mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
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Rework n pairs parens challenge (#145)
This commit is contained in:
Donne Martin
GitHub
parent
2f2e25c33d
commit
a06617f0eb
0
recursion_dynamic/n_pairs_parentheses/__init__.py
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0
recursion_dynamic/n_pairs_parentheses/__init__.py
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@ -18,7 +18,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Print all valid combinations of n-pairs of parentheses.\n",
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"## Problem: Find all valid combinations of n-pairs of parentheses.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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@ -33,7 +33,17 @@
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"metadata": {},
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"source": [
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"## Constraints\n",
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"* None"
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"\n",
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"* Is the input an integer representing the number of pairs?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Is the output a list of valid combinations?\n",
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" * Yes\n",
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"* Should the output have duplicates?\n",
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" * No\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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@ -42,10 +52,14 @@
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"source": [
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"## Test Cases\n",
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"\n",
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"<pre>\n",
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"* None -> Exception\n",
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"* Negative -> Exception\n",
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"* 0 -> []\n",
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"* 1 -> [()]\n",
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"* 2 -> [(()), ()()]\n",
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"* 3 -> [((())), (()()), (())(), ()(()), ()()()]"
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"* 1 -> ['()']\n",
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"* 2 -> ['(())', '()()']\n",
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"* 3 -> ['((()))', '(()())', '(())()', '()(())', '()()()']\n",
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"</pre>"
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]
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},
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{
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@ -72,17 +86,11 @@
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},
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"outputs": [],
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"source": [
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"def parentheses_util(no_left, no_right, pair_string, result):\n",
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" # TODO: implement parentheses pairing here\n",
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" pass\n",
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"class Parentheses(object):\n",
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"\n",
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"\n",
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"def pair_parentheses(n):\n",
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" result_set = set()\n",
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" if n == 0:\n",
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" return result_set\n",
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" parentheses_util(n, n, '', result_set)\n",
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" return result_set"
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" def find_pair(self, num_pairs):\n",
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" # TODO: implement me\n",
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" pass"
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]
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},
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{
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@ -101,27 +109,30 @@
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"outputs": [],
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"source": [
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"# %load test_n_pairs_parentheses.py\n",
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"from nose.tools import assert_equal\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestPairParentheses(object):\n",
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"\n",
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" def test_pair_parentheses(self, solution):\n",
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" assert_equal(solution(0), set([]))\n",
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" assert_equal(solution(1), set(['()']))\n",
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" assert_equal(solution(2), set(['(())', \n",
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" '()()']))\n",
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" assert_equal(solution(3), set(['((()))', \n",
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" '(()())', \n",
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" '(())()', \n",
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" '()(())', \n",
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" '()()()']))\n",
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" def test_pair_parentheses(self):\n",
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" parentheses = Parentheses()\n",
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" assert_raises(TypeError, parentheses.find_pair, None)\n",
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" assert_raises(ValueError, parentheses.find_pair, -1)\n",
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" assert_equal(parentheses.find_pair(0), [])\n",
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" assert_equal(parentheses.find_pair(1), ['()'])\n",
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" assert_equal(parentheses.find_pair(2), ['(())',\n",
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" '()()'])\n",
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" assert_equal(parentheses.find_pair(3), ['((()))',\n",
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" '(()())',\n",
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" '(())()',\n",
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" '()(())',\n",
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" '()()()'])\n",
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" print('Success: test_pair_parentheses')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestPairParentheses()\n",
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" test.test_pair_parentheses(pair_parentheses)\n",
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" test.test_pair_parentheses()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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@ -136,34 +147,25 @@
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"\n",
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"Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/n_pairs_parentheses/n_pairs_parentheses_solution.ipynb) for a discussion on algorithms and code solutions."
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 2",
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"display_name": "Python 3",
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"language": "python",
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"name": "python2"
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 2
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython2",
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"version": "2.7.10"
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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@ -18,7 +18,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Print all valid combinations of n-pairs of parentheses.\n",
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"## Problem: Find all valid combinations of n-pairs of parentheses.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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@ -32,7 +32,17 @@
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"metadata": {},
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"source": [
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"## Constraints\n",
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"* None"
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"\n",
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"* Is the input an integer representing the number of pairs?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Is the output a list of valid combinations?\n",
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" * Yes\n",
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"* Should the output have duplicates?\n",
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" * No\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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@ -41,10 +51,14 @@
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"source": [
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"## Test Cases\n",
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"\n",
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"* 0 -> ' '\n",
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"* 1 -> ()\n",
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"* 2 -> (()), ()()\n",
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"* 3 -> ((())), (()()), (())(), ()(()), ()()()"
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"<pre>\n",
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"* None -> Exception\n",
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"* Negative -> Exception\n",
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"* 0 -> []\n",
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"* 1 -> ['()']\n",
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"* 2 -> ['(())', '()()']\n",
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"* 3 -> ['((()))', '(()())', '(())()', '()(())', '()()()']\n",
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"</pre>"
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]
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},
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{
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@ -64,14 +78,14 @@
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" - Add the string generated to the result set\n",
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"* Case 1: `l > 0`\n",
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" - Add a left parenthesis to the parentheses string.\n",
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" - Call parentheses_util(l - 1, r, new_string, result_set)\n",
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" - Recurse (l - 1, r, new_string, result_set)\n",
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"* Case 2: `r > l`\n",
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" - Add a right parenthesis to the parentheses string.\n",
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" - Call parentheses_util(l, r - 1, new_string, result_set)\n",
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" - Recurse (l, r - 1, new_string, result_set)\n",
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"\n",
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"Complexity:\n",
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"* Time: `O(4^n/n^(3/2))`. See [Catalan numbers](https://en.wikipedia.org/wiki/Catalan_number#Applications_in_combinatorics)\n",
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"* Space complexity: `O(n)` (Due to the implicit call stack storing a maximum of 2n function calls)"
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"* Time: `O(4^n/n^(3/2))`, see [Catalan numbers](https://en.wikipedia.org/wiki/Catalan_number#Applications_in_combinatorics) - 1, 1, 2, 5, 14, 42, 132...\n",
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"* Space complexity: `O(n)`, due to the implicit call stack storing a maximum of 2n function calls)"
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]
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},
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{
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@ -89,22 +103,28 @@
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},
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"outputs": [],
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"source": [
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"def parentheses_util(no_left, no_right, pair_string, result):\n",
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" if no_left == 0 and no_right == 0:\n",
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" result.add(pair_string)\n",
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" else:\n",
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" if no_left > 0:\n",
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" parentheses_util(no_left - 1, no_right, pair_string + '(', result)\n",
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" if no_right > no_left:\n",
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" parentheses_util(no_left, no_right - 1, pair_string + ')', result)\n",
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"class Parentheses(object):\n",
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"\n",
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" def find_pair(self, num_pairs):\n",
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" if num_pairs is None:\n",
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" raise TypeError('num_pairs cannot be None')\n",
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" if num_pairs < 0:\n",
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" raise ValueError('num_pairs cannot be < 0')\n",
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" if not num_pairs:\n",
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" return []\n",
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" results = []\n",
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" curr_results = []\n",
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" self._find_pair(num_pairs, num_pairs, curr_results, results)\n",
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" return results\n",
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"\n",
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"def pair_parentheses(n):\n",
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" result_set = set()\n",
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" if n == 0:\n",
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" return result_set\n",
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" parentheses_util(n, n, '', result_set)\n",
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" return result_set"
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" def _find_pair(self, nleft, nright, curr_results, results):\n",
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" if nleft == 0 and nright == 0:\n",
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" results.append(''.join(curr_results))\n",
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" else:\n",
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" if nleft >= 0:\n",
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" self._find_pair(nleft-1, nright, curr_results+['('], results)\n",
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" if nright > nleft:\n",
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" self._find_pair(nleft, nright-1, curr_results+[')'], results)"
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]
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},
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{
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@ -131,27 +151,30 @@
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],
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"source": [
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"%%writefile test_n_pairs_parentheses.py\n",
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"from nose.tools import assert_equal\n",
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"from nose.tools import assert_equal, assert_raises\n",
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"\n",
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"\n",
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"class TestPairParentheses(object):\n",
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"\n",
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" def test_pair_parentheses(self, solution):\n",
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" assert_equal(solution(0), set([]))\n",
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" assert_equal(solution(1), set(['()']))\n",
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" assert_equal(solution(2), set(['(())', \n",
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" '()()']))\n",
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" assert_equal(solution(3), set(['((()))', \n",
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" '(()())', \n",
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" '(())()', \n",
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" '()(())', \n",
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" '()()()']))\n",
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" def test_pair_parentheses(self):\n",
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" parentheses = Parentheses()\n",
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" assert_raises(TypeError, parentheses.find_pair, None)\n",
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" assert_raises(ValueError, parentheses.find_pair, -1)\n",
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" assert_equal(parentheses.find_pair(0), [])\n",
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" assert_equal(parentheses.find_pair(1), ['()'])\n",
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" assert_equal(parentheses.find_pair(2), ['(())',\n",
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" '()()'])\n",
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" assert_equal(parentheses.find_pair(3), ['((()))',\n",
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" '(()())',\n",
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" '(())()',\n",
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" '()(())',\n",
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" '()()()'])\n",
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" print('Success: test_pair_parentheses')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestPairParentheses()\n",
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" test.test_pair_parentheses(pair_parentheses)\n",
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" test.test_pair_parentheses()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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@ -180,21 +203,21 @@
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 2",
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"display_name": "Python 3",
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"language": "python",
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"name": "python2"
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 2
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython2",
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"version": "2.7.10"
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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@ -1,24 +1,27 @@
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from nose.tools import assert_equal
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from nose.tools import assert_equal, assert_raises
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class TestPairParentheses(object):
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def test_pair_parentheses(self, solution):
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assert_equal(solution(0), set([]))
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assert_equal(solution(1), set(['()']))
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assert_equal(solution(2), set(['(())',
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'()()']))
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assert_equal(solution(3), set(['((()))',
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'(()())',
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'(())()',
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'()(())',
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'()()()']))
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def test_pair_parentheses(self):
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parentheses = Parentheses()
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assert_raises(TypeError, parentheses.find_pair, None)
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assert_raises(ValueError, parentheses.find_pair, -1)
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assert_equal(parentheses.find_pair(0), [])
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assert_equal(parentheses.find_pair(1), ['()'])
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assert_equal(parentheses.find_pair(2), ['(())',
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'()()'])
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assert_equal(parentheses.find_pair(3), ['((()))',
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'(()())',
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'(())()',
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'()(())',
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'()()()'])
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print('Success: test_pair_parentheses')
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def main():
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test = TestPairParentheses()
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test.test_pair_parentheses(pair_parentheses)
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test.test_pair_parentheses()
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if __name__ == '__main__':
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