冒泡排序

def bubble_sort(li):
    for i in range(len(li)-1): # i表示第幾趟
        exchange = False
        for j in range(len(li)-i-1): # j表示圖中的箭頭
            if li[j] > li[j+1]:
                li[j], li[j+1] = li[j+1], li[j]
                exchange = True
        if not exchange:
            return

選擇排序

def select_sort(li):
    for i in range(len(li)-1):
        # 第i趟開始時 無序區：li[i:]
        # 找無序區最小值，保存最小值的位置
        min_pos = i     # min_pos保存最小值的位置
        for j in range(i+1, len(li)):
            if li[j] < li[min_pos]:
                min_pos = j
        li[min_pos], li[i] = li[i], li[min_pos]
 

插入排序

def insert_sort(li):
    for i in range(1, len(li)): # i是摸到的牌的下標
        tmp = li[i]
        j = i - 1 # j是手裏最後一張牌的下標
        # 兩個終止條件：j小於0表示tmp是最小的 順序不要亂
        while j >= 0 and li[j] > tmp:  
            li[j+1] = li[j]
            j -= 1
        # for j in range(i-1, -1, -1):
        #     if li[j] > tmp:
        #         li[j+1] = li[j]
        #     else:
        #         break
        li[j+1] = tmp
 

快速排序

def partition(li, left, right):
    randi = random.randint(left, right)
    li[randi], li[left] = li[left], li[randi]

    tmp = li[left]
    while left < right:
        while left < right and li[right] >= tmp:
            right -= 1
        li[left] = li[right]
        while left < right and li[left] <= tmp:
            left += 1
        li[right] = li[left]
    li[left] = tmp
    return left


def _quick_sort(li, left, right):
    if left < right:    # 至少兩個元素
        mid = partition(li, left, right)
        _quick_sort(li, left, mid - 1)
        _quick_sort(li, mid + 1, right)

@cal_time
def quick_sort(li):
    return _quick_sort(li, 0, len(li)-1)


li = list(range(10000, 0, -1))
quick_sort(li)

堆排序

def sift(li, low, high):
    tmp = li[low]
    i = low
    j = 2 * i + 1
    while j <= high: # 退出條件2：當前i位置是葉子結點，j位置超過了high
        # j 指向更大的孩子
        if j + 1 <= high and li[j+1] > li[j]:
            j = j + 1 # 如果右孩子存在並且更大，j指向右孩子
        if tmp < li[j]:
            li[i] = li[j]
            i = j
            j = 2 * i + 1
        else:       # 退出條件1：tmp的值大於兩個孩子的值
            break
    li[i] = tmp

@cal_time
def heap_sort(li):
    # 1. 建堆
    n = len(li)
    for i in range(n//2-1, -1, -1):
        # i 是建堆時要調整的子樹的根的下標
        sift(li, i, n-1)
    # 2.挨個出數
    for i in range(n-1, -1, -1): #i表示當前的high值 也表示棋子的位置
        li[i], li[0] = li[0], li[i]
        # 現在堆的範圍 0~i-1
        sift(li, 0, i-1)

歸並排序

def merge(li, low, mid, high):
    i = low
    j = mid + 1
    ltmp = []
    while i <= mid and j <= high:
        if li[i] < li[j]:
            ltmp.append(li[i])
            i += 1
        else:
            ltmp.append(li[j])
            j += 1
    while i <= mid:
        ltmp.append(li[i])
        i += 1
    while j <= high:
        ltmp.append(li[j])
        j += 1
    # for k in range(low, high+1):
    #     li[k] = ltmp[k-low]
    li[low:high+1] = ltmp

def merge_sort(li, low, high):
    if low < high:
        mid = (low + high) // 2
        merge_sort(li, low, mid)
        merge_sort(li, mid+1, high)
        merge(li, low, mid, high)

# li = list(range(10000))
# random.shuffle(li)
# merge_sort(li, 0, len(li)-1)
# print(li)
li = [10,4,6,3,8,2,5,7]
merge_sort(li, 0, len(li)-1)

總結

常用algorithm及其Python實現