Project Euler Q39 - LO Man Hei

Download notebook

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a469358e-2f57-4bd6-9c8d-c59f3d77920b",
   "metadata": {},
   "source": [
    "### Q39\n",
    "For which value of \\(p \\le 1000\\), is the number of solutions maximised?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "255771bb-8696-4c1c-aeb2-f56c3bc62237",
   "metadata": {},
   "outputs": [],
   "source": [
    "def max_comb_int_right_triangle(n):\n",
    "    half_range = n//2\n",
    "    c_squares = {i*i:i for i in range(2,half_range)}\n",
    "    result = {}\n",
    "    for ab_sum in range(2,half_range):\n",
    "        for a in range(1,ab_sum//2+1):\n",
    "            b = ab_sum-a\n",
    "            ab_squares = a*a + b*b\n",
    "            if ab_squares in c_squares:\n",
    "                abc_sum = ab_sum+c_squares[ab_squares]\n",
    "                if abc_sum > n:\n",
    "                    break\n",
    "                else:\n",
    "                    result[abc_sum] = result.get(abc_sum,0) + 1\n",
    "    return max(result, key=result.get)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3d047ff9-52dc-4b20-b614-4192212ea5ad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 5.94 ms, sys: 1.04 ms, total: 6.98 ms\n",
      "Wall time: 6.71 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "840"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "max_comb_int_right_triangle(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cba0db36-d776-4352-a1ac-2196f6855de6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}

Loading