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https://github.com/donnemartin/interactive-coding-challenges
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Add min heap challenge
This commit is contained in:
0
graphs_trees/min_heap/__init__.py
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0
graphs_trees/min_heap/__init__.py
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66
graphs_trees/min_heap/min_heap.py
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66
graphs_trees/min_heap/min_heap.py
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@@ -0,0 +1,66 @@
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from __future__ import division
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import sys
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class MinHeap(object):
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def __init__(self):
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self.array = []
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def __len__(self):
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return len(self.array)
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def extract_min(self):
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if not self.array:
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return None
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if len(self.array) == 1:
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return self.array.pop(0)
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minimum = self.array[0]
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# Move the last element to the root
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self.array[0] = self.array.pop(-1)
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self._bubble_down(index=0)
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return minimum
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def peek_min(self):
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return self.array[0] if self.array else None
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def insert(self, key):
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if key is None:
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raise TypeError('key cannot be None')
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self.array.append(key)
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self._bubble_up(index=len(self.array)-1)
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def _bubble_up(self, index):
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if index == 0:
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return
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index_parent = (index-1) // 2
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if self.array[index] < self.array[index_parent]:
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# Swap the indices and recurse
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self.array[index], self.array[index_parent] = \
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self.array[index_parent], self.array[index]
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self._bubble_up(index_parent)
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def _bubble_down(self, index):
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min_child_index = self._find_smaller_child(index)
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if min_child_index == -1:
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return
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if self.array[index] > self.array[min_child_index]:
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# Swap the indices and recurse
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self.array[index], self.array[min_child_index] = \
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self.array[min_child_index], self.array[index]
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self._bubble_down(min_child_index)
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def _find_smaller_child(self, index):
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left_child_index = 2 * index + 1
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right_child_index = 2 * index + 2
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if right_child_index >= len(self.array):
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if left_child_index >= len(self.array):
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return -1
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else:
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return left_child_index
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else:
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if self.array[left_child_index] < self.array[right_child_index]:
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return left_child_index
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else:
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return right_child_index
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214
graphs_trees/min_heap/min_heap_challenge.ipynb
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214
graphs_trees/min_heap/min_heap_challenge.ipynb
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@@ -0,0 +1,214 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"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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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Challenge Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Implement a min heap with extract_min and insert methods.\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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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)\n",
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"* [Solution Notebook](#Solution-Notebook)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Can we assume the inputs are ints?\n",
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" * Yes\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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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"* Extract min of an empty tree\n",
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"* Extract min general case\n",
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"* Insert into an empty tree\n",
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"* Insert general case (left and right insert)\n",
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"\n",
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"<pre>\n",
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" _5_\n",
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" / \\\n",
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" 20 15\n",
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" / \\ / \\\n",
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" 22 40 25\n",
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" \n",
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"extract_min(): 5\n",
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"\n",
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" _15_\n",
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" / \\\n",
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" 20 25\n",
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" / \\ / \\\n",
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" 22 40 \n",
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"\n",
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"insert(2):\n",
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"\n",
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" _2_\n",
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" / \\\n",
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" 20 5\n",
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" / \\ / \\\n",
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" 22 40 25 15\n",
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"</pre>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"Refer to the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/min_heap/min_heap_solution.ipynb). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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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": false
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},
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"outputs": [],
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"source": [
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"class MinHeap(object):\n",
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"\n",
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" def __init__(self):\n",
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" # TODO: Implement me\n",
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" pass\n",
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"\n",
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" def extract_min(self):\n",
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" # TODO: Implement me\n",
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" pass \n",
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"\n",
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" def peek_min(self):\n",
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" # TODO: Implement me\n",
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" pass\n",
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"\n",
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" def insert(self, data):\n",
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" # TODO: Implement me\n",
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" pass\n",
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"\n",
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" def _bubble_up(self, index):\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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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**The following unit test is expected to fail until you solve the challenge.**"
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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": false
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},
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"outputs": [],
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"source": [
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"# %load test_min_heap.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestMinHeap(object):\n",
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"\n",
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" def test_min_heap(self):\n",
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" heap = MinHeap()\n",
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" assert_equal(heap.peek_min(), None)\n",
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" assert_equal(heap.extract_min(), None)\n",
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" heap.insert(20)\n",
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" assert_equal(heap.peek_min(), 20)\n",
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" heap.insert(5)\n",
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" assert_equal(heap.peek_min(), 5)\n",
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" heap.insert(15)\n",
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" heap.insert(22)\n",
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" heap.insert(40)\n",
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" heap.insert(5)\n",
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" assert_equal(heap.peek_min(), 5)\n",
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" heap.insert(3)\n",
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" assert_equal(heap.peek_min(), 3)\n",
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" assert_equal(heap.extract_min(), 3)\n",
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" assert_equal(heap.peek_min(), 5)\n",
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" print('Success: test_min_heap')\n",
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"\n",
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" \n",
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"def main():\n",
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" test = TestMinHeap()\n",
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" test.test_min_heap()\n",
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"\n",
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" \n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Solution Notebook\n",
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"\n",
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"Review the [Solution Notebook](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/min_heap/min_heap_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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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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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": 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": "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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"nbformat_minor": 0
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}
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411
graphs_trees/min_heap/min_heap_solution.ipynb
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411
graphs_trees/min_heap/min_heap_solution.ipynb
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@@ -0,0 +1,411 @@
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{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"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": {},
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"source": [
|
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"# Solution Notebook"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Problem: Implement a min heap with extract_min and insert methods.\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",
|
||||
"* Can we assume the inputs are ints?\n",
|
||||
" * Yes\n",
|
||||
"* Can we assume this fits memory?\n",
|
||||
" * Yes"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Test Cases\n",
|
||||
"\n",
|
||||
"* Extract min of an empty tree\n",
|
||||
"* Extract min general case\n",
|
||||
"* Insert into an empty tree\n",
|
||||
"* Insert general case (left and right insert)\n",
|
||||
"\n",
|
||||
"<pre>\n",
|
||||
" _5_\n",
|
||||
" / \\\n",
|
||||
" 20 15\n",
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" / \\ / \\\n",
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" 22 40 25\n",
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" \n",
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"extract_min(): 5\n",
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"\n",
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" _15_\n",
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" / \\\n",
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" 20 25\n",
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" / \\ / \\\n",
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" 22 40 \n",
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"\n",
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"insert(2):\n",
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"\n",
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" _2_\n",
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" / \\\n",
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" 20 5\n",
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" / \\ / \\\n",
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" 22 40 25 15\n",
|
||||
"</pre>"
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||||
]
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||||
},
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||||
{
|
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"cell_type": "markdown",
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"metadata": {},
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"source": [
|
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"## Algorithm\n",
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"\n",
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"A heap is a complete binary tree where each node is smaller than its children.\n",
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"\n",
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"### extract_min\n",
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"\n",
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"<pre>\n",
|
||||
" _5_\n",
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||||
" / \\\n",
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" 20 15\n",
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" / \\ / \\\n",
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" 22 40 25\n",
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"\n",
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"Save the root as the value to be returned: 5\n",
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"Move the right most element to the root: 25\n",
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"\n",
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" _25_\n",
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" / \\\n",
|
||||
" 20 15\n",
|
||||
" / \\ / \\\n",
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" 22 40 \n",
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"\n",
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"Bubble down 25: Swap 25 and 15 (the smaller child)\n",
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"\n",
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" _15_\n",
|
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" / \\\n",
|
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" 20 25\n",
|
||||
" / \\ / \\\n",
|
||||
" 22 40 \n",
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||||
"\n",
|
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"Return 5\n",
|
||||
"</pre>\n",
|
||||
"\n",
|
||||
"We'll use an array to represent the tree, here are the indices:\n",
|
||||
"\n",
|
||||
"<pre>\n",
|
||||
" _0_\n",
|
||||
" / \\\n",
|
||||
" 1 2\n",
|
||||
" / \\ / \\\n",
|
||||
" 3 4 \n",
|
||||
"</pre>\n",
|
||||
"\n",
|
||||
"To get to a child, we take 2 * index + 1 (left child) or 2 * index + 2 (right child).\n",
|
||||
"\n",
|
||||
"For example, the right child of index 1 is 2 * 1 + 2 = 4.\n",
|
||||
"\n",
|
||||
"Complexity:\n",
|
||||
"* Time: O(lg(n))\n",
|
||||
"* Space: O(lg(n)) for the recursion depth (tree height), or O(1) if using an iterative approach\n",
|
||||
"\n",
|
||||
"### insert\n",
|
||||
"\n",
|
||||
"<pre>\n",
|
||||
" _5_\n",
|
||||
" / \\\n",
|
||||
" 20 15\n",
|
||||
" / \\ / \\\n",
|
||||
" 22 40 25\n",
|
||||
"\n",
|
||||
"insert(2):\n",
|
||||
"Insert at the right-most spot to maintain the heap property.\n",
|
||||
"\n",
|
||||
" _5_\n",
|
||||
" / \\\n",
|
||||
" 20 15\n",
|
||||
" / \\ / \\\n",
|
||||
" 22 40 25 2\n",
|
||||
"\n",
|
||||
"Bubble up 2: Swap 2 and 15\n",
|
||||
"\n",
|
||||
" _5_\n",
|
||||
" / \\\n",
|
||||
" 20 2\n",
|
||||
" / \\ / \\\n",
|
||||
" 22 40 25 15\n",
|
||||
"\n",
|
||||
"Bubble up 2: Swap 2 and 5\n",
|
||||
"\n",
|
||||
" _2_\n",
|
||||
" / \\\n",
|
||||
" 20 5\n",
|
||||
" / \\ / \\\n",
|
||||
" 22 40 25 15\n",
|
||||
"</pre>\n",
|
||||
"\n",
|
||||
"We'll use an array to represent the tree, here are the indices:\n",
|
||||
"\n",
|
||||
"<pre>\n",
|
||||
" _0_\n",
|
||||
" / \\\n",
|
||||
" 1 2\n",
|
||||
" / \\ / \\\n",
|
||||
" 3 4 5 6\n",
|
||||
"</pre>\n",
|
||||
"\n",
|
||||
"To get to a parent, we take (index - 1) // 2. \n",
|
||||
"\n",
|
||||
"For example, the parent of index 6 is (6 - 1) // 2 = 2.\n",
|
||||
"\n",
|
||||
"Complexity:\n",
|
||||
"* Time: O(lg(n))\n",
|
||||
"* Space: O(lg(n)) for the recursion depth (tree height), or O(1) if using an iterative approach"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Code"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Overwriting min_heap.py\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%%writefile min_heap.py\n",
|
||||
"from __future__ import division\n",
|
||||
"\n",
|
||||
"import sys\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class MinHeap(object):\n",
|
||||
"\n",
|
||||
" def __init__(self):\n",
|
||||
" self.array = []\n",
|
||||
"\n",
|
||||
" def __len__(self):\n",
|
||||
" return len(self.array)\n",
|
||||
"\n",
|
||||
" def extract_min(self):\n",
|
||||
" if not self.array:\n",
|
||||
" return None\n",
|
||||
" if len(self.array) == 1:\n",
|
||||
" return self.array.pop(0)\n",
|
||||
" minimum = self.array[0]\n",
|
||||
" # Move the last element to the root\n",
|
||||
" self.array[0] = self.array.pop(-1)\n",
|
||||
" self._bubble_down(index=0)\n",
|
||||
" return minimum\n",
|
||||
"\n",
|
||||
" def peek_min(self):\n",
|
||||
" return self.array[0] if self.array else None\n",
|
||||
"\n",
|
||||
" def insert(self, key):\n",
|
||||
" if key is None:\n",
|
||||
" raise TypeError('key cannot be None')\n",
|
||||
" self.array.append(key)\n",
|
||||
" self._bubble_up(index=len(self.array) - 1)\n",
|
||||
"\n",
|
||||
" def _bubble_up(self, index):\n",
|
||||
" if index == 0:\n",
|
||||
" return\n",
|
||||
" index_parent = (index - 1) // 2\n",
|
||||
" if self.array[index] < self.array[index_parent]:\n",
|
||||
" # Swap the indices and recurse\n",
|
||||
" self.array[index], self.array[index_parent] = \\\n",
|
||||
" self.array[index_parent], self.array[index]\n",
|
||||
" self._bubble_up(index_parent)\n",
|
||||
"\n",
|
||||
" def _bubble_down(self, index):\n",
|
||||
" min_child_index = self._find_smaller_child(index)\n",
|
||||
" if min_child_index == -1:\n",
|
||||
" return\n",
|
||||
" if self.array[index] > self.array[min_child_index]:\n",
|
||||
" # Swap the indices and recurse\n",
|
||||
" self.array[index], self.array[min_child_index] = \\\n",
|
||||
" self.array[min_child_index], self.array[index]\n",
|
||||
" self._bubble_down(min_child_index)\n",
|
||||
"\n",
|
||||
" def _find_smaller_child(self, index):\n",
|
||||
" left_child_index = 2 * index + 1\n",
|
||||
" right_child_index = 2 * index + 2\n",
|
||||
" # No right child\n",
|
||||
" if right_child_index >= len(self.array):\n",
|
||||
" # No left child\n",
|
||||
" if left_child_index >= len(self.array):\n",
|
||||
" return -1\n",
|
||||
" # Left child only\n",
|
||||
" else:\n",
|
||||
" return left_child_index\n",
|
||||
" else:\n",
|
||||
" # Compare left and right children\n",
|
||||
" if self.array[left_child_index] < self.array[right_child_index]:\n",
|
||||
" return left_child_index\n",
|
||||
" else:\n",
|
||||
" return right_child_index"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"collapsed": true
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"%run min_heap.py"
|
||||
]
|
||||
},
|
||||
{
|
||||
"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_min_heap.py\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%%writefile test_min_heap.py\n",
|
||||
"from nose.tools import assert_equal\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"class TestMinHeap(object):\n",
|
||||
"\n",
|
||||
" def test_min_heap(self):\n",
|
||||
" heap = MinHeap()\n",
|
||||
" assert_equal(heap.peek_min(), None)\n",
|
||||
" assert_equal(heap.extract_min(), None)\n",
|
||||
" heap.insert(20)\n",
|
||||
" assert_equal(heap.array[0], 20)\n",
|
||||
" heap.insert(5)\n",
|
||||
" assert_equal(heap.array[0], 5)\n",
|
||||
" assert_equal(heap.array[1], 20)\n",
|
||||
" heap.insert(15)\n",
|
||||
" assert_equal(heap.array[0], 5)\n",
|
||||
" assert_equal(heap.array[1], 20)\n",
|
||||
" assert_equal(heap.array[2], 15)\n",
|
||||
" heap.insert(22)\n",
|
||||
" assert_equal(heap.array[0], 5)\n",
|
||||
" assert_equal(heap.array[1], 20)\n",
|
||||
" assert_equal(heap.array[2], 15)\n",
|
||||
" assert_equal(heap.array[3], 22)\n",
|
||||
" heap.insert(40)\n",
|
||||
" assert_equal(heap.array[0], 5)\n",
|
||||
" assert_equal(heap.array[1], 20)\n",
|
||||
" assert_equal(heap.array[2], 15)\n",
|
||||
" assert_equal(heap.array[3], 22)\n",
|
||||
" assert_equal(heap.array[4], 40)\n",
|
||||
" heap.insert(3)\n",
|
||||
" assert_equal(heap.array[0], 3)\n",
|
||||
" assert_equal(heap.array[1], 20)\n",
|
||||
" assert_equal(heap.array[2], 5)\n",
|
||||
" assert_equal(heap.array[3], 22)\n",
|
||||
" assert_equal(heap.array[4], 40)\n",
|
||||
" assert_equal(heap.array[5], 15)\n",
|
||||
" mins = []\n",
|
||||
" while heap:\n",
|
||||
" mins.append(heap.extract_min())\n",
|
||||
" assert_equal(mins, [3, 5, 15, 20, 22, 40])\n",
|
||||
" print('Success: test_min_heap')\n",
|
||||
"\n",
|
||||
" \n",
|
||||
"def main():\n",
|
||||
" test = TestMinHeap()\n",
|
||||
" test.test_min_heap()\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_min_heap\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"%run -i test_min_heap.py"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Python 3",
|
||||
"language": "python",
|
||||
"name": "python3"
|
||||
},
|
||||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.4.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 0
|
||||
}
|
||||
50
graphs_trees/min_heap/test_min_heap.py
Normal file
50
graphs_trees/min_heap/test_min_heap.py
Normal file
@@ -0,0 +1,50 @@
|
||||
from nose.tools import assert_equal
|
||||
|
||||
|
||||
class TestMinHeap(object):
|
||||
|
||||
def test_min_heap(self):
|
||||
heap = MinHeap()
|
||||
assert_equal(heap.peek_min(), None)
|
||||
assert_equal(heap.extract_min(), None)
|
||||
heap.insert(20)
|
||||
assert_equal(heap.array[0], 20)
|
||||
heap.insert(5)
|
||||
assert_equal(heap.array[0], 5)
|
||||
assert_equal(heap.array[1], 20)
|
||||
heap.insert(15)
|
||||
assert_equal(heap.array[0], 5)
|
||||
assert_equal(heap.array[1], 20)
|
||||
assert_equal(heap.array[2], 15)
|
||||
heap.insert(22)
|
||||
assert_equal(heap.array[0], 5)
|
||||
assert_equal(heap.array[1], 20)
|
||||
assert_equal(heap.array[2], 15)
|
||||
assert_equal(heap.array[3], 22)
|
||||
heap.insert(40)
|
||||
assert_equal(heap.array[0], 5)
|
||||
assert_equal(heap.array[1], 20)
|
||||
assert_equal(heap.array[2], 15)
|
||||
assert_equal(heap.array[3], 22)
|
||||
assert_equal(heap.array[4], 40)
|
||||
heap.insert(3)
|
||||
assert_equal(heap.array[0], 3)
|
||||
assert_equal(heap.array[1], 20)
|
||||
assert_equal(heap.array[2], 5)
|
||||
assert_equal(heap.array[3], 22)
|
||||
assert_equal(heap.array[4], 40)
|
||||
assert_equal(heap.array[5], 15)
|
||||
mins = []
|
||||
while heap:
|
||||
mins.append(heap.extract_min())
|
||||
assert_equal(mins, [3, 5, 15, 20, 22, 40])
|
||||
print('Success: test_min_heap')
|
||||
|
||||
|
||||
def main():
|
||||
test = TestMinHeap()
|
||||
test.test_min_heap()
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
main()
|
||||
Reference in New Issue
Block a user