Numbers that are a power of their sum of digits.ipynb

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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Best Solution on CodeWars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def power_sumDigTerm(n):\n",
    "    return sorted([i**j for j in range(2,50) for i in range(2,100) if i == sum(map(int, str(i**j)))])[n-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#The most important thing is set a range/boundary instead of calculating every number.\n",
    "#Calculate from bottom up instead from the top down."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# My Working Progress"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sum_digits(n):\n",
    "    r = 0\n",
    "    while n:\n",
    "        r,n = r + n%10, n//10\n",
    "    return r\n",
    "#This is the function to calculate sum of the digits.\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "512"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "8**3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.482202253184497"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "512**(1./5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "math.log(512, 8).is_integer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_power_sum(n):\n",
    "    import math\n",
    "    try:\n",
    "        return round(math.log(n, sum_digits(n)), ndigits=10).is_integer()\n",
    "    except ZeroDivisionError:    \n",
    "        return False "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_power_sum(82)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def power_sumDigTerm(n):\n",
    "    i = 0\n",
    "    numtry = 10\n",
    "    while i < n:\n",
    "        numtry += 1\n",
    "        if is_power_sum(numtry):\n",
    "            i += 1\n",
    "    return numtry\n",
    "                "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4913"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power_sumDigTerm(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(math.log(2741, 14), 6).is_integer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 2.48 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1679616"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%%time\n",
    "power_sumDigTerm(11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Review a little bit about try and except\n",
    "def try_play(n):\n",
    "    try:\n",
    "        return round(math.log(n, sum_digits(n)), ndigits= 3).is_integer()\n",
    "    except:\n",
    "        return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.0"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.log(2401, 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "try_play(4913)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "179.999"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(179.999, ndigits=5)#.is_integer()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum_digits(4913)\n",
    "is_power_sum(4913)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#After all the effort above, I timed out. Need to think of a new strategy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2401"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "power_sumDigTerm(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "def power_sumDigTerm(n):\n",
    "    listOfN = []\n",
    "    for base in range(2, 100):\n",
    "        num = base\n",
    "        for _ in range(2, 10):\n",
    "            num *= base\n",
    "            if sum(map(int, str(num))) == base:\n",
    "                listOfN.append(num)\n",
    "    return sorted(listOfN)[n-1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "234256"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "powerOfSum(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2401, 512, 81]"
      ]
     },
     "execution_count": 153,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "listOfN= []\n",
    "for base in range(2, 10):\n",
    "    num = base\n",
    "    for _ in range(2, 10):\n",
    "        num *= base\n",
    "        if sum(map(int, str(num))) == base:\n",
    "            listOfN.append(num)\n",
    "listOfN"
   ]
  },
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