以Python實作資料結構 – Data Structure Implements in Python

2018 年 10 月 17 日2022 年 11 月 30 日
Python

以Python實作資料結構

tags: `data-structure`, `python`

簡介
陣列 Array
連結串列 Linked List & 雙向連結串列 Double Linked List
堆疊 Stack
佇列 Queue
二元搜尋樹 Binary Search Tree
平衡二元搜尋樹 Balancing Binary Search Tree, AVL Tree
紅黑樹 Red-Black Tree
二元堆積 Binary Heap
關聯陣列/對映/字典 Associative Array/ Map/ Dictionary
三元搜尋樹 Ternary Search Tree

簡介

什麼是資料結構？為什麼要使用資料結構？

是電腦中儲存、組織資料的方式，可以讓我們有效地儲存資料，並讓所有運算能最有效率地完成

演算法的運行時間是根據資料結構決定的，所以使用適當的資料結構來降低演算法的時間複雜度，如：

最短路徑演算法若無適當的資料結構，運行時間是O(N^2)，使用(heap/priority queue)可以大幅降低運行時間至O(N*logN)

抽象資料型態 Abstract Data Types

簡單而言，ADT是針對資料結構的「規範」或「描述」，像是物件導向語言裡面的interface，但不會實作細節

舉例堆疊的ADT描述：

push(): 插入元素 item 至堆疊頂端
pop(): 移除並回傳堆疊頂端的元素
peek(): 看堆疊頂端的資料而不取出
size(): 看堆疊的長度

ADT跟資料結構的關係

每個ADT在底層都有相對應的資料結構去實作ADT裡定義過的行為(method)

ADT	Data Structures
Stack	array, linked list
Queue	array, linked list
Priority Queue	heap
Dictionary/Hashmap	array

時間複雜度 Big O notation

描述演算法的效率（複雜度），舉例來說，A宅想要分享他的D槽給B宅，有以下幾種做法：

從台北騎車到屏東B宅家
用網路傳輸，不考慮被FBI攔截的情況

	1GB	1TB	500TB
騎車運送硬碟	600 min	600 min	600 min
網路傳輸	3 min	3072 min	1536000 min

從上表來看，騎車這個選項雖然聽起來很蠢，但不管硬碟有多大，都能確保10個小時內可以送達—— O(1)；至於網路傳輸隨著檔案越大，所需的時間也越長 —— O(N)；從這裡就可以看出常數時間(constant time)和線性時間(linear time)的差別對效率的影響有多大了

在表現複雜度函數的時候，有幾個通用的規則：

多個步驟用加法: O(a+b)

def func():

# step a

# step b

省略常數: ~~O(3n)~~ O(n)

def func(lst):

for i in lst: # O(n)

# do something ...

for i in lst: # O(n)

# do something ...

for i in lst: # O(n)

# do something ...

不同的input用不同的變數表示: ~~O(N^2)~~ O(a*b)

def func(la, lb):

for a in la:

for b in lb:

# do something ...

省略影響不大的變數: ~~O(n+n^2)~~ O(n^2)

1 2	O(n^2) <= O(n+n^2) <= O(n^2 + n^2)

# n^2是主導的變項，所以省略n

def func(la):

for a in la: # O(n)

# do something ...

for a in la: # O(n^2)

for b in la:

# do something

陣列 Array

物件或值的集合，每個物件或值可以被陣列的索引(index, key)識別

索引從0開始
因為有索引，我們可以對陣列做隨機存取(Random Access)

優點：

隨機存取不用搜尋就能訪問陣列當中所有值，執行速度快O(1)
不會因為鏈結斷裂而遺失資料
循序存取快

缺點：

重建或插入陣列須要逐一複製裏頭的值，時間複雜度是O(N)
編譯的時候必須事先知道陣列的大小，這讓陣列這個資料結構不夠動態(dynamic)
通常陣列只能存同一種型別
不支援連結串列的共享

Implements

	行為	big O
search	搜尋	O(1)
insert	插入第一項	O(N)
append	插入最後一項	O(1)
remove	移除第一項	O(N)
removeLast	移除最後一項	O(1)

以Python實作

random indexing: O(1)

arr = [1, 2, 3]

arr[0]

linear search: O(n)

max = arr[0]

for i in arr:

if i > max:

max = i

連結串列 Linked List & 雙向連結串列 Double Linked List

節點包含data和referenced object
連結的方式是節點(node)記住其他節點的參考(reference)
最後一個節點的參考是NULL

優點

各節點型態、記憶體大小不用相同
動態佔用的記憶體，不須事先宣告大小
插入、刪除快O(1)

缺點

不支援隨機存取，只能循序存取(sequencial access)，時間複雜度為O(N)
須額外空間儲存其他節點的參考
可靠性較差，連結斷裂容易遺失資料
難以向前(backward)訪問，可以用雙向連結串列來處理，不過會多佔用記憶體空間

Implements

	行為	big O
search	搜尋	O(N)
insert	插入第一項	O(1)
append	插入最後一項	O(N)
remove	移除第一項	O(1)
removeLast	移除最後一項	O(N)

註：連結串列沒有index，處理插入或移除第N項會需要先循序找到插入/移除位置，因此會需要O(N)的時間

以Python實作

以下的代碼是我實作的範例，有錯誤煩請指正。

主要概念是實作__getitem__來循序存取(indexing)，另外Double Linked List支援反向存取，故訪問lst[0]和lst[-1]皆可以達成O(1)的時間複雜度

執行結果請參考travishen/gist/linked-list.md

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from collections import Iterable

class Node:

def __init__(self, data=None, next_node=None):

self.data = data

self.next_node = next_node

def __repr__(self):

return 'Node(data={!r}, next_node={!r})'.format(self.data, self.next_node)

class LinkedList(object):

def __init__(self, inital_nodes=None):

self.head = None

self.inital_nodes = inital_nodes

# garbage collect

for node in self:

del node

if isinstance(inital_nodes, Iterable):

for node in reversed(list(inital_nodes)):

self.insert(node) # insert to head

elif inital_nodes:

raise NotImplementedError('Inital with not iterable object')

def __repr__(self):

return 'LinkedList(inital_nodes={!r})'.format(self.inital_nodes)

def __len__(self):

count = 0

for node in self:

count += 1

return count

def __setitem__(self, index, data):

self.insert(data, index)

def __delitem__(self, index):

self.remove(index, by='index')

def __getitem__(self, index):

count = 0

current = self.head

index = self.positive_index(index)

while count < index and current is not None:

current = current.next_node

count += 1

if current:

return current

else:

raise IndexError

def positive_index(self, index): # inplement negative indexing

"""

Use nagative indexing will increase O(N) time complexity

We can improve it with double linded list

"""

if index < 0:

index = len(self) + index

return index

def insert(self, data, index=0):

index = self.positive_index(index)

if self.head is None: # initial

self.head = Node(data, None)

elif index == 0: # insert to head

new_node = Node(data, self.head)

self.head = new_node

else: # insert to lst[index]

last_node = self[index]

last_node.next_node = Node(data, last_node.next_node)

return None # this instance has changed and didn't create instance

def search(self, data):

for node in self:

if node.data == data:

return node

return None

def remove(self, data_or_index, by='data'):

for i, node in enumerate(self):

if (by == 'data' and node.data == data_or_index) or (by == 'index' and i == data_or_index):

if i == 0:

self.head = node.next_node

node.next_node = None

else:

prev_node.next_node = node.next_node

break

prev_node = node

return None # this instance has changed and didn't create instance

class DoubleLinkedNode(Node):

def __init__(self, data=None, last_node=None, next_node=None):

self.data = data

self.next_node = next_node

self.last_node = last_node

if next_node:

next_node.last_node = self

class DoubleLinkedList(LinkedList):

def __init__(self, *args, **kwargs):

self.foot = None

super(DoubleLinkedList, self).__init__(*args, **kwargs)

def __repr__(self):

return 'DoubleLinkedList(inital_nodes={})'.format(self.inital_nodes)

def __getitem__(self, index):

"""

Support negative indexing in O(N) by setting footer

"""

count = 0

if index >= 0:

current = self.head

while count < index and current is not None:

current = current.next_node

count += 1

else:

current = self.foot

while count > (index + 1) and current is not None:

current = current.last_node

count -= 1

if current:

return current

else:

raise IndexError

def insert(self, data, index=0):

if self.head is None: # initial

self.head = self.foot = DoubleLinkedNode(data, None, None)

elif index == 0: # insert to head

new_node = DoubleLinkedNode(data, None, self.head)

self.head = new_node

else: # insert to lst[index]

last_node = self[index]

last_node.next_node = DoubleLinkedNode(data, last_node, last_node.next_node)

if last_node.next_node.next_node is None: # set foot

self.foot = last_node.next_node

return None # this instance has changed and didn't create instance

Linked List現實中的應用

低級別的內存管理（Low Level Memory Management），以C語言為例：

malloc()、 free(): 見Heap Management
chart * chart_ptr = (chart*)malloc(30);: 取得30byte的heap memory

許多Windows的應用程式：工具列視窗切換、PhotoViewer
區塊鏈技術

[圖片來源]

堆疊 Stack

推疊是一種抽象資料型態，特性是先進後出（LIFO, last in first out）
在高階程式語言，容易用array、linked list來實作
大部分的程式語言都是Stack-Oriented，因為仰賴堆疊來處理method call(呼叫堆疊, Call Stack)。

Implements

	行為	big O
push	將資料放入堆疊的頂端	O(1)
pop	回傳堆疊頂端資料	O(1)
peek	看堆疊頂端的資料而不取出	O(1)

應用

call stack + stack memory
深度優先搜尋演算法（Depth-First-Search）
尤拉迴路（Eulerian Circuit）
瀏覽器回上一頁
PhotoShop上一步(undo)

註：任何遞迴(recursion)形式的演算法，都可以用Stack改寫，例如DFS。不過就算我們使用遞迴寫法，程式最終被parsing還是Stack

def factorial(n, cache={}):

if n == 0: # declare base case to prevent stack overflow

return 1

return n * factorial(n-1)

Stack memory vs Heap memory

stack memory	heap memory
有限的記憶體配置空間	記憶體配置空間較大
存活時間規律可預測的	存活時間不規律不可預測的
CPU自動管理空間(GC)	使用者自主管理空間
區域變數宣告的空間不能更動	物件的值可以變動，如realloc()

以Python實作

class Stack(object):

def __init__(self, initial_data):

self.stack = []

self.initial_data = initial_data

if isinstance(initial_data, Iterable):

self.stack = list(initial_data)

else:

raise NotImplementedError('Inital with not iterable object')

def __repr__(self):

return 'Stack(initial_data={!r})'.format(self.initial_data)

def __len__(self):

return len(self.stack)

def __getitem__(self, i):

return self.stack[i]

@property

def is_empty(self):

return len(self.stack) == 0

def push(self, data):

self.stack.append(data)

def pop(self):

if not self.is_empty:

return self.stack.pop()

def peek(self):

return self.stack[-1]

Using Lists as Stacks

>>> stack = [3, 4, 5]

>>> stack.append(6)

>>> stack.append(7)

>>> stack

[3, 4, 5, 6, 7]

>>> stack.pop()

>>> stack

[3, 4, 5, 6]

>>> stack.pop()

>>> stack

[3, 4]

佇列 Queue

佇列是一種抽象資料型態，特性是先進先出（FIFO, first in first out）
在高階程式語言，容易用array、linked list來實作

應用

多個程序的資源共享，例如CPU排程
非同步任務佇列，例如I/O Buffer
廣度優先搜尋演算法（Depth-First-Search）

以Python實作

class Queue(object):

def __init__(self, initial_data):

self.queue = []

self.initial_data = initial_data

if isinstance(initial_data, Iterable):

self.queue = list(initial_data)

else:

raise NotImplementedError('Inital with not iterable object')

def __repr__(self):

return 'Queue(initial_data={!r})'.format(self.initial_data)

def __len__(self):

return len(self.queue)

def __getitem__(self, i):

return self.queue[i]

@property

def is_empty(self):

return len(self.queue) == 0

def enqueue(self, data):

return self.queue.append(data)

def dequeue(self):

return self.queue.pop(0)

def peek(self):

return self.queue[0]

參考

multiprocessing實作的的Queue
Using Lists as Queues

>>> from collections import deque

>>> queue = deque(["Eric", "John", "Michael"])

>>> queue.append("Terry") # Terry arrives

>>> queue.append("Graham") # Graham arrives

>>> queue.popleft() # The first to arrive now leaves

'Eric'

>>> queue.popleft() # The second to arrive now leaves

'John'

>>> queue # Remaining queue in order of arrival

deque(['Michael', 'Terry', 'Graham'])

二元搜尋樹 Binary Search Tree

主要的優點就是時間複雜度能優化至O(logN)

每個節點最多有兩個子節點
子節點有左右之分
左子樹的節點小於根節點、右子樹的節點大於根節點
節點值不重複

	Average case	Worst case
insert	O(logN)	O(N)
delete	O(logN)	O(N)
search	O(logN)	O(N)

以Python實作insert, remove, search，執行結果請參考gist

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class Node(object):

def __init__(self, data):

self._left, self._right = None, None

self.data = int(data)

def __repr__(self):

return 'Node({})'.format(self.data)

@property

def left(self):

return self._left

@left.setter

def left(self, node):

self._left = node

@property

def right(self):

return self._right

@right.setter

def right(self, node):

self._right = node

class BinarySearchTree(object):

def __init__(self, root=None):

self.root = root

self.search_mode = 'in_order'

# O(logN) time complexity if balanced, it could reduce to O(N)

def insert(self, data, **kwargs):

"""Insert from root"""

BinarySearchTree.insert_node(self.root, data, **kwargs)

# O(logN) time complexity if balanced, it could reduce to O(N)

def remove(self, data):

"""Insert from root"""

BinarySearchTree.remove_node(self.root, data)

@staticmethod

def insert_node(node, data, **kwargs):

node_consturctor = kwargs.get('node_constructor', None) or Node

if node:

if data < node.data:

if node.left is None:

node.left = node_consturctor(data)

else:

BinarySearchTree.insert_node(node.left, data, **kwargs)

elif data > node.data:

if node.right is None:

node.right = node_consturctor(data)

else:

BinarySearchTree.insert_node(node.right, data, **kwargs)

else:

node.data = data

return node

@staticmethod

def remove_node(node, data):

if not node:

return None

if data < node.data:

node.left = BinarySearchTree.remove_node(node.left, data)

elif data > node.data:

node.right = BinarySearchTree.remove_node(node.right, data)

else:

if not (node.left and node.right): # leaf

del node

return None

if not node.left:

tmp = node.right

del node

return tmp

if not node.right:

tmp = node.left

del node

return tmp

predeccessor = BinarySearchTree.get_max_node(node.left)

node.data = predeccessor.data

node.left = BinarySearchTree.remove_node(node.left, predeccessor.data)

return node

def get_min(self):

return self.get_min_node(self.root)

@staticmethod

def get_min_node(node):

if node.left:

return BinarySearchTree.get_max_node(node.left)

return node

def get_max(self):

return self.get_max_node(self.root)

@staticmethod

def get_max_node(node):

if node.right:

return BinarySearchTree.get_max_node(node.right)

return node

def search_decorator(func):

def interface(*args, **kwargs):

res = func(*args, **kwargs)

if isinstance(res, Node):

return res

elif 'data' in kwargs:

for node in res:

if node.data == kwargs['data']:

return node

return res

return interface

@staticmethod

@search_decorator

def in_order(root, **kwargs):

"""left -> root -> right"""

f = BinarySearchTree.in_order

res = []

if root:

left = f(root.left, **kwargs)

if isinstance(left, Node):

return left

right = f(root.right, **kwargs)

if isinstance(right, Node):

return right

res = left + [root] + right

return res

@staticmethod

@search_decorator

def pre_order(root, **kwargs):

"""root -> left -> right"""

f = BinarySearchTree.pre_order

res = []

if root:

left = f(root.left, **kwargs)

if isinstance(left, Node):

return left

right = f(root.right, **kwargs)

if isinstance(right, Node):

return right

res = [root] + left + right

return res

@staticmethod

@search_decorator

def post_order(root, **kwargs):

"""root -> right -> root"""

f = BinarySearchTree.post_order

res = []

if root:

left = f(root.left, **kwargs)

if isinstance(left, Node):

return left

right = f(root.right, **kwargs)

if isinstance(right, Node):

return right

res = left + right + [root]

return res

def traversal(self,

order:"in_order|post_order|post_order"=None,

data=None):

order = order or self.search_mode

if order == 'in_order':

return BinarySearchTree.in_order(self.root, data=data)

elif order == 'pre_order':

return BinarySearchTree.pre_order(self.root, data=data)

elif order == 'post_order':

return BinarySearchTree.post_order(self.root, data=data)

else:

raise NotImplementedError()

def search(self, data, *args, **kwargs):

return self.traversal(*args, data=data, **kwargs)

BST現實中的應用

OS file system
機器學習：決策樹

平衡二元搜尋樹 Balancing Binary Search Tree, AVL Tree

能保證O(logN)的時間複雜度
每次insert, delete都要檢查平衡，非平衡需要額外做rotation
判斷是否平衡：
- 左子樹高度 - 右子樹高度 > 1: rotate to right
- 左子樹高度 - 右子樹高度 < -1: rotate to left

	Average case	Worst case
insert	O(logN)	O(logN)
delete	O(logN)	O(logN)
search	O(logN)	O(logN)

不適合用在排序，時間複雜度為O(N*logN)

插入n個：O(N*logN)
in-order迭代：O(N)

繼承上面BST繼續往下實作，有bug請協助指正，執行結果請參考gist

任一節點設定完left或right，更新該節點height
每個insert的call stack檢查檢查節點是否平衡，不平衡則rotate

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class HNode(Node):

def __init__(self, *args, **kwargs):

super(HNode, self).__init__(*args, **kwargs)

self._height = 0

def __repr__(self):

return 'HNode({})'.format(self.data)

@property

def height(self):

return self._height

def set_height(self):

if self.left is None and self.right is None:

self._height = 0

else:

self._height = max(self.left_height, self.right_height) + 1

return self._height

@Node.left.setter

def left(self, node):

self._left = node

self.set_height()

@Node.right.setter

def right(self, node):

self._right = node

self.set_height()

@property

def sub_diff(self):

return self.left_height - self.right_height

@property

def left_height(self):

if self.left:

return self.left.height

return -1

@property

def right_height(self):

if self.right:

return self.right.height

return -1

@property

def is_balance(self):

return abs(self.sub_diff) <= 1

def balance(self, data):

if self.sub_diff > 1:

if data < self.left.data: # left left heavy

return self.rotate('right')

if data > self.left.data: # left right heavy

self.left = self.left.rotate('left')

return self.rotate('right')

if self.sub_diff < -1:

if data > self.right.data:

return self.rotate('left') # right right heavy

if data < self.right.data: # right left heavy

self.right = self.right.rotate('right')

return self.rotate('left')

return self

def rotate(self, to:"left|right"):

if to == 'right':

tmp = self.left

tmp_right = tmp.right

# update

tmp.right = self

self.left = tmp_right

print('Node {} right rotate to {}!'.format(self, tmp))

return tmp # return new root

if to == 'left':

tmp = self.right

tmp_left = tmp.left

# update

tmp.left = self

self.right = tmp_left

print('Node {} left rotate to {}!'.format(self, tmp))

return tmp # return new root

raise NotImplementedError()

class AVLTree(BinarySearchTree):

def __init__(self, *args, **kwargs):

super(AVLTree, self).__init__(*args, **kwargs)

def insert(self, data):

AVLTree.insert_node(self.root, data, tree=self) # pass self as keyword argument to update self.root

self.update_height()

def remove(self, data):

AVLTree.remove_node(self.root, data, tree=self) # pass self as keyword argument to update self.root

self.update_height()

def rotate_decorator(func):

def interface(*args, **kwargs):

node = func(*args, **kwargs)

data = args[1]

tree = kwargs.get('tree')

new_root = node.balance(data)

if node == tree.root:

tree.root = new_root

return interface

def update_height(self):

for n in self.traversal(order='in_order'):

n.set_height()

@property

def is_balance(self):

return self.root.is_balance

@rotate_decorator

def insert_node(*args, **kwargs):

return BinarySearchTree.insert_node(*args, node_constructor=HNode, **kwargs)

@rotate_decorator

def remove_node(*args, **kwargs):

return BinarySearchTree.remove_node(*args, **kwargs)

紅黑樹 Red-Black Tree

相較於AVL樹，紅黑樹犧牲了部分平衡性換取插入/刪除操作時更少的翻轉操作，整體效能較佳（插入、刪除快）
不像AVL樹的節點屬性用height來判斷是否須翻轉，而是用紅色/黑色來判斷
- 根節點、末端節點（NULL）是黑色
- 紅色節點的父節點和子節點是黑色
- 每條路徑上黑色節點的數量相同
- 每個新節點預設是紅色，若違反以上規則：
- 翻轉，或
- 更新節點顏色

	Average case	Worst case
insert	O(logN)	O(logN)
delete	O(logN)	O(logN)
search	O(logN)	O(logN)

github上用python實作的範例：Red-Black-Tree

優先權佇列 Priority Queue

相較於Stack或Queue，對資料項目的取出順序是以權重(priority)來決定
常用heap來實作

二元堆積 Binary Heap

是一種二元樹資料結構，通常透過一維陣列(one dimension array)
根據排序行為分成min及max：
- max heap: 父節點的值(value)或權重(key)大於子節點
- min heap: 父節點的值(value)或權重(key)小於子節點
必須是完全(compelete)二元樹或近似完全二元樹

註：

heap資料結構跟heap memory沒有關聯
優勢在於取得最大權重或最小權重項目(root)，時間複雜度為O(1)

	time complexity
insert	O(N) + O(logN) reconsturct times
delete	O(N) + O(logN) reconsturct times

應用

堆積排序法（Heap Sort）
普林演算法（Prim’s Algorithm）
戴克斯特拉演算法（Dijkstra’s Algorithm）

堆積排序 Heapsort

是一種比較排序法（Comparision Sort）
主要優勢在於能確保O(NlogN)的時間複雜度
屬於原地演算法(in-place algorithm)，缺點是每次排序都須重建heap——增加O(N)時間複雜度
在一維陣列起始位置為0的indexing:

用Python實作Max Binary Heap，請參考gist

class Heap(object):

"""Max Binary Heap"""

def __init__(self, capacity=10):

self._default = object()

self.capacity = capacity

self.heap = [self._default] * self.capacity

def __len__(self):

return len(self.heap) - self.heap.count(self._default)

def __getitem__(self, i):

return self.heap[i]

def insert(self, item):

"""O(1) + O(logN) time complexity"""

if self.capacity == len(self): # full

return

self.heap[len(self)] = item

self.fix_up(self.heap.index(item)) # check item's validation

def fix_up(self, index):

"""

O(logN) time complexity

Violate:

1. child value > parent value

"""

parent_index = (index-1)//2

if index > 0 and self.heap[index] > self.heap[parent_index]:

# swap

self.swap(index, parent_index)

self.fix_up(parent_index) # recursive

def fix_down(self, index):

"""

O(logN) time complexity

Violate:

1. child value > parent value

"""

parent = self.heap[index]

left_child_index = 2 * index + 1

right_child_index = 2 * index + 2

largest_index = index

if left_child_index < len(self) and self.heap[left_child_index] > parent:

largest_index = left_child_index

if right_child_index < len(self) and self.heap[right_child_index] > self.heap[largest_index]:

largest_index = right_child_index

if index != largest_index:

self.swap(index, largest_index)

self.fix_down(largest_index) # recursive

def heap_sort(self):

"""

O(NlogN) time complixity

"""

for i in range(0, len(self)):

self.poll()

def swap(self, i1, i2):

self.heap[i1], self.heap[i2] = self.heap[i2], self.heap[i1]

def poll(self):

max_ = self.max_

self.swap(0, len(self) - 1) # swap first and last

self.heap[len(self) - 1] = self._default

self.fix_down(0)

return max_

@property

def max_(self):

return self.heap[0]

python build-in heapq

關聯陣列/對映/字典 Associative Array/ Map/ Dictionary

鍵、值的配對(key-value)
相較於樹狀資料結構，劣勢在於排序困難
主要操作：
- 新增、刪除、修改值
- 搜尋已知的鍵

hash function

division method: modulo operator

h(x) = n % m

n: number of keys, m: number of buckets

Collision

當多個key存取同一個bucket（slot），解決collision會導致時間複雜度提高

h(26) = 26 mod 6 = 2

h(50) = 50 mod 6 = 2

解法：

chaining: 在同一個slot用linked list存放多個關聯
open addressing: 分配另一個空的slot
- linear probing: 線性探測
- quadratic probing: 二次方探測，如1, 2, 4, 8…
- rehashing

Dynamic resizing

load factor（佔用率）: n / m

load factor會影響到存取的效能，因此須要根據使用率動態變更陣列大小；
舉例來說，Java觸發resize的時機點大約是佔用超過75%時、Python則約是66%

應用

資料庫
Network Routing
Rabin-Karp演算法
Hashing廣泛用於資料加密

以Python實作，請參考gist

from collections import Iterable

from functools import reduce

class HashTable(object):

def __init__(self, size=10):

self.size = 10

self.keys = [None] * self.size

self.values = [None] * self.size

def __repr__(self):

return 'HashTable(size={})'.format(self.size)

def put(self, key, value):

index = self.hash(key)

while self.keys[index] is not None: # collision

if self.keys[index] == key: # update

self.values[index] = value

return

index = (index + 1) % self.size # rehash

self.keys[index] = key

self.values[index] = value

def get(self, key):

if key in self.keys:

return self.values[self.hash(key)]

return None

def hash(self, key):

if isinstance(key, Iterable):

sum = reduce(lambda prev, n: prev + ord(n), key, 0)

else:

sum = key

return sum % self.size

	Average case	Worst case
insert	O(1)	O(N)
delete	O(1)	O(N)
search	O(1)	O(N)

三元搜尋樹 Ternary Search Tree, TST

相較其他樹狀資料結構而言，佔用記憶體空間較小
只儲存string，不存NULL或其他物件
父節點可以有3個子節點：left(less)、middle(equal)、right(greater)
可以同時用來當作hashmap使用，也可以做排序
效能上比hashmap更佳，在解析key時是漸進式的（如cat若root沒有c就不用繼續找了）

應用

autocompelete
拼字檢查
最近鄰居搜尋（Near-neighbor）
WWW package routing
最長前綴匹配(perfix matching)
Google Search

以Python實作，請參考gist

class Node(object):

def __init__(self, char):

self.char = char

self.left = self.middle = self.right = None

self.value = None

class TernarySearchTree(object):

def __init__(self):

self.root = None

def __repr__(self):

return 'TernarySearchTree()'

def put(self, key, value):

self.root = self.recursive(key, value)(self.root, 0)

def get(self, key):

node = self.recursive(key)(self.root, 0)

if node:

return node.value

return -1

def recursive(self, key, value=None):

def putter(node, index):

char = key[index]

if node is None:

node = Node(char)

if char < node.char:

node.left = putter(node.left, index)

elif char > node.char:

node.right = putter(node.right, index)

elif index < len(key) - 1:

node.middle = putter(node.middle, index+1)

else:

node.value = value

return node

def getter(node, index):

char = key[index]

if node is None:

return None

if char < node.char:

return getter(node.left, index)

elif char > node.char:

return getter(node.right, index)

elif index < len(key) - 1:

return getter(node.middle, index+1)

else:

return node

if value:

return putter

else:

return getter

互斥集 Disjoint sets / union-find data structure

一堆沒有交集的集合，如10個學生分成4組
主要操作: union、find、makeSet
通常以linked list或tree來實作
訪問disjoint set中的任何節點都回傳同一個root value

set在union過程中會遇到不平衡的問題，有兩種最佳化方法：

union by rank: 讓小的樹接到較大的樹
path compression: 訪問節點時調整樹的結構，直接與root連結

應用

Kruskal: 檢查圖中是否有cycle

以Python實作，輸出請參考gist

class Edge:

"""Sortable edge in the graph"""

def __init__(self, weight, start, target):

self.weight = weight

self.start = start # Node

self.target = target # Node

def __repr__(self):

return 'Edge(weight={}, start={}, target={})'.format(self.weight,

self.start,

self.target)

def __cmp__(self, other):

return self.cmp(self.weight, other.weight)

def __lt__(self, other):

return self.weight < other.weight

class Node:

"""Node live in a graph / disjoint set"""

def __init__(self, name):

self.name = name

self.parent = None

self.set_ = None

def __repr__(self):

return self.name

parent = None

if self.parent:

parent = self.parent.name

return 'Node(name={}, parent={})'.format(self.name, parent)

class DisjointSet:

"""Represent a disjoint set"""

def __init__(self, node):

"""make set"""

self.nodes = set([node])

self.root = node

self.root.set_ = self

def __str__(self):

if not self.nodes:

return 'Empty'

return str(self.nodes)

def __len__(self):

return len(self.nodes)

@staticmethod

def find(node):

"""Find root node in nodes and do path compression"""

root = node

while root.parent is not None:

root = root.parent

# path compression

while node is not root:

temp = node.parent

node.parent = root

node = temp

return root

@staticmethod

def merge(s1, s2):

"""Merge two set base on """

if s1 is s2: # is equal

return

if len(s1) < len(s2): # s1 --> s2

s1.root.parent = s2.root

for n in s1.nodes: # point all node to new set

n.set_ = s2

s2.nodes.update(s1.nodes)

s1.nodes = set()

else: # s2 --> s1

s2.root.parent = s1.root

for n in s2.nodes: # point all node to new set

n.set_ = s1

s1.nodes.update(s2.nodes)

s2.nodes = set()

array

以Python實作資料結構 – Data Structure Implements in Python

以Python實作資料結構

tags: data-structure, python

TOC

簡介

什麼是資料結構？為什麼要使用資料結構？

抽象資料型態 Abstract Data Types

ADT跟資料結構的關係

時間複雜度 Big O notation

陣列 Array

Implements

以Python實作

連結串列 Linked List & 雙向連結串列 Double Linked List

Implements

以Python實作

Linked List現實中的應用

堆疊 Stack

Implements

應用

Stack memory vs Heap memory

以Python實作

佇列 Queue

應用

以Python實作

二元搜尋樹 Binary Search Tree

BST現實中的應用

平衡二元搜尋樹 Balancing Binary Search Tree, AVL Tree

紅黑樹 Red-Black Tree

優先權佇列 Priority Queue

二元堆積 Binary Heap

應用

堆積排序 Heapsort

關聯陣列/對映/字典 Associative Array/ Map/ Dictionary

hash function

Collision

Dynamic resizing

應用

三元搜尋樹 Ternary Search Tree, TST

應用

互斥集 Disjoint sets / union-find data structure

應用

以Python實作，輸出請參考gist

tags: `data-structure`, `python`