mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
Added binary tree balance check challenge.
This commit is contained in:
Donne Martin
parent
bf4222d6e1
commit
53034144d4
|
|
@ -208,6 +208,7 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup
|
|||
| Determine the height of a tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_solution.ipynb) |
|
||||
| Create a binary search tree with minimal height from a sorted array | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst_min/bst_min_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst_min/bst_min_solution.ipynb) |
|
||||
| Create a linked list for each level of a binary tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_level_lists/tree_level_lists_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_level_lists/tree_level_lists_solution.ipynb) |
|
||||
| Check if a binary tree is balanced | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/check_balance/check_balance_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/check_balance/check_balance_solution.ipynb) |
|
||||
| Implement a binary search tree | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst/bst_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/bst/bst_solution.ipynb) |
|
||||
| Implement depth-first search on a graph | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_dfs/dfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_dfs/dfs_solution.ipynb) |
|
||||
| Implement breadth-first search on a graph | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_bfs/bfs_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_bfs/bfs_solution.ipynb) |
|
||||
|
|
@ -217,7 +218,6 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup
|
|||
| Determine the lowest common ancestor of two nodes | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
|
||||
| Transform a binary tree into a heap | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
|
||||
| Implement a right and left rotation on a tree | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
|
||||
| Check if a binary tree is balanced | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
|
||||
| Check if a binary tree is binary search tree | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
|
||||
| Add a challenge | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
|
||||
|
||||
|
|
|
|||
0
graphs_trees/check_balance/__init__.py
Normal file
0
graphs_trees/check_balance/__init__.py
Normal file
180
graphs_trees/check_balance/check_balance_challenge.ipynb
Normal file
180
graphs_trees/check_balance/check_balance_challenge.ipynb
Normal file
|
|
@ -0,0 +1,180 @@
|
|||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<small><i>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).</i></small>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Challenge Notebook"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Problem: Check if a binary tree is balanced.\n",
|
||||
"\n",
|
||||
"* [Constraints](#Constraints)\n",
|
||||
"* [Test Cases](#Test-Cases)\n",
|
||||
"* [Algorithm](#Algorithm)\n",
|
||||
"* [Code](#Code)\n",
|
||||
"* [Unit Test](#Unit-Test)\n",
|
||||
"* [Solution Notebook](#Solution-Notebook)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Constraints\n",
|
||||
"\n",
|
||||
"* Is a balanced tree one where the heights of two sub trees of any node doesn't differ by more than 1?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume we already have a Node class with an insert method?\n",
|
||||
" * Yes"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Test Cases\n",
|
||||
"\n",
|
||||
"* 5, 3, 8, 1, 4 -> Yes\n",
|
||||
"* 5, 3, 8, 9, 10 -> No"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Algorithm\n",
|
||||
"\n",
|
||||
"Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/check_balance/check_balance_solution.ipynb). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Code"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"%run ../bst/bst.py\n",
|
||||
"%load ../bst/bst.py"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def check_balance(root):\n",
|
||||
" # TODO: Implement me\n",
|
||||
" pass"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Unit Test"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"**The following unit test is expected to fail until you solve the challenge.**"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"# %load test_check_balance.py\n",
|
||||
"from nose.tools import assert_equal\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class TestCheckBalance(object):\n",
|
||||
"\n",
|
||||
" def test_check_balance(self):\n",
|
||||
" node = Node(5)\n",
|
||||
" insert(node, 3)\n",
|
||||
" insert(node, 8)\n",
|
||||
" insert(node, 1)\n",
|
||||
" insert(node, 4)\n",
|
||||
" assert_equal(check_balance(node), True)\n",
|
||||
"\n",
|
||||
" node = Node(5)\n",
|
||||
" insert(node, 3)\n",
|
||||
" insert(node, 8)\n",
|
||||
" insert(node, 9)\n",
|
||||
" insert(node, 10)\n",
|
||||
" assert_equal(check_balance(node), False)\n",
|
||||
"\n",
|
||||
" print('Success: test_check_balance')\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def main():\n",
|
||||
" test = TestCheckBalance()\n",
|
||||
" test.test_check_balance()\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"if __name__ == '__main__':\n",
|
||||
" main()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Solution Notebook\n",
|
||||
"\n",
|
||||
"Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/check_balance/check_balance_solution.ipynb) for a discussion on algorithms and code solutions."
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 2",
|
||||
"language": "python",
|
||||
"name": "python2"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.10"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 0
|
||||
}
|
||||
218
graphs_trees/check_balance/check_balance_solution.ipynb
Normal file
218
graphs_trees/check_balance/check_balance_solution.ipynb
Normal file
|
|
@ -0,0 +1,218 @@
|
|||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"<small><i>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).</i></small>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Solution Notebook"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Problem: Check if a binary tree is balanced.\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",
|
||||
"* Is a balanced tree one where the heights of two sub trees of any node doesn't differ by more than 1?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume we already have a Node class with an insert method?\n",
|
||||
" * Yes"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Test Cases\n",
|
||||
"\n",
|
||||
"* 5, 3, 8, 1, 4 -> Yes\n",
|
||||
"* 5, 3, 8, 9, 10 -> No"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Algorithm\n",
|
||||
"\n",
|
||||
"The algorithm will be similar to where we get the height of a tree as seen in [here](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/tree_height/height_solution.ipynb).\n",
|
||||
"\n",
|
||||
"However, we could check whether the tree is balanced while also checking for the heights.\n",
|
||||
"\n",
|
||||
"* Base case: If the root is None, return 0\n",
|
||||
"* Check the height of `root.left`, if -1, return -1\n",
|
||||
"* Check the height of `root.right`, if -1, return -1\n",
|
||||
"* If the height differences is greater than 1, return -1\n",
|
||||
"* Otherwise, return 1 + max(left height, right height)\n",
|
||||
" \n",
|
||||
"Complexity:\n",
|
||||
"* Time: O(n)\n",
|
||||
"* Space: O(log n)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Code"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"%run ../bst/bst.py"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def check_balance(root):\n",
|
||||
" if check_height(root) == -1:\n",
|
||||
" return False\n",
|
||||
" else:\n",
|
||||
" return True\n",
|
||||
"\n",
|
||||
"def check_height(root):\n",
|
||||
" if root is None:\n",
|
||||
" return 0\n",
|
||||
" left_height = check_height(root.left)\n",
|
||||
" if left_height == -1:\n",
|
||||
" return -1\n",
|
||||
" right_height = check_height(root.right)\n",
|
||||
" if right_height == -1:\n",
|
||||
" return -1\n",
|
||||
" diff_height = left_height - right_height\n",
|
||||
" if abs(diff_height) > 1:\n",
|
||||
" return -1\n",
|
||||
" else:\n",
|
||||
" return 1 + max(left_height, right_height)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Unit Test"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Overwriting test_check_balance.py\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%%writefile test_check_balance.py\n",
|
||||
"from nose.tools import assert_equal\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class TestCheckBalance(object):\n",
|
||||
"\n",
|
||||
" def test_check_balance(self):\n",
|
||||
" node = Node(5)\n",
|
||||
" insert(node, 3)\n",
|
||||
" insert(node, 8)\n",
|
||||
" insert(node, 1)\n",
|
||||
" insert(node, 4)\n",
|
||||
" assert_equal(check_balance(node), True)\n",
|
||||
"\n",
|
||||
" node = Node(5)\n",
|
||||
" insert(node, 3)\n",
|
||||
" insert(node, 8)\n",
|
||||
" insert(node, 9)\n",
|
||||
" insert(node, 10)\n",
|
||||
" assert_equal(check_balance(node), False)\n",
|
||||
"\n",
|
||||
" print('Success: test_check_balance')\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def main():\n",
|
||||
" test = TestCheckBalance()\n",
|
||||
" test.test_check_balance()\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"if __name__ == '__main__':\n",
|
||||
" main()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Success: test_check_balance\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%run -i test_check_balance.py"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 2",
|
||||
"language": "python",
|
||||
"name": "python2"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.10"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 0
|
||||
}
|
||||
30
graphs_trees/check_balance/test_check_balance.py
Normal file
30
graphs_trees/check_balance/test_check_balance.py
Normal file
|
|
@ -0,0 +1,30 @@
|
|||
from nose.tools import assert_equal
|
||||
|
||||
|
||||
class TestCheckBalance(object):
|
||||
|
||||
def test_check_balance(self):
|
||||
node = Node(5)
|
||||
insert(node, 3)
|
||||
insert(node, 8)
|
||||
insert(node, 1)
|
||||
insert(node, 4)
|
||||
assert_equal(check_balance(node), True)
|
||||
|
||||
node = Node(5)
|
||||
insert(node, 3)
|
||||
insert(node, 8)
|
||||
insert(node, 9)
|
||||
insert(node, 10)
|
||||
assert_equal(check_balance(node), False)
|
||||
|
||||
print('Success: test_check_balance')
|
||||
|
||||
|
||||
def main():
|
||||
test = TestCheckBalance()
|
||||
test.test_check_balance()
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
main()
|
||||
Loading…
Reference in New Issue
Block a user