTrees(1, n)\n",
    "    \n",
    "    def subTrees(self, lo, hi):\n",
    "        if lo >= hi:\n",
    "            return 1\n",
    "        total = 0\n",
    "        for i in range(lo, hi+1):\n",
    "            total += self.subTrees(lo, i - 1) * self.subTrees(i + 1, hi)\n",
    "        return total"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### submit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-04-06T14:23:46.934482Z",
     "start_time": "2020-04-06T14:23:46.929472Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(Image('../images/096_S3.PNG'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "257px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}