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   "cell_type": "markdown",
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   "source": [
    "# Monotone substrings\n",
    "\n",
    "Given a list of numbers, find the length of longest increasing or decreasing substring in the list.\n",
    "\n",
    "For instance, the sequence\n",
    "  10, 1, 2, 3, 4, 5, 5, 5, 6, 4, 3, 5, 6\n",
    "contains these increasing or decreasing substrings:\n",
    "* 10, 1\n",
    "* 1, 2, 3, 4, 5\n",
    "* 5, 6\n",
    "* 6, 4, 3\n",
    "* 3, 5, 6\n",
    "\n",
    "As an extension, allow the substring to contain runs of identical numbers, each of which is included in the length of the longest substring.\n",
    "\n",
    "If identical numbers are allowed, the above sequence contains substrings:\n",
    "* 10, 1\n",
    "* 1, 2, 3, 4, 5, 5, 5, 6\n",
    "* 6, 4, 3\n",
    "* 3, 5, 6\n",
    "\n",
    "The list is given as a single line of comma-separated integers. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import itertools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cmp(x, y):\n",
    "    if x == y:\n",
    "        return 0\n",
    "    elif x > y:\n",
    "        return -1\n",
    "    else:\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def longest_monotone(seq, allow_same=False, debug=False):\n",
    "    \"\"\"Find the longest monotonic substring. If allow_same is True, \n",
    "    instead find the longest non-decreasing or non-increasing substring\"\"\"\n",
    "    cmps = [cmp(x, y) for x, y in zip(seq, seq[1:])]\n",
    "    groups = [(k, len(list(g)) + 1) for k, g in itertools.groupby(cmps)]\n",
    "    if allow_same:\n",
    "        groups = merged(groups)\n",
    "    if debug:\n",
    "        return max(t[1] for t in groups), groups\n",
    "    else:\n",
    "        return max(t[1] for t in groups)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def merged(gs):\n",
    "    padded = gs + [(0, 0)]\n",
    "    mgs = []\n",
    "    prev = (0, 1)\n",
    "    for curr, nxt in zip(padded, padded[1:]):\n",
    "        if prev[0] == 0:\n",
    "            prev = (curr[0], prev[1] + curr[1] - 1)\n",
    "        elif curr[0] == 0:\n",
    "            prev = (prev[0], prev[1] + curr[1] - 1)\n",
    "            if prev[0] != nxt[0]:\n",
    "                mgs += [prev]\n",
    "                prev = (0, curr[1])\n",
    "        elif prev[0] == curr[0]:\n",
    "            prev = (prev[0], prev[1] + curr[1] - 1)\n",
    "        else:\n",
    "            mgs += [prev]\n",
    "            prev = curr\n",
    "    mgs += [prev]\n",
    "    return mgs          "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([1,2,3,4,5,4,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5, [(1, 5), (-1, 2), (1, 3)])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([1,2,3,4,5,4,5,6], debug=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([10,1,2,3,4,5,4,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([10,1,2,3,4,5,5,5,4,3,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([10,1,2,3,4,5,5,5,4,3,5,6], allow_same=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([10,1,2,5,5,5,4,3,2,1,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([10,1,2,5,5,5,4,3,2,1,5,6], allow_same=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([10,1,2,5,5,5,4,3,2,5,6,6,6,6,6,6,6,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([10,1,2,5,5,5,4,3,2,5,6,6,6,6,6,6,6,2], allow_same=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([10,1,2,5,5,5,6,7,7,8,8,3,2,5,6,6,6,6,6,6,6,2], allow_same=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "longest_monotone([10,1,2,5,5,5,6,7,7,8,8,3,2,5,6,6,6,6,6,6,6,2], allow_same=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 24\n"
     ]
    }
   ],
   "source": [
    "for i in range(1):\n",
    "    with open('sequence{:03}.txt'.format(i)) as f:\n",
    "        sseq = f.read()\n",
    "        seq = [int(s) for s in sseq.split(',')]\n",
    "        s = longest_monotone(seq)\n",
    "        print(i, s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 24\n",
      "1 34\n",
      "2 23\n",
      "3 23\n",
      "4 22\n",
      "5 27\n",
      "6 27\n",
      "7 24\n",
      "8 22\n",
      "9 21\n"
     ]
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    with open('sequence{:03}.txt'.format(i)) as f:\n",
    "        sseq = f.read()\n",
    "        seq = [int(s) for s in sseq.split(',')]\n",
    "        s = longest_monotone(seq)\n",
    "        print(i, s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 29\n",
      "1 34\n",
      "2 25\n",
      "3 30\n",
      "4 29\n",
      "5 27\n",
      "6 27\n",
      "7 28\n",
      "8 23\n",
      "9 26\n"
     ]
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    with open('sequence{:03}.txt'.format(i)) as f:\n",
    "        sseq = f.read()\n",
    "        seq = [int(s) for s in sseq.split(',')]\n",
    "        s = longest_monotone(seq, allow_same=True)\n",
    "        print(i, s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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