08-a-star.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A* – využití heuristik"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from math import inf\n",
    "from search import parse_state, is_goal, actions, move\n",
    "from search import show_plan, visualize_search, log_search_step\n",
    "import solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Heuristiky\n",
    "\n",
    "Všechny uvedené algoritmy zatím nevyužívali informace, jak moc jsou zkoumané stavy blízko cíli. Takovou informaci typicky neznáme přesně,\n",
    "ale dokážeme ji přibližně odhadnout. Takovému optimistickému odhadu zbývající ceny (vzdálenosti do cíle) říkáme *heuristika* a hledání pak označujeme za *informované*.\n",
    "\n",
    "Nechť na světě nejsou červí díry (zjednoduší nám to vymyšlení vhodné heuristiky). \n",
    "Příkladem dolního odhadu na cenu do cíle pak může být vertikální vzdálenost od cíle vynásobená cenou cesty vpřed.\n",
    "Pokud se na mapě nacházejí slepé uličky, nebude tento odhad vždy přesný, nicméně poskytuje dolní mez skutečné zbývající ceny."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ACTION_COSTS = {'l': 3, 'f': 2, 'r': 3}\n",
    "\n",
    "def heuristic_distance(state):\n",
    "    vertical_distance = state.height - state.row\n",
    "    # Jaka by byla cena, kdyby raketka mohla letet porad rovne.\n",
    "    return vertical_distance * ACTION_COSTS['f']\n",
    "\n",
    "state = parse_state(\n",
    "'| | | | | |'\n",
    "'|A| |A| | |'\n",
    "'| |A|A| |A|'\n",
    "'| |S|A| | |'\n",
    "'| | | | | |')\n",
    "heuristic_distance(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Informované hledání\n",
    "\n",
    "Pokud máme heuristiku, můžeme ji přímočaře zakomponovat jak do hladového hledání (v každém kroku poletíme do stavu s nejnižším heuristickým odhadem vzdálenosti do cíle), tak do prohledávání s cenou (UCS).\n",
    "\n",
    "Algoritmus, který vzniky přidáním heuristiky do UCS se nazývá A* a jde o velmi jednoduché rozšíření: místo toho, abychom vybírali z okraje stavy s nejnižší cenou dosavadního plánu, budeme vybírat stav minimalizující součet ceny dosavadního plánu a heuristického odhadu ceny za zbytek cesty (součet udává dolní odhad celkové ceny cesty ze startu do cíle).\n",
    "\n",
    "\n",
    "## A* krok za krokem\n",
    "\n",
    "Podívejme se, jak by vypadal prohledávací strom pro A\\*. Pro každý stav v prohledávacím stromě nyní uvádíme *g+h=f*, kde *g* je cena plánu do tohoto stavu, *h* je hodnota heuristiky pro zbytek cesty a *f* je jejich součet. Všimněte si, které stavy nebylo nutné prozkoumat oproti neinformovanému UCS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Explored: Fringe:              Plans:                  Costs:               Heuristic:\n",
      "0: -      [c1]                 c1:''                   c1:0                 c1:8 \n",
      "1: c1     [b2, d2]             + b2:l, d2:r            + b2:3, d2:3         + b2:6, d2:6\n",
      "2: b2     [a3, d2]             + a3:ll                 + a3:6               + a3:4\n",
      "3: d2     [a3, d3]             + d3:rf                 + d3:5               + d3:4\n",
      "4: d3     [a3, d4, e4]         + d4:rff, e4:rfr        + d4:7, e4:8         + d4:2, e4:2\n",
      "5: d4     [a3, d5, e4, e5]     + d5:rfff, e5:rffr      + d5:9, e5:10        + d5:0, e5:0\n",
      "6: d5     [a3, e4, e5]                                                           \n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f63fecf9668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "state = parse_state(\n",
    "'| | |A| | |'\n",
    "'|A| |A| | |'\n",
    "'| |A|A| |A|'\n",
    "'| | |A| | |'\n",
    "'| | |S| | |')\n",
    "with visualize_search(state, costs=True, heuristic=True,\n",
    "                      text=True, interactive=False):\n",
    "    solutions.a_star(state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementace\n",
    "\n",
    "<div class=\"alert alert-block alert-success\">\n",
    "<b>Úkol 8.1: A*</b><br/>\n",
    "Implementujte funkci <i>a_star(initial_state)</i>,\n",
    "která vrací nejkratší plán pro cestu z <i>initial_state</i> do cílového stavu nalezený pomocí cen a heuristik.\n",
    "\n",
    "<p>\n",
    "Tipy:\n",
    "<ul>\n",
    "<li>\n",
    "Vyjděte z vašeho řešení UCS - stačí 2 malé změny a je hotovo.\n",
    "</li>\n",
    "<li>\n",
    "První změnou je ukládání vypočtených heuristických hodnot:<br>\n",
    "`heuristic[next_state] = heuristic_distance(next_state)`.<br>\n",
    "Tento výpočet stačí provést jednou při objevení stavu.\n",
    "</li>\n",
    "<li>\n",
    "Druhou změnou je výpočet priority, která je nyní součtem dosavadní ceny a heuristického odhadu ceny zbytku plánu, tj. `costs[s] + heuristic[s]`.\n",
    "</li>\n",
    "</ul>\n",
    "</p>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f63f74b62e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f63f74b6320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def a_star(initial_state):\n",
    "    fringe = {initial_state}\n",
    "    costs = {initial_state: 0}\n",
    "    heuristic = {initial_state: heuristic_distance(initial_state)}\n",
    "    plans = {initial_state: ''}\n",
    "    log_search_step(None, fringe, plans, costs, heuristic)\n",
    "    while fringe:\n",
    "        # TODO: Implementujte krok A*.\n",
    "        log_search_step(state, fringe, plans, costs, heuristic)\n",
    "\n",
    "state = parse_state(\n",
    "'| | | | | |'\n",
    "'|A| |A| | |'\n",
    "'| |A|A| |A|'\n",
    "'| | |A| | |'\n",
    "'| | |S| | |')\n",
    "with visualize_search(state, costs=True, heuristic=True, interactive=False):\n",
    "    plan = solutions.a_star(state)  # Vzorove reseni.\n",
    "    #plan = a_star(state)  # Vase reseni.\n",
    "show_plan(state, plan)"
   ]
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    "## Vymýšlení heuristik\n",
    "\n",
    "Aby bylo zaručeno nalezení nejkratší cesty, musí být heuristika optimistickým (spodním) odhadem na skutečnou cenu.\n",
    "Na druhou stranu, čím těsnější (přesnější) odhad bude, tím efektivnější\n",
    "prohledávání.\n",
    "\n",
    "Heuristiky závisí na řešeném problému.\n",
    "Základním přístupem k vymýšlení heuristik je \"relaxace problému\",\n",
    "což znamená vypuštění nějakých podmínek ze zadání problému tak,\n",
    "aby bylo problém triviální vyřešit (aby šlo heuristiku rychle spočítat).\n",
    "Naše heuristika vznikla tak, že jsme odstranili podmínku,\n",
    "že nelze letět přes asteroidy.\n",
    "\n",
    "\n",
    "## Shrnutí\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "<ul>\n",
    "<li>\n",
    "A-star je rozšíření UCS, ve kterém z okraje vybíráme stav s nejnižším součtem cena dosavadního plánu + odhad ceny za zbývající cestu do cíle. </li>\n",
    "<li>\n",
    "Aby bylo zaručeno nalezení nejkratší cesty, musí být heuristika optimistickým (spodním) odhadem na skutečnou cenu.\n",
    "Na druhou stranu, čím těsnější (přesnější) odhad bude, tím efektivnější\n",
    "prohledávání.\n",
    "</li>\n",
    "<li>\n",
    "Přípustnou heuristiku lze získat ze zadání problému vypuštěním některých jeho omezení tak, aby se stal triviálním na vyřešení.\n",
    "</li>\n",
    "</ul>\n",
    "</div>\n",
    "\n",
    "Co jsme se dneska naučili a kam dál? [00 - Plánování v AI](./00-planning-in-AI.ipynb)"
   ]
  }
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       "outputs": [
        {
         "data": {
          "image/png": 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          "text/plain": "<matplotlib.figure.Figure at 0x7f79c579d080>"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "c498d2d898084bf183a39fa2041a55c1": {
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      "model_name": "LayoutModel",
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     },
     "d69c017bc8514c5087260020f4c721f9": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.0.0",
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     "d849d1d42f8a47b6bb239d06764f8e7f": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.0.0",
      "model_name": "LayoutModel",
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     },
     "d891c1fc1b434fcb96ab17e8ed417343": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.0.0",
      "model_name": "VBoxModel",
      "state": {
       "_dom_classes": [
        "widget-interact"
       ],
       "children": [
        "IPY_MODEL_669b0b45dba54805b5aea4ce8603696e",
        "IPY_MODEL_518213d9c1d2402a9911687a20219837"
       ],
       "layout": "IPY_MODEL_7908f9d9f0b0467f884101ae8c41c6fe"
      }
     },
     "eaf3df9729424f62bd153ed332053b4f": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.0.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "eb64d4b5266b4f308a71321a0f84c51d": {
      "model_module": "@jupyter-widgets/controls",
      "model_module_version": "1.0.0",
      "model_name": "VBoxModel",
      "state": {
       "_dom_classes": [
        "widget-interact"
       ],
       "children": [
        "IPY_MODEL_a45e349f196b494cae977e6da5c9b838",
        "IPY_MODEL_54cc9d28c9fc4333bbaeb32c74262ea4"
       ],
       "layout": "IPY_MODEL_81580ee1350f44778e7bbf0d6c4789ce"
      }
     },
     "ebd5518599a945f7a54739b1d7b3ee39": {
      "model_module": "@jupyter-widgets/base",
      "model_module_version": "1.0.0",
      "model_name": "LayoutModel",
      "state": {}
     },
     "f08e779637d342469a88eab227c921ab": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_4714af76ab8f4325a720f661b4fb1688",
       "outputs": [
        {
         "data": {
          "image/png": 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          "text/plain": "<matplotlib.figure.Figure at 0x7f79c58c3cc0>"
         },
         "metadata": {},
         "output_type": "display_data"
        }
       ]
      }
     },
     "f5c27d07517d41f5a1fe52da5439231f": {
      "model_module": "@jupyter-widgets/output",
      "model_module_version": "1.0.0",
      "model_name": "OutputModel",
      "state": {
       "layout": "IPY_MODEL_6ca8dfea53214a97839304e3034221e5",
       "outputs": [
        {
         "data": {
          "image/png": 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