add problem 67

notebooks/problem0067.ipynb

@@ -0,0 +1,84 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "35b56ed4",
+   "metadata": {},
+   "source": [
+    "# [Maximum Path Sum II](https://projecteuler.net/problem=67)\n",
+    "\n",
+    "Since we took the time to find an efficient method in [problem 18](https://projecteuler.net/problem=18), we can just reuse that method here.\n",
+    "\n",
+    "So just read the triangle into a list-of-lists."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "194eef78",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "with open(\"txt/0067_triangle.txt\") as f:\n",
+    "    triangle = [[int(n) for n in line.split(' ')] for line in f]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b39b979e",
+   "metadata": {},
+   "source": [
+    "Then we'll use the bottom-up method from before (you could also use the top-down method)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "fa8a353f",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "7273"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "def max_path_sum(tri):\n",
+    "    for i in reversed(range(0, len(tri) - 1)):\n",
+    "        for j in range(0, len(tri[i])):\n",
+    "            tri[i][j] += max(tri[i+1][j], tri[i+1][j+1])\n",
+    "            \n",
+    "    return tri[0][0]\n",
+    "\n",
+    "max_path_sum(triangle)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "SageMath 9.5",
+   "language": "sage",
+   "name": "sagemath"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.11.2"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}