Solved 61, 62, 63.

ipython/EulerProblem061.ipynb

@@ -37,6 +37,93 @@
     "Find the sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set."
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_four_digit_numbers(function):\n",
+    "    r = []\n",
+    "    n = 1\n",
+    "    f = function\n",
+    "    while f(n) < 10000:\n",
+    "        if f(n) > 999:\n",
+    "            r.append(f(n))\n",
+    "        n += 1\n",
+    "    return r\n",
+    "\n",
+    "triangles = get_four_digit_numbers(lambda n: n * (n + 1) // 2)\n",
+    "squares = get_four_digit_numbers(lambda n: n**2)\n",
+    "pentas = get_four_digit_numbers(lambda n: n * (3 * n - 1) // 2)\n",
+    "hexas = get_four_digit_numbers(lambda n: n * (2 * n - 1))\n",
+    "heptas = get_four_digit_numbers(lambda n: n * (5*n - 3) // 2)\n",
+    "octas = get_four_digit_numbers(lambda n: n * (3*n - 2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def is_cyclic(a, b):\n",
+    "    return str(a)[-2:] == str(b)[:2]\n",
+    "\n",
+    "assert(is_cyclic(3328, 2877))\n",
+    "assert(is_cyclic(3329, 2877) == False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[8256, 5625, 2512, 1281, 8128, 2882]\n",
+      "28684\n"
+     ]
+    }
+   ],
+   "source": [
+    "def search_solution(aggregator, polygonals):\n",
+    "    if not polygonals:\n",
+    "        if is_cyclic(aggregator[-1], aggregator[0]):\n",
+    "            return aggregator\n",
+    "        else:\n",
+    "            return []\n",
+    "\n",
+    "    if not aggregator:\n",
+    "        for polygonal in polygonals:\n",
+    "            for number in polygonal:\n",
+    "                aggregator.append(number)\n",
+    "                s = search_solution(aggregator, [p for p in polygonals if p != polygonal])\n",
+    "                if s:\n",
+    "                    return s\n",
+    "                aggregator.pop()\n",
+    "\n",
+    "    for polygonal in polygonals:\n",
+    "        for number in polygonal:\n",
+    "            if is_cyclic(aggregator[-1], number) and not number in aggregator:\n",
+    "                aggregator.append(number)\n",
+    "                s = search_solution(aggregator, [p for p in polygonals if p != polygonal])\n",
+    "                if s:\n",
+    "                    return s\n",
+    "                aggregator.pop()\n",
+    "    return []\n",
+    "\n",
+    "s = search_solution([], [triangles, squares, pentas, hexas, heptas, octas])\n",
+    "print(s)\n",
+    "s = sum(s)\n",
+    "print(s)\n",
+    "assert(s == 28684)"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -48,7 +135,7 @@
   }
  ],
  "metadata": {
-  "completion_date": "",
+  "completion_date": "Sun, 6 Jan 2019, 05:32",
   "kernelspec": {
    "display_name": "Python 3",
    "language": "python3.6",
@@ -66,7 +153,10 @@
    "pygments_lexer": "ipython3",
    "version": "3.6.5"
   },
-  "tags": []
+  "tags": [
+   "search",
+   "cyclic"
+  ]
  },
  "nbformat": 4,
  "nbformat_minor": 2