Prime Combinatons

prime-combinations.ipynb

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    "def bfs(root, get_children, is_goal):\n",
    "  queue = [root]\n",
    "  parents = {}\n",
    "  seen = set(queue)\n",
    "  \n",
    "  while len(queue) > 0:\n",
    "    current, queue = queue[0], queue[1:]\n",
    "    \n",
    "    if is_goal(current):\n",
    "      return path(current, parents)\n",
    "    \n",
    "    for child in get_children(current):\n",
    "      if child not in seen:\n",
    "        seen.add(child)\n",
    "        parents[child] = current\n",
    "        queue.append(child)\n",
    "\n",
    "  return None\n",
    "\n",
    "def path(node, parents):\n",
    "  p = []\n",
    "  \n",
    "  while node is not None:\n",
    "    p.append(node)\n",
    "    node = parents.get(node)\n",
    "    \n",
    "  return p[::-1]"
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Precompute all primes <= 99999\n",
    "primes = set()\n",
    "for n in range(2, 100000):\n",
    "  if not any(n % p == 0 for p in primes):\n",
    "    primes.add(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_child_combinations(n):\n",
    "  for i in range(5):\n",
    "    d = (n//(10**i)) % 10\n",
    "    \n",
    "    if d-1 >= 0:\n",
    "      yield n - (10**i)\n",
    "    else:\n",
    "      yield n + 9*(10**i)\n",
    "    \n",
    "    if d+1 < 10:\n",
    "      yield n + (10**i)\n",
    "    else:\n",
    "      yield n - 9*(10**i)\n",
    "      \n",
    "def get_prime_child_combinations(n):\n",
    "  return (c for c in get_child_combinations(n) if c in primes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'00001 -> 00002 -> 00003 -> 00013 -> 00023 -> 90023 -> 99023 -> 99923 -> 99823 -> 99833 -> 99733 -> 09733 -> 00733 -> 10733 -> 10723'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = bfs(1, get_prime_child_combinations, lambda n: n == 10723)\n",
    "\" -> \".join(\"%05d\" % c for c in p)"
   ]
  }
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