{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Comparison Between TreeValue and DM-Tree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "In this section, we will compare the feature and performance of the [dm-tree](https://github.com/deepmind/tree) library, which is developed by deepmind."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Before starting the comparison, let us define some thing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:13.129096Z",
     "iopub.status.busy": "2023-10-22T14:55:13.128797Z",
     "iopub.status.idle": "2023-10-22T14:55:13.137809Z",
     "shell.execute_reply": "2023-10-22T14:55:13.136984Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "origin = {'a': 1, 'b': 2, 'c': {'x': 3, 'y': 4}}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Mapping Operation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Mapping operation is quite common in the processing of trees. A mapping function should be provided to create a new tree based on the mapped tree."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### TreeValue's mapping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "In TreeValue, mapping is provided to simply create a new tree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:13.142536Z",
     "iopub.status.busy": "2023-10-22T14:55:13.141847Z",
     "iopub.status.idle": "2023-10-22T14:55:15.540313Z",
     "shell.execute_reply": "2023-10-22T14:55:15.539351Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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      "image/png": 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       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>node_7f5aa0eedfd0&#45;&gt;value__node_7f5aa0eedfd0__y</title>\n",
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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<FastTreeValue 0x7f5aa0eeda00>\n",
       "├── 'a' --> 1\n",
       "├── 'b' --> 2\n",
       "└── 'c' --> <FastTreeValue 0x7f5aa0eedfd0>\n",
       "    ├── 'x' --> 3\n",
       "    └── 'y' --> 4"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from treevalue import FastTreeValue, mapping\n",
    "\n",
    "tv = FastTreeValue(origin)\n",
    "tv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:15.593107Z",
     "iopub.status.busy": "2023-10-22T14:55:15.591897Z",
     "iopub.status.idle": "2023-10-22T14:55:15.716028Z",
     "shell.execute_reply": "2023-10-22T14:55:15.715095Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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      "image/png": 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      ],
      "text/plain": [
       "<FastTreeValue 0x7f59c1599910>\n",
       "├── 'a' --> 2\n",
       "├── 'b' --> 4\n",
       "└── 'c' --> <FastTreeValue 0x7f59c1599880>\n",
       "    ├── 'x' --> 6\n",
       "    └── 'y' --> 8"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mapping(tv, lambda x: x * 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Here is the performance test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:15.720551Z",
     "iopub.status.busy": "2023-10-22T14:55:15.719948Z",
     "iopub.status.idle": "2023-10-22T14:55:17.895185Z",
     "shell.execute_reply": "2023-10-22T14:55:17.894117Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.65 µs ± 51.1 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit mapping(tv, lambda x: x * 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "In order to support the cased that the mapped value is related to both path and value of each node, we can use the 'path mapping mode' by simply use the second parameter of the mapping function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:17.900363Z",
     "iopub.status.busy": "2023-10-22T14:55:17.900068Z",
     "iopub.status.idle": "2023-10-22T14:55:18.044048Z",
     "shell.execute_reply": "2023-10-22T14:55:18.043272Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
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",
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       "</g>\n",
       "<!-- node_7f59c1599f10&#45;&gt;value__node_7f59c1599f10__y -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>node_7f59c1599f10&#45;&gt;value__node_7f59c1599f10__y</title>\n",
       "<path fill=\"none\" stroke=\"#1f9929\" stroke-opacity=\"0.800000\" d=\"M611.95,-89.19C636.77,-75.04 674.32,-53.62 701.4,-38.17\"/>\n",
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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<FastTreeValue 0x7f59c1599ca0>\n",
       "├── 'a' --> ('path', ('a',), 'value', 1)\n",
       "├── 'b' --> ('path', ('b',), 'value', 2)\n",
       "└── 'c' --> <FastTreeValue 0x7f59c1599f10>\n",
       "    ├── 'x' --> ('path', ('c', 'x'), 'value', 3)\n",
       "    └── 'y' --> ('path', ('c', 'y'), 'value', 4)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mapping(tv, lambda x, p: ('path', p, 'value', x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "And here is the performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:18.048777Z",
     "iopub.status.busy": "2023-10-22T14:55:18.048048Z",
     "iopub.status.idle": "2023-10-22T14:55:20.222235Z",
     "shell.execute_reply": "2023-10-22T14:55:20.221514Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.68 µs ± 19.6 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit mapping(tv, lambda x, p: ('path', p, 'value', x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### DM-Tree's mapping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "In DM-Tree, mapping operation is supported by [map_structure](https://tree.readthedocs.io/en/latest/api.html#tree.map_structure) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:20.225997Z",
     "iopub.status.busy": "2023-10-22T14:55:20.225539Z",
     "iopub.status.idle": "2023-10-22T14:55:20.232347Z",
     "shell.execute_reply": "2023-10-22T14:55:20.231632Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from tree import map_structure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:20.236229Z",
     "iopub.status.busy": "2023-10-22T14:55:20.235574Z",
     "iopub.status.idle": "2023-10-22T14:55:20.243999Z",
     "shell.execute_reply": "2023-10-22T14:55:20.243231Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': 2, 'b': 4, 'c': {'x': 6, 'y': 8}}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "map_structure(lambda x: x * 2, origin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "This is the performance of `map_structure`, obviously much slower than `mapping` in TreeValue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:20.247859Z",
     "iopub.status.busy": "2023-10-22T14:55:20.247588Z",
     "iopub.status.idle": "2023-10-22T14:55:35.238871Z",
     "shell.execute_reply": "2023-10-22T14:55:35.237750Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "18.5 µs ± 236 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit map_structure(lambda x: x * 2, origin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "To supported the second situation in the last section, [map_structure_with_path](https://tree.readthedocs.io/en/latest/api.html#tree.map_structure_with_path) can be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:35.244236Z",
     "iopub.status.busy": "2023-10-22T14:55:35.243403Z",
     "iopub.status.idle": "2023-10-22T14:55:35.249179Z",
     "shell.execute_reply": "2023-10-22T14:55:35.248506Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from tree import map_structure_with_path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:35.252920Z",
     "iopub.status.busy": "2023-10-22T14:55:35.252225Z",
     "iopub.status.idle": "2023-10-22T14:55:35.262646Z",
     "shell.execute_reply": "2023-10-22T14:55:35.261640Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': ('path', ('a',), 'value', 1),\n",
       " 'b': ('path', ('b',), 'value', 2),\n",
       " 'c': {'x': ('path', ('c', 'x'), 'value', 3),\n",
       "  'y': ('path', ('c', 'y'), 'value', 4)}}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "map_structure_with_path(lambda path, x: ('path', path, 'value', x), origin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Here is the performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:35.267491Z",
     "iopub.status.busy": "2023-10-22T14:55:35.266944Z",
     "iopub.status.idle": "2023-10-22T14:55:38.588413Z",
     "shell.execute_reply": "2023-10-22T14:55:38.586990Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40.9 µs ± 944 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit map_structure_with_path(lambda path, x: ('path', path, 'value', x), origin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Flatten and Unflatten"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "In tree operations, flatten is often used to linearly expand the tree structure for operations such as parallel processing. Based on flatten, unflatten is its inverse operation, which can recover the tree structure from the linear data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### TreeValue's Performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "In TreeValue, flatten and unflatten are provided, which usage are simple."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:38.592987Z",
     "iopub.status.busy": "2023-10-22T14:55:38.592266Z",
     "iopub.status.idle": "2023-10-22T14:55:38.736421Z",
     "shell.execute_reply": "2023-10-22T14:55:38.735350Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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      "image/png": 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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<FastTreeValue 0x7f5aa0eed580>\n",
       "├── 'a' --> 1\n",
       "├── 'b' --> 2\n",
       "└── 'c' --> <FastTreeValue 0x7f59c1579b50>\n",
       "    ├── 'x' --> 3\n",
       "    └── 'y' --> 4"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from treevalue import FastTreeValue, flatten, unflatten\n",
    "\n",
    "origin_tree = FastTreeValue(origin)\n",
    "origin_tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:38.740920Z",
     "iopub.status.busy": "2023-10-22T14:55:38.740152Z",
     "iopub.status.idle": "2023-10-22T14:55:38.746259Z",
     "shell.execute_reply": "2023-10-22T14:55:38.745598Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(('a',), 1), (('b',), 2), (('c', 'x'), 3), (('c', 'y'), 4)]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flatted = flatten(origin_tree)\n",
    "flatted"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Here is the performance of `flatten`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:38.750074Z",
     "iopub.status.busy": "2023-10-22T14:55:38.749541Z",
     "iopub.status.idle": "2023-10-22T14:55:45.570495Z",
     "shell.execute_reply": "2023-10-22T14:55:45.569270Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "838 ns ± 10.2 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit flatten(origin_tree)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The tree can be re-created from `flatted` with function `unflatten`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:45.575098Z",
     "iopub.status.busy": "2023-10-22T14:55:45.574522Z",
     "iopub.status.idle": "2023-10-22T14:55:45.692329Z",
     "shell.execute_reply": "2023-10-22T14:55:45.691341Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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      "image/png": 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       "<text text-anchor=\"middle\" x=\"198\" y=\"-101.3\" font-family=\"monospace bold\" font-size=\"14.00\" fill=\"#003304\">&lt;root&gt;.c</text>\n",
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       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<TreeValue 0x7f59c15b7610>\n",
       "├── 'a' --> 1\n",
       "├── 'b' --> 2\n",
       "└── 'c' --> <TreeValue 0x7f59c15b7160>\n",
       "    ├── 'x' --> 3\n",
       "    └── 'y' --> 4"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unflatten(flatted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "And here is the performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:45.697033Z",
     "iopub.status.busy": "2023-10-22T14:55:45.696422Z",
     "iopub.status.idle": "2023-10-22T14:55:53.706887Z",
     "shell.execute_reply": "2023-10-22T14:55:53.705855Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "985 ns ± 9.63 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit unflatten(flatted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### DM-Tree's Performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "[Flatten](https://tree.readthedocs.io/en/latest/api.html#tree.flatten) is provided in DM-Tree as well, but it differs from that in TreeValue, as the following"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:53.712537Z",
     "iopub.status.busy": "2023-10-22T14:55:53.710846Z",
     "iopub.status.idle": "2023-10-22T14:55:53.719443Z",
     "shell.execute_reply": "2023-10-22T14:55:53.718793Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from tree import flatten\n",
    "\n",
    "flatten(origin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Here is the performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:55:53.722762Z",
     "iopub.status.busy": "2023-10-22T14:55:53.722490Z",
     "iopub.status.idle": "2023-10-22T14:56:03.608212Z",
     "shell.execute_reply": "2023-10-22T14:56:03.607083Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.22 µs ± 16.3 ns per loop (mean ± std. dev. of 7 runs, 1,000,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit flatten(origin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The structure of the tree is dropped, only the data is extracted from the tree. This means the `flatten` function in DM-Tree is irreversible, we can not recover the original tree with the result above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The reversible resolution provided in DM-Tree is [flatten_with_path](https://tree.readthedocs.io/en/latest/api.html#tree.flatten_with_path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:56:03.612532Z",
     "iopub.status.busy": "2023-10-22T14:56:03.611969Z",
     "iopub.status.idle": "2023-10-22T14:56:03.620063Z",
     "shell.execute_reply": "2023-10-22T14:56:03.619257Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(('a',), 1), (('b',), 2), (('c', 'x'), 3), (('c', 'y'), 4)]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from tree import flatten_with_path\n",
    "\n",
    "flatten_with_path(origin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Here is the performance, much slower than `flatten` in TreeValue."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:56:03.624272Z",
     "iopub.status.busy": "2023-10-22T14:56:03.623565Z",
     "iopub.status.idle": "2023-10-22T14:56:19.339245Z",
     "shell.execute_reply": "2023-10-22T14:56:19.338099Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19.3 µs ± 166 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit flatten_with_path(origin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "To re-create the original tree, we need a tree structure with any objects filled inside. Use the [unflatten_as](https://tree.readthedocs.io/en/latest/api.html#tree.unflatten_as) to archive this goal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:56:19.343238Z",
     "iopub.status.busy": "2023-10-22T14:56:19.342696Z",
     "iopub.status.idle": "2023-10-22T14:56:19.351545Z",
     "shell.execute_reply": "2023-10-22T14:56:19.350838Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': 1, 'b': 2, 'c': {'x': 3, 'y': 4}}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from tree import unflatten_as\n",
    "\n",
    "unflatten_as({'a': None, 'b': None, 'c': {'x': None, 'y': None}}, [1, 2, 3, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Here is the performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:56:19.355410Z",
     "iopub.status.busy": "2023-10-22T14:56:19.354746Z",
     "iopub.status.idle": "2023-10-22T14:56:31.802771Z",
     "shell.execute_reply": "2023-10-22T14:56:31.801535Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.4 µs ± 141 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit unflatten_as({'a': None, 'b': None, 'c': {'x': None, 'y': None}}, [1, 2, 3, 4])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "### Positional Replacement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "It is obvious that the `unflatten_as` in DM-Tree is quite different from `unflatten` in TreeValue, for the former one is `replacing` and the latter one is `constructing`. This means the `unflatten_as` in DM-Tree may supported some more features, such as creating a new tree with another tree's structure and the given values. So we need an experiment on this, called 'positional replacement'."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "First, in TreeValue, we can build a function named `replace` to realize this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:56:31.807914Z",
     "iopub.status.busy": "2023-10-22T14:56:31.807363Z",
     "iopub.status.idle": "2023-10-22T14:56:31.813528Z",
     "shell.execute_reply": "2023-10-22T14:56:31.812760Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from treevalue import flatten, unflatten\n",
    "\n",
    "def replace(t, v):\n",
    "    pairs = flatten(t)\n",
    "    return unflatten([(path, vi) for (path, _), vi in zip(pairs, v)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Create a new tree based on `origin_tree`'s structure and new values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:56:31.817214Z",
     "iopub.status.busy": "2023-10-22T14:56:31.816551Z",
     "iopub.status.idle": "2023-10-22T14:56:31.948431Z",
     "shell.execute_reply": "2023-10-22T14:56:31.947347Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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      "image/png": 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      ],
      "text/plain": [
       "<TreeValue 0x7f59c15b0b50>\n",
       "├── 'a' --> 3\n",
       "├── 'b' --> 5\n",
       "└── 'c' --> <TreeValue 0x7f59c155c580>\n",
       "    ├── 'x' --> 7\n",
       "    └── 'y' --> 9"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "replace(origin_tree, [3, 5, 7, 9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Here is the performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:56:31.952547Z",
     "iopub.status.busy": "2023-10-22T14:56:31.952062Z",
     "iopub.status.idle": "2023-10-22T14:56:34.340811Z",
     "shell.execute_reply": "2023-10-22T14:56:34.339532Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.93 µs ± 43.9 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit replace(origin_tree, [3, 5, 7, 9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "In DM-Tree, `unflatten_as` can be directly used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:56:34.345883Z",
     "iopub.status.busy": "2023-10-22T14:56:34.345100Z",
     "iopub.status.idle": "2023-10-22T14:56:34.352345Z",
     "shell.execute_reply": "2023-10-22T14:56:34.351665Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a': 3, 'b': 5, 'c': {'x': 7, 'y': 9}}"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from tree import unflatten_as\n",
    "\n",
    "unflatten_as(origin, [3, 5, 7, 9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Here is the performance, even much slower than the `replace` function for integration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-10-22T14:56:34.356155Z",
     "iopub.status.busy": "2023-10-22T14:56:34.355626Z",
     "iopub.status.idle": "2023-10-22T14:56:46.509838Z",
     "shell.execute_reply": "2023-10-22T14:56:46.508568Z"
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15 µs ± 95.4 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "%timeit unflatten_as(origin, [3, 5, 7, 9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The mapping operation is supported by both library, and `mapping` in TreeValue's performance is significantly higher than the `map_structure` and `map_structure_with_path` in DM-Tree."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "The `flatten` and `unflatten` in TreeValue is reversible, but in DM-Tree not. DM-Tree's performance on flatten and unflatten operation is lower than that in TreeValue in all aspects."
   ]
  }
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