{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This problem is very similar to [Problem 15](https://xojoc.pw/challenges/euler/15). We build a DAG and then find the longest path taking in consideration the weight of each node.\n",
    "This algorithm solves [Problem 67](https://xojoc.pw/challenges/euler/67) too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1074\n",
      "7273\n"
     ]
    }
   ],
   "source": [
    "import networkx as nx\n",
    "from urllib.request import urlopen\n",
    "\n",
    "\n",
    "def read_triangle(file):\n",
    "    triangle_data = \"\"\n",
    "    try:\n",
    "        with open(file) as f:\n",
    "            triangle_data = f.read()\n",
    "    except FileNotFoundError:\n",
    "        with urlopen(\"https://xojoc.pw/challenges/euler/\" + file) as response:\n",
    "            triangle_data = response.read().decode()\n",
    "\n",
    "    return [[int(n) for n in line.split(' ')] for line in triangle_data[:-1].split('\\n')]\n",
    "\n",
    "\n",
    "def build_graph(triangle):\n",
    "    g = nx.DiGraph()\n",
    "\n",
    "    def T(n):\n",
    "        return n * (n + 1) // 2\n",
    "\n",
    "    def i(row, col):\n",
    "        return 1 + T(row) + col\n",
    "\n",
    "    for r in range(len(triangle)):\n",
    "        for c in range(r + 1):\n",
    "            g.add_node(i(r, c), weight=triangle[r][c])\n",
    "\n",
    "    for r in range(len(triangle)-1):\n",
    "        for c in range(r+1):\n",
    "            g.add_edge(i(r, c), i(r + 1, c))\n",
    "            g.add_edge(i(r, c), i(r + 1, c + 1))\n",
    "\n",
    "    return g\n",
    "\n",
    "\n",
    "def longest_path(g):\n",
    "    sorted_nodes = list(nx.topological_sort(g))\n",
    "    first_node = sorted_nodes[0]\n",
    "    node_weights = nx.get_node_attributes(g, 'weight')\n",
    "    cache = {}\n",
    "    for n in reversed(sorted_nodes):\n",
    "        max_weight = 0\n",
    "        for s in g.successors(n):\n",
    "            max_weight = max(cache[s], max_weight)\n",
    "        cache[n] = node_weights[n] + max_weight\n",
    "    return cache[first_node]\n",
    "\n",
    "\n",
    "for f in [\"18.txt\", \"67.txt\"]:\n",
    "    triangle = read_triangle(f)\n",
    "    g = build_graph(triangle)\n",
    "    print(longest_path(g))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "title": "Maximum path sum I"
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