{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class City:\n",
    "    def __init__(self, id, links = []):\n",
    "        self.id = id\n",
    "        self.links = links"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "City1 = City(1, [(2, 10), (3, 15), (4, 20)])\n",
    "City2 = City(2, [(1, 10), (3, 35), (4, 25)])\n",
    "City3 = City(3, [(1, 15), (2, 35), (4, 30)])\n",
    "City4 = City(4, [(1, 20), (2, 25), (3, 30)])\n",
    "\n",
    "cities = [City1, City2, City3, City4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "def findShortestPath(curr_id, visited_ids, cities, cost = 0):\n",
    "    curr_index = curr_id - 1\n",
    "\n",
    "    if len(visited_ids) == len(cities):\n",
    "        for link in cities[curr_index].links:\n",
    "            if link[0] == visited_ids[0]:\n",
    "                return (visited_ids + [visited_ids[0]], cost + link[1])\n",
    "\n",
    "    curr_cost = 0\n",
    "    min_cost = ((), 1000)\n",
    "    for link in cities[curr_index].links:\n",
    "        if link[0] not in visited_ids:\n",
    "            curr_cost = findShortestPath(link[0], visited_ids + [link[0]], cities, cost + link[1])\n",
    "            if curr_cost[1] < min_cost[1]:\n",
    "                min_cost = curr_cost\n",
    "\n",
    "    return min_cost\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "([1, 2, 4, 3, 1], 80)\n",
      "([2, 1, 3, 4, 2], 80)\n",
      "([3, 1, 2, 4, 3], 80)\n",
      "([4, 2, 1, 3, 4], 80)\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, len(cities) + 1):\n",
    "    print(findShortestPath(i, [i], cities))"
   ]
  }
 ],
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