mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
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
Normal file
0
recursion_dynamic/n_pairs_parentheses/__init__.py
Normal file
|
|
@ -18,7 +18,7 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Problem: Print all valid combinations of n-pairs of parentheses.\n",
|
||||
"## Problem: Find all valid combinations of n-pairs of parentheses.\n",
|
||||
"\n",
|
||||
"* [Constraints](#Constraints)\n",
|
||||
"* [Test Cases](#Test-Cases)\n",
|
||||
|
|
@ -33,7 +33,17 @@
|
|||
"metadata": {},
|
||||
"source": [
|
||||
"## Constraints\n",
|
||||
"* None"
|
||||
"\n",
|
||||
"* Is the input an integer representing the number of pairs?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume the inputs are valid?\n",
|
||||
" * No\n",
|
||||
"* Is the output a list of valid combinations?\n",
|
||||
" * Yes\n",
|
||||
"* Should the output have duplicates?\n",
|
||||
" * No\n",
|
||||
"* Can we assume this fits memory?\n",
|
||||
" * Yes"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -42,10 +52,14 @@
|
|||
"source": [
|
||||
"## Test Cases\n",
|
||||
"\n",
|
||||
"<pre>\n",
|
||||
"* None -> Exception\n",
|
||||
"* Negative -> Exception\n",
|
||||
"* 0 -> []\n",
|
||||
"* 1 -> [()]\n",
|
||||
"* 2 -> [(()), ()()]\n",
|
||||
"* 3 -> [((())), (()()), (())(), ()(()), ()()()]"
|
||||
"* 1 -> ['()']\n",
|
||||
"* 2 -> ['(())', '()()']\n",
|
||||
"* 3 -> ['((()))', '(()())', '(())()', '()(())', '()()()']\n",
|
||||
"</pre>"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -72,17 +86,11 @@
|
|||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def parentheses_util(no_left, no_right, pair_string, result):\n",
|
||||
" # TODO: implement parentheses pairing here\n",
|
||||
" pass\n",
|
||||
"class Parentheses(object):\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def pair_parentheses(n):\n",
|
||||
" result_set = set()\n",
|
||||
" if n == 0:\n",
|
||||
" return result_set\n",
|
||||
" parentheses_util(n, n, '', result_set)\n",
|
||||
" return result_set"
|
||||
" def find_pair(self, num_pairs):\n",
|
||||
" # TODO: implement me\n",
|
||||
" pass"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -101,27 +109,30 @@
|
|||
"outputs": [],
|
||||
"source": [
|
||||
"# %load test_n_pairs_parentheses.py\n",
|
||||
"from nose.tools import assert_equal\n",
|
||||
"from nose.tools import assert_equal, assert_raises\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class TestPairParentheses(object):\n",
|
||||
"\n",
|
||||
" def test_pair_parentheses(self, solution):\n",
|
||||
" assert_equal(solution(0), set([]))\n",
|
||||
" assert_equal(solution(1), set(['()']))\n",
|
||||
" assert_equal(solution(2), set(['(())', \n",
|
||||
" '()()']))\n",
|
||||
" assert_equal(solution(3), set(['((()))', \n",
|
||||
" '(()())', \n",
|
||||
" '(())()', \n",
|
||||
" '()(())', \n",
|
||||
" '()()()']))\n",
|
||||
" def test_pair_parentheses(self):\n",
|
||||
" parentheses = Parentheses()\n",
|
||||
" assert_raises(TypeError, parentheses.find_pair, None)\n",
|
||||
" assert_raises(ValueError, parentheses.find_pair, -1)\n",
|
||||
" assert_equal(parentheses.find_pair(0), [])\n",
|
||||
" assert_equal(parentheses.find_pair(1), ['()'])\n",
|
||||
" assert_equal(parentheses.find_pair(2), ['(())',\n",
|
||||
" '()()'])\n",
|
||||
" assert_equal(parentheses.find_pair(3), ['((()))',\n",
|
||||
" '(()())',\n",
|
||||
" '(())()',\n",
|
||||
" '()(())',\n",
|
||||
" '()()()'])\n",
|
||||
" print('Success: test_pair_parentheses')\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def main():\n",
|
||||
" test = TestPairParentheses()\n",
|
||||
" test.test_pair_parentheses(pair_parentheses)\n",
|
||||
" test.test_pair_parentheses()\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"if __name__ == '__main__':\n",
|
||||
|
|
@ -136,34 +147,25 @@
|
|||
"\n",
|
||||
"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."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 2",
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python2"
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.10"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.5.0"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -18,7 +18,7 @@
|
|||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Problem: Print all valid combinations of n-pairs of parentheses.\n",
|
||||
"## Problem: Find all valid combinations of n-pairs of parentheses.\n",
|
||||
"\n",
|
||||
"* [Constraints](#Constraints)\n",
|
||||
"* [Test Cases](#Test-Cases)\n",
|
||||
|
|
@ -32,7 +32,17 @@
|
|||
"metadata": {},
|
||||
"source": [
|
||||
"## Constraints\n",
|
||||
"* None"
|
||||
"\n",
|
||||
"* Is the input an integer representing the number of pairs?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume the inputs are valid?\n",
|
||||
" * No\n",
|
||||
"* Is the output a list of valid combinations?\n",
|
||||
" * Yes\n",
|
||||
"* Should the output have duplicates?\n",
|
||||
" * No\n",
|
||||
"* Can we assume this fits memory?\n",
|
||||
" * Yes"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -41,10 +51,14 @@
|
|||
"source": [
|
||||
"## Test Cases\n",
|
||||
"\n",
|
||||
"* 0 -> ' '\n",
|
||||
"* 1 -> ()\n",
|
||||
"* 2 -> (()), ()()\n",
|
||||
"* 3 -> ((())), (()()), (())(), ()(()), ()()()"
|
||||
"<pre>\n",
|
||||
"* None -> Exception\n",
|
||||
"* Negative -> Exception\n",
|
||||
"* 0 -> []\n",
|
||||
"* 1 -> ['()']\n",
|
||||
"* 2 -> ['(())', '()()']\n",
|
||||
"* 3 -> ['((()))', '(()())', '(())()', '()(())', '()()()']\n",
|
||||
"</pre>"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -64,14 +78,14 @@
|
|||
" - Add the string generated to the result set\n",
|
||||
"* Case 1: `l > 0`\n",
|
||||
" - Add a left parenthesis to the parentheses string.\n",
|
||||
" - Call parentheses_util(l - 1, r, new_string, result_set)\n",
|
||||
" - Recurse (l - 1, r, new_string, result_set)\n",
|
||||
"* Case 2: `r > l`\n",
|
||||
" - Add a right parenthesis to the parentheses string.\n",
|
||||
" - Call parentheses_util(l, r - 1, new_string, result_set)\n",
|
||||
" - Recurse (l, r - 1, new_string, result_set)\n",
|
||||
"\n",
|
||||
"Complexity:\n",
|
||||
"* Time: `O(4^n/n^(3/2))`. See [Catalan numbers](https://en.wikipedia.org/wiki/Catalan_number#Applications_in_combinatorics)\n",
|
||||
"* Space complexity: `O(n)` (Due to the implicit call stack storing a maximum of 2n function calls)"
|
||||
"* 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",
|
||||
"* Space complexity: `O(n)`, due to the implicit call stack storing a maximum of 2n function calls)"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -89,22 +103,28 @@
|
|||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def parentheses_util(no_left, no_right, pair_string, result):\n",
|
||||
" if no_left == 0 and no_right == 0:\n",
|
||||
" result.add(pair_string)\n",
|
||||
"class Parentheses(object):\n",
|
||||
"\n",
|
||||
" def find_pair(self, num_pairs):\n",
|
||||
" if num_pairs is None:\n",
|
||||
" raise TypeError('num_pairs cannot be None')\n",
|
||||
" if num_pairs < 0:\n",
|
||||
" raise ValueError('num_pairs cannot be < 0')\n",
|
||||
" if not num_pairs:\n",
|
||||
" return []\n",
|
||||
" results = []\n",
|
||||
" curr_results = []\n",
|
||||
" self._find_pair(num_pairs, num_pairs, curr_results, results)\n",
|
||||
" return results\n",
|
||||
"\n",
|
||||
" def _find_pair(self, nleft, nright, curr_results, results):\n",
|
||||
" if nleft == 0 and nright == 0:\n",
|
||||
" results.append(''.join(curr_results))\n",
|
||||
" else:\n",
|
||||
" if no_left > 0:\n",
|
||||
" parentheses_util(no_left - 1, no_right, pair_string + '(', result)\n",
|
||||
" if no_right > no_left:\n",
|
||||
" parentheses_util(no_left, no_right - 1, pair_string + ')', result)\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def pair_parentheses(n):\n",
|
||||
" result_set = set()\n",
|
||||
" if n == 0:\n",
|
||||
" return result_set\n",
|
||||
" parentheses_util(n, n, '', result_set)\n",
|
||||
" return result_set"
|
||||
" if nleft >= 0:\n",
|
||||
" self._find_pair(nleft-1, nright, curr_results+['('], results)\n",
|
||||
" if nright > nleft:\n",
|
||||
" self._find_pair(nleft, nright-1, curr_results+[')'], results)"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -131,27 +151,30 @@
|
|||
],
|
||||
"source": [
|
||||
"%%writefile test_n_pairs_parentheses.py\n",
|
||||
"from nose.tools import assert_equal\n",
|
||||
"from nose.tools import assert_equal, assert_raises\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class TestPairParentheses(object):\n",
|
||||
"\n",
|
||||
" def test_pair_parentheses(self, solution):\n",
|
||||
" assert_equal(solution(0), set([]))\n",
|
||||
" assert_equal(solution(1), set(['()']))\n",
|
||||
" assert_equal(solution(2), set(['(())', \n",
|
||||
" '()()']))\n",
|
||||
" assert_equal(solution(3), set(['((()))', \n",
|
||||
" '(()())', \n",
|
||||
" '(())()', \n",
|
||||
" '()(())', \n",
|
||||
" '()()()']))\n",
|
||||
" def test_pair_parentheses(self):\n",
|
||||
" parentheses = Parentheses()\n",
|
||||
" assert_raises(TypeError, parentheses.find_pair, None)\n",
|
||||
" assert_raises(ValueError, parentheses.find_pair, -1)\n",
|
||||
" assert_equal(parentheses.find_pair(0), [])\n",
|
||||
" assert_equal(parentheses.find_pair(1), ['()'])\n",
|
||||
" assert_equal(parentheses.find_pair(2), ['(())',\n",
|
||||
" '()()'])\n",
|
||||
" assert_equal(parentheses.find_pair(3), ['((()))',\n",
|
||||
" '(()())',\n",
|
||||
" '(())()',\n",
|
||||
" '()(())',\n",
|
||||
" '()()()'])\n",
|
||||
" print('Success: test_pair_parentheses')\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def main():\n",
|
||||
" test = TestPairParentheses()\n",
|
||||
" test.test_pair_parentheses(pair_parentheses)\n",
|
||||
" test.test_pair_parentheses()\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"if __name__ == '__main__':\n",
|
||||
|
|
@ -180,21 +203,21 @@
|
|||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 2",
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python2"
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.10"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.5.0"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -1,24 +1,27 @@
|
|||
from nose.tools import assert_equal
|
||||
from nose.tools import assert_equal, assert_raises
|
||||
|
||||
|
||||
class TestPairParentheses(object):
|
||||
|
||||
def test_pair_parentheses(self, solution):
|
||||
assert_equal(solution(0), set([]))
|
||||
assert_equal(solution(1), set(['()']))
|
||||
assert_equal(solution(2), set(['(())',
|
||||
'()()']))
|
||||
assert_equal(solution(3), set(['((()))',
|
||||
def test_pair_parentheses(self):
|
||||
parentheses = Parentheses()
|
||||
assert_raises(TypeError, parentheses.find_pair, None)
|
||||
assert_raises(ValueError, parentheses.find_pair, -1)
|
||||
assert_equal(parentheses.find_pair(0), [])
|
||||
assert_equal(parentheses.find_pair(1), ['()'])
|
||||
assert_equal(parentheses.find_pair(2), ['(())',
|
||||
'()()'])
|
||||
assert_equal(parentheses.find_pair(3), ['((()))',
|
||||
'(()())',
|
||||
'(())()',
|
||||
'()(())',
|
||||
'()()()']))
|
||||
'()()()'])
|
||||
print('Success: test_pair_parentheses')
|
||||
|
||||
|
||||
def main():
|
||||
test = TestPairParentheses()
|
||||
test.test_pair_parentheses(pair_parentheses)
|
||||
test.test_pair_parentheses()
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user