{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-07-03T14:43:00.143871Z",
     "start_time": "2024-07-03T14:43:00.105294Z"
    }
   },
   "outputs": [],
   "source": [
    "from src.models import OuterKey, InnerKey, AlphabetKey"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "outputs": [],
   "source": [
    "height = 10\n",
    "width = 7\n",
    "\n",
    "a0 = AlphabetKey.init_matrix(width, height, 255)\n",
    "\n",
    "o0 = OuterKey.init_matrix(height)\n",
    "o1 = OuterKey.init_matrix(height)\n",
    "o2 = OuterKey.init_matrix(height)\n",
    "o3 = OuterKey.init_matrix(height)\n",
    "\n",
    "i0 = InnerKey.init_matrix(width, height)\n",
    "i1 = InnerKey.init_matrix(width, height)\n",
    "i2 = InnerKey.init_matrix(width, height)\n"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-07-03T14:43:11.536945Z",
     "start_time": "2024-07-03T14:43:11.532046Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "outputs": [
    {
     "data": {
      "text/plain": "True"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a0_i0_o0_v0 = a0 << (i0 < o0)\n",
    "a0_i0_o0_v1 = ((a0 < ~o0) << i0) < o0\n",
    "\n",
    "a0_i0_o0_v0 == a0_i0_o0_v1"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-07-03T14:43:36.810538Z",
     "start_time": "2024-07-03T14:43:36.805348Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "a0_o0_i0_v0 = (a0 < o0) << i0\n",
    "a0_o0_i0_v1 = (a0 << (i0 < ~o0)) < o0\n",
    "a0_i0_o0_v0 == a0_i0_o0_v1"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-07-03T14:44:07.321778Z",
     "start_time": "2024-07-03T14:44:07.318402Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "outputs": [
    {
     "data": {
      "text/plain": "True"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a0_o0_i0_v0 = (a0 < o0) << i0\n",
    "a0_o0_i0_v1 = (a0 << (i0 < ~o0)) < o0\n",
    "a0_o0_i0_v0 == a0_o0_i0_v1"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-07-03T14:44:48.380940Z",
     "start_time": "2024-07-03T14:44:48.377032Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "outputs": [
    {
     "data": {
      "text/plain": "True"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_i0_i1 = ~(i0 << i1)\n",
    "ni1_ni0 = ~i1 << ~i0\n",
    "ni1_ni0 == n_i0_i1"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-07-03T14:45:01.588349Z",
     "start_time": "2024-07-03T14:45:01.584641Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "outputs": [
    {
     "data": {
      "text/plain": "True"
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i0_i1_i2_v0 = i0 << i1 << i2\n",
    "i0_i1_i2_v1 = i0 << (i1 << i2)\n",
    "i0_i1_i2_v2 = (i0 << i1) << i2\n",
    "i0_i1_i2_v0 == i0_i1_i2_v1 == i0_i1_i2_v2"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-07-03T14:45:41.860153Z",
     "start_time": "2024-07-03T14:45:41.855897Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "outputs": [
    {
     "data": {
      "text/plain": "True"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i0_i2_i1 = i0 << i2 << i1\n",
    "i0 == i0_i2_i1 << ~(i2 << i1) == i0_i2_i1 << ~i1 << ~i2"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-07-03T14:47:02.948800Z",
     "start_time": "2024-07-03T14:47:02.944314Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "outputs": [
    {
     "data": {
      "text/plain": "True"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i0_o0_o1_o2_v1 = ((i0 < o0) < o1) < o2\n",
    "i0_o0_o1_o2_v2 = (i0 < (o0 << o1)) < o2\n",
    "i0_o0_o1_o2_v3 = ((i0 < o0) < (o1 << o2))\n",
    "\n",
    "i0_o0_o1_o2_v1 == i0_o0_o1_o2_v2 == i0_o0_o1_o2_v3"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-07-03T14:48:17.489611Z",
     "start_time": "2024-07-03T14:48:17.485650Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "outputs": [
    {
     "data": {
      "text/plain": "True"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i0 < (o0 << o1 << o2) != i0_o0_o1_o2_v1 # not equal"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2024-07-03T14:48:18.120561Z",
     "start_time": "2024-07-03T14:48:18.116436Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   }
  }
 ],
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