Project Euler Q15 - LO Man Hei

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   "source": [
    "### Q15\n",
    "How many such routes are there through a \\(20 \\times 20\\) grid?"
   ]
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    "def num_routes_of_m_n_grid(m,n):\n",
    "    if n > m:\n",
    "        m, n = n, m\n",
    "    routes_of_edge = [[0 for j in range(n+1)] for i in range(m+1)]\n",
    "    for i in range(m+1):\n",
    "        routes_of_edge[i][0] = 1\n",
    "    for j in range(n+1):\n",
    "        routes_of_edge[0][j] = 1        \n",
    "    for i in range(1,m+1):\n",
    "        for j in range(1,min([i+1,n+1])):\n",
    "            routes_of_edge[i][j] = routes_of_edge[i-1][j] + routes_of_edge[i][j-1]\n",
    "            if i <= n:\n",
    "                routes_of_edge[j][i] = routes_of_edge[i][j]\n",
    "    return routes_of_edge[m][n]"
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     "text": [
      "CPU times: user 48 µs, sys: 0 µs, total: 48 µs\n",
      "Wall time: 49.1 µs\n"
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   "source": [
    "%%time\n",
    "num_routes_of_m_n_grid(20,20)"
   ]
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   "id": "69e94a95-4e1e-44e8-9bcb-6c72c0d48636",
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   "source": [
    "def factorial(n):\n",
    "    return n*factorial(n-1) if n > 1 else 1\n",
    "\n",
    "def nCr(n,r):\n",
    "    return factorial(n)//factorial(n-r)//factorial(r)"
   ]
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   "execution_count": 4,
   "id": "76c88946-14bd-4a20-8de6-0f6ab69b96a0",
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     "name": "stdout",
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     "text": [
      "CPU times: user 13 µs, sys: 0 ns, total: 13 µs\n",
      "Wall time: 13.6 µs\n"
     ]
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     "data": {
      "text/plain": [
       "137846528820"
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     "execution_count": 4,
     "metadata": {},
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   ],
   "source": [
    "%%time\n",
    "nCr(40,20)"
   ]
  },
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   "execution_count": null,
   "id": "83aed11b-72a6-4f86-a4f4-536647079846",
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