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   "source": [
    "## Sorting example\n",
    "\n",
    "This example is meant as a demonstration of the capabilities of simulated annealing. There are of course better algorithms than metaheuristic approaches."
   ]
  },
  {
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     "start_time": "2025-12-20T19:34:48.250482Z"
    }
   },
   "source": [
    "from collections.abc import Sequence\n",
    "\n",
    "from altbacken.external.neighbourhood.permutation import PermutationNeighbourhood\n",
    "from altbacken.external.annealing import SimpleSimulatedAnnealing\n"
   ],
   "outputs": [],
   "execution_count": 1
  },
  {
   "cell_type": "code",
   "id": "c86c51aa1b86a25f",
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   },
   "source": [
    "unsorted = [4, 2, 9, 7, 1, 6, 0, 8, 5, 3]\n"
   ],
   "outputs": [],
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "id": "e44c1852bad35cd",
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   "source": [
    "### Fitness function\n",
    "\n",
    "We will use inversion count as it provides a simple measure of the quality of a permutation and provides some local optima.\n"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "def inversion_count(seq: Sequence[int]) -> int:\n",
    "    return sum(\n",
    "        1 for i in range(len(seq))\n",
    "        for j in range(i+1, len(seq))\n",
    "        if seq[i] > seq[j]\n",
    "    )"
   ],
   "outputs": [],
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "id": "47e08ea8246b2fbe",
   "metadata": {},
   "source": [
    "### Annealing strategy\n",
    "\n",
    "We choose a simple simulated annealing strategy with a temperature of 10000.0."
   ]
  },
  {
   "cell_type": "code",
   "id": "e78f5bfc585109ef",
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   },
   "source": [
    "annealing: SimpleSimulatedAnnealing = SimpleSimulatedAnnealing(\n",
    "    inversion_count,\n",
    "    PermutationNeighbourhood(),\n",
    "    10000.0\n",
    ")"
   ],
   "outputs": [],
   "execution_count": 4
  },
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   "cell_type": "code",
   "id": "a2924cc298cc34ea",
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    }
   },
   "source": [
    "best_match, best_value = annealing.simulate(unsorted)\n",
    "\n",
    "print(\"Best match:\", best_match)\n",
    "print(\"Best value:\", best_value)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best match: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)\n",
      "Best value: 0\n"
     ]
    }
   ],
   "execution_count": 5
  }
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