From 1a0fbbb1c82d97f353f3e31a3c435e49aab71212 Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Tue, 6 Feb 2018 08:33:31 +0100
Subject: [PATCH] Tryed to solve 21 in ipython.

---
 ipython/EulerProblem020.ipynb |  87 ++++++++++++++
 ipython/EulerProblem021.ipynb | 219 ++++++++++++++++++++++++++++++++++
 2 files changed, 306 insertions(+)
 create mode 100644 ipython/EulerProblem020.ipynb
 create mode 100644 ipython/EulerProblem021.ipynb

diff --git a/ipython/EulerProblem020.ipynb b/ipython/EulerProblem020.ipynb
new file mode 100644
index 0000000..e0c01b4
--- /dev/null
+++ b/ipython/EulerProblem020.ipynb
@@ -0,0 +1,87 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Euler Problem 20\n",
+    "\n",
+    "n! means n × (n − 1) × ... × 3 × 2 × 1\n",
+    "\n",
+    "For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,\n",
+    "and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.\n",
+    "\n",
+    "Find the sum of the digits in the number 100!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Write our own factorial implementation and get the solution."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def factorial(n):\n",
+    "    assert(n > 0)\n",
+    "    if n == 1:\n",
+    "        return 1\n",
+    "    else:\n",
+    "        return n * factorial(n - 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "648\n"
+     ]
+    }
+   ],
+   "source": [
+    "f100 = factorial(100)\n",
+    "print(sum(map(int, str(f100))))\n",
+    "assert(sum(map(int, str(f100))) == 648)"
+   ]
+  }
+ ],
+ "metadata": {
+  "completion_date": "Fri, 5 Sep 2014, 10:42",
+  "kernelspec": {
+   "display_name": "Python 3",
+   "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": "3.5.4"
+  },
+  "tags": [
+   "factorial"
+  ]
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
diff --git a/ipython/EulerProblem021.ipynb b/ipython/EulerProblem021.ipynb
new file mode 100644
index 0000000..cab692f
--- /dev/null
+++ b/ipython/EulerProblem021.ipynb
@@ -0,0 +1,219 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Euler Problem 21\n",
+    "\n",
+    "Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).\n",
+    "If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.\n",
+    "\n",
+    "For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.\n",
+    "\n",
+    "Evaluate the sum of all the amicable numbers under 10000."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Reuse factorization function from problem 12."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def get_primes_smaller(number):\n",
+    "    primes = []\n",
+    "    prospects = [n for n in range(2, number)]\n",
+    "    while prospects:\n",
+    "        p = prospects[0]\n",
+    "        prospects = [x for x in prospects if x % p != 0]\n",
+    "        primes.append(p)\n",
+    "    return primes\n",
+    "\n",
+    "primes_smaller_10000 = get_primes_smaller(10000)\n",
+    "\n",
+    "def get_prime_factors(number):\n",
+    "    remainder = number\n",
+    "    factors = []\n",
+    "    for p in primes_smaller_10000:\n",
+    "        while remainder % p == 0:\n",
+    "            remainder /= p\n",
+    "            factors.append(p)\n",
+    "        if remainder == 1 or p * p > number:\n",
+    "            break\n",
+    "    if remainder != 1:\n",
+    "        factors.append(remainder)\n",
+    "    return factors"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "If we have a list of all factors we group them. To get all potential divisors for each group we may use each factor 0 to len(factor_group). We then combine the potential divisors of all factor groups. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def product(xs):\n",
+    "    from operator import mul\n",
+    "    from functools import reduce\n",
+    "    return reduce(mul, xs, 1)\n",
+    "\n",
+    "def group(xs):\n",
+    "    from functools import reduce\n",
+    "    def f(xss, x):\n",
+    "        if xss and x in xss[-1]:\n",
+    "            xss[-1].append(x)\n",
+    "        else:\n",
+    "            xss.append([x])\n",
+    "        return xss\n",
+    "    return reduce(f, xs, [])\n",
+    "\n",
+    "def combinations(xss):\n",
+    "    from functools import reduce\n",
+    "    def f(xs, ys):\n",
+    "        return [x + [y]\n",
+    "            for y in ys\n",
+    "            for x in xs\n",
+    "        ]          \n",
+    "    return reduce(f, list(xss), [[]])\n",
+    "\n",
+    "def get_divisors_for_factor_group(factor_group):\n",
+    "    factor = factor_group[0]\n",
+    "    return [factor**i for i in range(len(factor_group) + 1)]\n",
+    "\n",
+    "def get_proper_divisors(number):\n",
+    "    factors = get_prime_factors(number)\n",
+    "    factor_groups = map(get_divisors_for_factor_group, group(factors))\n",
+    "    factor_combinations = combinations(factor_groups)\n",
+    "    divisors = map(product, factor_combinations)\n",
+    "    factors = list(divisors)\n",
+    "    factors.sort()\n",
+    "    return factors[:-1] # last value is not a proper divisor\n",
+    "\n",
+    "assert(get_proper_divisors(220) == [1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can finally start to get the solution."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def sum_of_proper_divisors(number):\n",
+    "    return sum(get_proper_divisors(number))\n",
+    "\n",
+    "assert(sum_of_proper_divisors(220) == 284)\n",
+    "assert(sum_of_proper_divisors(284) == 220)\n",
+    "\n",
+    "def is_amicable(number):\n",
+    "    s = sum_of_proper_divisors(number)\n",
+    "    return number == sum_of_proper_divisors(s)\n",
+    "\n",
+    "assert(is_amicable(220))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "ename": "KeyboardInterrupt",
+     "evalue": "",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
+      "\u001b[1;32m<ipython-input-4-afe32366db14>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mamicable_till_10000\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m10000\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mis_amicable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[1;32m<ipython-input-4-afe32366db14>\u001b[0m in \u001b[0;36m<listcomp>\u001b[1;34m(.0)\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mamicable_till_10000\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[0mi\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m10000\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mis_amicable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[1;32m<ipython-input-3-4ae1320a291d>\u001b[0m in \u001b[0;36mis_amicable\u001b[1;34m(number)\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mis_amicable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumber\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m     \u001b[0ms\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msum_of_proper_divisors\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumber\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 9\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mnumber\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0msum_of_proper_divisors\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ms\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     10\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     11\u001b[0m \u001b[1;32massert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mis_amicable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m220\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+      "\u001b[1;32m<ipython-input-3-4ae1320a291d>\u001b[0m in \u001b[0;36msum_of_proper_divisors\u001b[1;34m(number)\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0msum_of_proper_divisors\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumber\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mget_proper_divisors\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumber\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;32massert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msum_of_proper_divisors\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m220\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m284\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;32massert\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msum_of_proper_divisors\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m284\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m220\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+      "\u001b[1;32m<ipython-input-2-741d0e28361b>\u001b[0m in \u001b[0;36mget_proper_divisors\u001b[1;34m(number)\u001b[0m\n\u001b[0;32m     28\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     29\u001b[0m \u001b[1;32mdef\u001b[0m \u001b[0mget_proper_divisors\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumber\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 30\u001b[1;33m     \u001b[0mfactors\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mget_prime_factors\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumber\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     31\u001b[0m     \u001b[0mfactor_groups\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmap\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mget_divisors_for_factor_group\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mgroup\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfactors\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     32\u001b[0m     \u001b[0mfactor_combinations\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcombinations\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfactor_groups\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+      "\u001b[1;32m<ipython-input-1-87689c2c868f>\u001b[0m in \u001b[0;36mget_prime_factors\u001b[1;34m(number)\u001b[0m\n\u001b[0;32m     15\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mp\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mprimes_smaller_10000\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     16\u001b[0m         \u001b[1;32mwhile\u001b[0m \u001b[0mremainder\u001b[0m \u001b[1;33m%\u001b[0m \u001b[0mp\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 17\u001b[1;33m             \u001b[0mremainder\u001b[0m \u001b[1;33m/=\u001b[0m \u001b[0mp\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     18\u001b[0m             \u001b[0mfactors\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mp\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     19\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mremainder\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;36m1\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mp\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mp\u001b[0m \u001b[1;33m>\u001b[0m \u001b[0mnumber\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
+     ]
+    }
+   ],
+   "source": [
+    "amicable_till_10000 = [i for i in range(1, 10000) if is_amicable(i)]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "for a in amicable_till_10000:\n",
+    "    print(a)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "completion_date": "Fri, 5 Sep 2014, 14:39",
+  "kernelspec": {
+   "display_name": "Python 3",
+   "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": "3.5.4"
+  },
+  "tags": [
+   "amicable",
+   "factors",
+   "combinations",
+   "reduce",
+   "prime"
+  ]
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}