partial permutations

partial_permutations.ipynb

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   "source": [
    "# Partial Permutations\n",
    "\n",
    "**Given:** positive integers $n$ and $k$ such that $100 \\geq n > 0$ and $10 \\geq k > 0$\n",
    "\n",
    "**Return:** the total number of partial permutations $P(n, k)$ mod $1e6$\n",
    "\n",
    "$$P(n, k) = \\frac{n!}{(n-k)!}$$\n"
   ]
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   "source": [
    "from math import factorial\n",
    "\n",
    "def pp(n, k):\n",
    "    x =  factorial(n) / factorial(n-k)\n",
    "    return int(x % 1e6)\n",
    "    \n",
    "# example data\n",
    "pp(21, 7)"
   ]
  },
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   "source": [
    "## Rosalind Data\n",
    "and reading from file"
   ]
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   "source": [
    "def partial_permutations(path):\n",
    "    \n",
    "    # open file and get values as a list\n",
    "    nums = map(int, open(path).read().split(\" \"))\n",
    "    \n",
    "    # pass first two numbers to `f()`\n",
    "    return pp(nums[0], nums[1])\n",
    "\n",
    "my_file = \"/home/scott/Dropbox/rosalind/rosalind_pper.txt\"\n",
    "partial_permutations(my_file)"
   ]
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   "source": [
    "## If you're stuck in the 1980's (or using R)\n",
    "\n",
    "Have iterate through and modulo as you go to avoid integer overflow"
   ]
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   "source": [
    "n = 83\n",
    "k = 9\n",
    "\n",
    "def part_permute(n, k):\n",
    "    \n",
    "    vals = range(n, n-k, -1)\n",
    "    \n",
    "    def f(n, k):\n",
    "        return (n*k) % 1e6\n",
    "    \n",
    "    return int(reduce(f, vals))\n",
    "\n",
    "part_permute(n, k)\n"
   ]
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     "execution_count": 4,
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   ],
   "source": [
    "# one liner\n",
    "reduce(lambda n, k: (n*k) % 1e6, range(n, n-k, -1))"
   ]
  }
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