interactive-coding-challenges/online_judges/merge_ranges/merge_ranges_solution.ipynb

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   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Given a list of tuples representing ranges, condense the ranges.  \n",
    "\n",
    "Example: [(2, 3), (3, 5), (7, 9), (8, 10)] -> [(2, 5), (7, 10)]\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Are the tuples in sorted order?\n",
    "    * No\n",
    "* Are the tuples ints?\n",
    "    * Yes\n",
    "* Will all tuples have the first element less than the second?\n",
    "    * Yes\n",
    "* Is there an upper bound on the input range?\n",
    "    * No\n",
    "* Is the output a list of tuples?\n",
    "    * Yes\n",
    "* Is the output a new array?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * No, check for None\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "<pre>\n",
    "* None input -> TypeError\n",
    "* [] - []\n",
    "* [(2, 3), (7, 9)] -> [(2, 3), (7, 9)]\n",
    "* [(2, 3), (3, 5), (7, 9), (8, 10)] -> [(2, 5), (7, 10)]\n",
    "* [(2, 3), (3, 5), (7, 9), (8, 10), (1, 11)] -> [(1, 11)]\n",
    "* [(2, 3), (3, 8), (7, 9), (8, 10)] -> [(2, 10)]\n",
    "</pre>"
   ]
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   "source": [
    "## Algorithm\n",
    "\n",
    "* Sort the tuples based on start time\n",
    "* Check each adjacent tuple to see if they can be merged\n",
    "\n",
    "<pre>\n",
    "Case: * [(2, 3), (3, 8), (7, 9), (8, 10)] -> [(2, 10)]\n",
    "\n",
    "* Sort by start time (already sorted)\n",
    "* Add the first tuple to the merged_array\n",
    "* Loop through each item in sorted_array starting at index 1\n",
    "    * If there is no overlap\n",
    "        * Add the current item to merged_array\n",
    "    * Else\n",
    "        * Update the last item in merged_array\n",
    "            * The end time will be the max of merged_array[-1][1] and sorted_array[i][1]\n",
    "\n",
    "Start:\n",
    "                           i\n",
    "                   0       1       2       3\n",
    "sorted_array = [(2, 3), (3, 8), (7, 9), (8, 10)]\n",
    "merged_array = [(2, 3)]\n",
    "\n",
    "Overlap with (2, 3), (3, 8):\n",
    "                           i\n",
    "                   0       1       2       3\n",
    "sorted_array = [(2, 3), (3, 8), (7, 9), (8, 10)]\n",
    "merged_array = [(2, 8)]\n",
    "\n",
    "Overlap with (2, 8), (7, 9):\n",
    "                                   i\n",
    "                   0       1       2       3\n",
    "sorted_array = [(2, 3), (3, 8), (7, 9), (8, 10)]\n",
    "merged_array = [(2, 9)]\n",
    "\n",
    "Overlap with (2, 9) (8, 10):\n",
    "                                   i\n",
    "                   0       1       2       3\n",
    "sorted_array = [(2, 3), (3, 8), (7, 9), (8, 10)]\n",
    "merged_array = [(2, 10)]\n",
    "</pre>\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n log(n))\n",
    "* Space: O(n)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "class Solution(object):\n",
    "\n",
    "    def merge_ranges(self, array):\n",
    "        if array is None:\n",
    "            raise TypeError('array cannot be None')\n",
    "        if not array:\n",
    "            return array\n",
    "        sorted_array = sorted(array)\n",
    "        merged_array = [sorted_array[0]]\n",
    "        for index, item in enumerate(sorted_array):\n",
    "            if index == 0:\n",
    "                continue\n",
    "            start_prev, end_prev = merged_array[-1]\n",
    "            start_curr, end_curr = item\n",
    "            if end_prev < start_curr:\n",
    "                # No overlap, add the entry\n",
    "                merged_array.append(item)\n",
    "            else:\n",
    "                # Overlap, update the previous entry's end value\n",
    "                merged_array[-1] = (start_prev, max(end_prev, end_curr))\n",
    "        return merged_array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_merge_ranges.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_merge_ranges.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestMergeRanges(object):\n",
    "\n",
    "    def test_merge_ranges(self):\n",
    "        solution = Solution()\n",
    "        assert_raises(TypeError, solution.merge_ranges, None)\n",
    "        assert_equal(solution.merge_ranges([]), [])\n",
    "        array = [(2, 3), (7, 9)]\n",
    "        expected = [(2, 3), (7, 9)]\n",
    "        assert_equal(solution.merge_ranges(array), expected)\n",
    "        array = [(3, 5), (2, 3), (7, 9), (8, 10)]\n",
    "        expected = [(2, 5), (7, 10)]\n",
    "        assert_equal(solution.merge_ranges(array), expected)\n",
    "        array = [(2, 3), (3, 5), (7, 9), (8, 10), (1, 11)]\n",
    "        expected = [(1, 11)]\n",
    "        assert_equal(solution.merge_ranges(array), expected)\n",
    "        print('Success: test_merge_ranges')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestMergeRanges()\n",
    "    test.test_merge_ranges()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_merge_ranges\n"
     ]
    }
   ],
   "source": [
    "%run -i test_merge_ranges.py"
   ]
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