Simplifying multilinear polynomials.ipynb

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   "outputs": [],
   "source": [
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Most Clever Answers on Codewars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# My Working Progress and Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'+3xy+y-2x+2xy'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#This is gonna be a long one.\n",
    "\n",
    "#Check if the first character is a sign:\n",
    "Input = '3xy+y-2x+2xy'\n",
    "if Input[0] !='-':\n",
    "    Input = '+'+Input\n",
    "Input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['+', '3', 'x', 'y', '+', 'y', '-', '2', 'x', '+', '2', 'x', 'y']"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "13"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L = list(Input)\n",
    "L\n",
    "len(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['']\n",
      "2\n",
      "3\n",
      "4\n",
      "['', '+3xy']\n",
      "2\n",
      "['', '+3xy', '+y']\n",
      "2\n",
      "3\n",
      "['', '+3xy', '+y', '-2x']\n",
      "2\n",
      "3\n",
      "4\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "['+3xy', '+y', '-2x', '+2xy']"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Put each monomial in a list as an element\n",
    "Temp, e = [], ''\n",
    "for i in L:\n",
    "    if i != '+' and i != '-':\n",
    "        e += i\n",
    "        print(len(e))\n",
    "    else:\n",
    "        Temp.append(e)\n",
    "        print(Temp)\n",
    "        e = ''\n",
    "        e += i\n",
    "#The last one will be left out\n",
    "Temp.append(e)\n",
    "Temp.pop(0)\n",
    "Temp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['+3xy', '+1y', '-2x', '+2xy']"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Watch out for the format for list comprehension with if else\n",
    "SortAndGiveOne = [''.join(e[0] + '1' + e[1:]) if not e[1].isdigit() else e for e in Temp]\n",
    "SortAndGiveOne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['xy', 'y', 'x', 'xy']"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "['+3', '+1', '-2', '+2']"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Try to get letters from each element of the list\n",
    "Letter = [''.join(sorted(i for i in e if i.isalpha())) for e in SortAndGiveOne]\n",
    "Coe = [''.join(i for i in e if not i.isalpha()) for e in SortAndGiveOne]\n",
    "Letter \n",
    "Coe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'xy'"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "'+2'"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "['xy', 'y', 'x']"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "['5', '+1', '-2']"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Try to merge the monopolials\n",
    "Play1 = Letter[:]\n",
    "Play2 = Coe[:]\n",
    "for i in range(len(Play1) - 1):\n",
    "    for j in range(i+1, len(Play1)):\n",
    "        if Play1[i] == Play1[j]:\n",
    "            Play1.pop(j)\n",
    "            Play2[i] = str(int(Play2[i]) + int(Play2[j]))\n",
    "            Play2.pop(j)\n",
    "Play1\n",
    "Play2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['+5xy', '+1y', '-2x']"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Put the new lists together\n",
    "Put_t = list(map(lambda x,y : y + x, Play1, Play2))\n",
    "# Add the plus sign \n",
    "FinalSign = ['+'+ e if e[0] != '+' and e[0] != '-' else e for e in Put_t]\n",
    "FinalSign"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Try sort the elements based on length of the letters part\n",
    "+"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['xy+3', 'y+1', 'x-2', 'xy+2']"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Play1 = Letter[:]\n",
    "Play2 = Coe[:]\n",
    "list(map(lambda x,y : x + y, Play1, Play2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('+3', 'xy'), ('+1', 'y'), ('-2', 'x'), ('+2', 'xy')]"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ZipTry = list(zip(Play2, Play1))\n",
    "ZipTry\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "441"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i = 1\n",
    "while not (i%2 == 1 and i%3 == 0 and i%4 == 1 and i%5 == 1 and i%6 == 3 and i%7 == 0 and i%8 == 1 and i% 9 == 0):\n",
    "    i += 1\n",
    "i\n",
    "441%7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int('-1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'+25xyz'"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''.join(sorted('+25xzy'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['+3xy+y-2x+2xy', '5']"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Temp.append('5')\n",
    "Temp"
   ]
  }
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