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"metadata": {},
"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)."
]
},
{
"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"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Test Cases\n",
"\n",
"\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",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"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",
"\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",
"\n",
"\n",
"Complexity:\n",
"* Time: O(n log(n))\n",
"* Space: O(n)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Code"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"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()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Success: test_merge_ranges\n"
]
}
],
"source": [
"%run -i test_merge_ranges.py"
]
}
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