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256 lines (210 loc) · 6.94 KB
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#!/usr/bin/env python
# -*- coding=utf-8 -*-
# O(n^2)
# i=0, 1, 2, ..., n-1の各要素で、
# n-1回の比較 + n-2回の比較 + ... + 1 = (n * (n-1) / 2)回の計算
#
# nによらず、i, j, min_idxが必要になるだけ => O(1) space
#
# stable
def selection_sort(data):
if data is None:
return None
# i番目とj=i+1番目以降の要素を比較
# data[i] > data[j]の中でminな要素とswap
for i in range(len(data)-1):
min_idx = i
for j in range(i+1, len(data)):
# i+1番目以降の要素でminな要素のindexに逐次更新
if data[min_idx] > data[j]:
min_idx = j
# 最終的にmin_idxと現在のi番目の要素をswap
data[i], data[min_idx] = data[min_idx], data[i]
print(data)
return data
# recursive
def do_selection_sort_r(data):
return selection_sort_r(data, 0)
def selection_sort_r(data, start):
# base caseはpivot位置が(len(data) - 1) - 1になるとき
if start < len(data) - 1:
min_pos = find_min_idx(data, start)
data[start], data[min_pos] = data[min_pos], data[start]
selection_sort_r(data, start + 1)
return data
def selection_sort_stable(data):
if data is None:
return None
for i in range(len(data) - 1):
data = insert(data, i)
print(data)
return data
def insert(data, i):
min_idx = i
for j in range(i + 1, len(data)):
if data[min_idx] > data[j]:
min_idx = j
val = data[min_idx]
for k in range(min_idx, i, -1):
data[k] = data[k - 1]
data[i] = val
return data
def find_min_idx(data, start):
min_pos = start
for i in range(start + 1, len(data)):
if data[min_pos] > data[i]:
min_pos = i
return min_pos
# worst case: O(n^2)
# average case: O(n^2)
# best case: O(n)
# Note: stable and in-place
def insertion_sort(data):
for i in range(1, len(data)):
pivot = data[i]
j = i - 1
# Repeat until the pivot is greater than data[j]
while j >= 0 and pivot < data[j]:
data[j+1] = data[j]
j -= 1
data[j+1] = pivot
return data
# worst case = pivotがsmallestもしくはlargetstなとき
# 分割後が1ずつ少なくなりながら比較, n-1 + n-2 + n-3 + ... + 2 + 1 = o(n^2)
# best case = pivotがmediumなとき
# 分割の回数は2分割していってleafが全て1になったとき => logn
# 比較回数は各深さで合計するとnなので、O(nlogn)
# average caseも同様に、O(nlogn)
#
# leftとrightがleafのときにはlogn必要 => O(logn)
#
# not stable sort
def quick_sort(data):
if len(data) < 2:
return data
pivot = data[len(data) // 2]
left, right, equal = [], [], []
for d in data:
if d < pivot: left.append(d)
elif d == pivot: equal.append(d)
else: right.append(d)
return quick_sort(left) + equal + quick_sort(right)
def quick_sort_in_place(data):
"""quick sort in place partition
Args:
data (list): an input list
Returns:
list: a sorted list
"""
def _quick_sort(data, l, r):
if l > r:
return
mid = partition(data, l, r)
_quick_sort(data, l, mid - 1)
_quick_sort(data, mid + 1, r)
return data
return _quick_sort(data, 0, len(data) - 1) if len(data) > 0 else []
def partition(data, l, r):
# m indicate the tail position of lesser elements
m = l
for i in range(l + 1, r + 1):
if data[i] <= data[l]:
m += 1
data[i], data[m] = data[m], data[i]
data[l], data[m] = data[m], data[l]
return m
def merge(left, right):
merged = []
left_idx = 0
right_idx = 0
while left_idx < len(left) and right_idx < len(right):
# Use '<=' so as to be stable in the order
if left[left_idx] <= right[right_idx]:
merged.append(left[left_idx])
left_idx += 1
else:
merged.append(right[right_idx])
right_idx += 1
# Append what is remained in either of the lists
return merged + left[left_idx:] + right[right_idx:]
# Time complexity: O(nlogn)
# Space complexity: O(n)
def merge_sort(data):
# base case or data is empty
if len(data) <= 1:
return data
# Split the data until reaching the base case
mid_idx = len(data) // 2
left = merge_sort(data[:mid_idx])
right = merge_sort(data[mid_idx:])
# Sort and Merge
merged = merge(left, right)
return merged
def heapify(data, i, n):
# 親ノードをlargestと仮定
largest = i
l = 2 * i + 1
r = 2 * i + 2
# leftとrightがnを超えないようにチェックしながら
# largestが親ノードでなくなるまで(base case)行う
if l <= n and data[largest] < data[l]:
largest = l
if r <= n and data[largest] < data[r]:
largest = r
# not base case = recursive case
if largest != i:
data[i], data[largest] = data[largest], data[i]
data = heapify(data, largest, n)
return data
# O(nlogn) time, O(1) space
#
# data全体のheapifyでは、dataの半分の繰り返しが行われる(親ノードpから始まる)
# 各繰り返しにおいては、最大でtreeの深さ分(logn)の繰り返しheapifyが行われる
# したがって (n/2) * logn
#
# sort stageでは、n-1回の繰り返しで各繰り返しで同様に
# 最大でtreeの高さ分(logn)の繰り返しが発生し、nlogn
#
def heap_sort(data):
if data is None:
return None
last_idx = len(data) - 1
last_pidx = last_idx // 2 if last_idx % 2 != 0 else last_idx // 2 - 1
# data全体をheap構造化
for p in range(last_pidx, -1, -1):
data = heapify(data, p, last_idx)
print('heapified:', data)
# 最大値をheapのroot（配列の先頭）から取り出して最後尾と交換
# 交換すると残りのheap構造が崩れるので再度heapify
# 以降は繰り返し
for i in range(last_idx, 0, -1):
data[i], data[0] = data[0], data[i]
data = heapify(data, 0, i - 1)
return data
if __name__ == "__main__":
data = [64, 25, 12, 22, 11]
print('org', data)
print('--selection sort--')
print('result', selection_sort(data))
data = [4, 3, 4, 2, 1]
print('org', data)
print('--selection sort stable--')
print('result', selection_sort_stable(data))
data = [64, 25, 12, 22, 11]
print('--insertion sort--')
print('result', insertion_sort(data))
data = [64, 25, 12, 22, 11]
print('--quick sort--')
print('result', quick_sort(data))
data = [97, 200, 100, 101, 211, 107]
print('--quick sort in place--')
print('result', quick_sort_in_place(data))
data = [6, 5, 3, 1, 8, 7, 2, 4]
print('org', data)
print('--merge sort--')
print('result', merge_sort(data))
#data = [4, 1, 6, 2, 9, 7, 3, 8]
data = [6, 5, 1, 8, 2, 4]
print('org', data)
print('heap sort')
print('result', heap_sort(data))