Added 24 and 25 to ipython.

ipython/EulerProblem024.ipynb

@@ -0,0 +1,109 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Euler Problem 24 \n",
+    "\n",
+    "A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:\n",
+    "\n",
+    "012   021   102   120   201   210\n",
+    "\n",
+    "What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "I tried to solve this by thinking and failed to be hones. So we implement a generator and get the millionth element."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "from collections import deque\n",
+    "\n",
+    "def permutation_generator(xs):\n",
+    "    if not xs:\n",
+    "        yield deque()\n",
+    "    r = []\n",
+    "    for i in range(len(xs)):\n",
+    "        x = xs[i]\n",
+    "        ys = permutation_generator(xs[:i] + xs[i+1:])\n",
+    "        for y in ys:\n",
+    "            y.appendleft(x)\n",
+    "            yield y\n",
+    "    raise StopIteration\n",
+    "\n",
+    "assert(list(map(lambda s: \"\".join(s), permutation_generator(\"012\"))) == ['012', '021', '102', '120', '201', '210'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "All right, now we reuse the function to get the nth element from problem 7 and give ourselves a solution."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "2783915460\n"
+     ]
+    }
+   ],
+   "source": [
+    "def get_nth(generator, n):\n",
+    "    import itertools\n",
+    "    return next(itertools.islice(generator, n - 1, n))\n",
+    "\n",
+    "ps = permutation_generator(\"0123456789\")\n",
+    "s = int(\"\".join(get_nth(ps, 1000000)))\n",
+    "assert(s == 2783915460)\n",
+    "print(s)"
+   ]
+  }
+ ],
+ "metadata": {
+  "completion_date": "Thu, 5 Nov 2015, 16:04",
+  "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": [
+   "permutation"
+  ]
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}