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  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9440954a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import randint\n",
    "\n",
    "capacity = 10\n",
    "# items are (weight, value)\n",
    "items = [(8,13),(3,7),(5,10),(5,10),(2,1),(2,1),(2,1)]\n",
    "\n",
    "capacity = 22\n",
    "items = [(randint(5,20),randint(5,20)) for _ in range(200)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f411bd48",
   "metadata": {},
   "outputs": [],
   "source": [
    "# to help you write recursive functions, always plan out\n",
    "#   SUPER explicitly what the inputs and outputs are\n",
    "# input:\n",
    "#   items_left: list of remaining items to choose from\n",
    "#                 (at the start, all items are remaining)\n",
    "#   capacity_left: remaining capacity\n",
    "# output:\n",
    "#   the best solution (as a list of 2-tuples) using just\n",
    "#   \"items_left\" with capacity <= \"capacity_left\"\n",
    "def solve(items_left, capacity_left):\n",
    "    # return the set of items in the best solution\n",
    "    # print(\"call with\",(items_left, capacity_left))\n",
    "    \n",
    "    #if not items_left:\n",
    "    if len(items_left) == 0:\n",
    "        return []\n",
    "    \n",
    "    # item = (weight, value)\n",
    "    first_item_weight = items_left[0][0]\n",
    "    \n",
    "    sol_without_item = solve(items_left[1:], capacity_left)\n",
    "    \n",
    "    # if we have room for the first item, add it and recursively solve\n",
    "    if first_item_weight <= capacity_left:\n",
    "        sol_with_item = [items_left[0]] + solve(items_left[1:], capacity_left-first_item_weight)\n",
    "    else:\n",
    "        # if not, then only possible solution is exclusing the item\n",
    "        return sol_without_item\n",
    "        \n",
    "    # compare sol_with and sol_without, and return the best\n",
    "    score_with = sum(item[1] for item in sol_with_item)\n",
    "    score_without = sum(item[1] for item in sol_without_item)\n",
    "    \n",
    "    if score_with > score_without:\n",
    "        return sol_with_item\n",
    "    return sol_without_item"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bda8de48",
   "metadata": {},
   "source": [
    "```\n",
    "items = [(8,13),(3,7),(5,10)]\n",
    "\n",
    "solve([(8,13),(3,7),(5,10)], 10)\n",
    " --> solve([(3,7),(5,10)], 10)\n",
    "     --> solve([(5,10)], 10)\n",
    "         solve([(5,10)], 7)\n",
    "     vs\n",
    "     solve([(3,7),(5,10)], 2)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fc29be45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(5, 20), (5, 19), (5, 18), (7, 20)]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(items, capacity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "af21f0ba",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f02be70d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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