折半查詢

迴圈實現

'''
    折半查詢
        迴圈實現
'''


def binarySearch(list, key):
    low = 0
    high = len(list) - 1
    while (low <= high):  # 迴圈法的判斷條件，就是遞迴法的基線條件
        mid = (low + high) // 2
        gess = list[mid]
        if gess > key:
            high = mid - 1
        if gess < key:
            low = mid + 1
 

        if gess == key:
            return mid
    return -1


print(binarySearch([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 6))

遞迴實現

# 遞迴實現折半查詢
def binarySearch2(list, low, high, key):
    if (low > high):  # 遞迴的基線條件
        return -1
    else:
        mid = (low + high) // 2
        if (list[mid] == key):
            return
 
 mid
        if (key > list[mid]):
            return binarySearch2(list, mid + 1, high, key)  # 在序列的後半部分查詢
        else:
            return binarySearch2(list, low, mid - 1, key)  # 在序列的前半部分查詢


print(binarySearch2([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 0, 10, 6))

快速排序

開闢新空間儲存中間結果

'''
    快速排序
        遞迴實現，分而治之
            實現1, 開闢新空間儲存中間結果
            實現2, 不開闢多餘空間來儲存中間結果
'''
 



# 合併陣列
# print([1, 2, 3, 4] + [5, 6, 7, 8])

# 遞迴法快速排序實現1
def qSort(list):
    if len(list) < 2:  # 基線條件，陣列只有一個元素或者沒有元素是，不需要排序，直接返回
        return list
    else:  # 需要排序的陣列
        pivot = list[0]
        less = [i for i in list[1:] if i < pivot]
        greater = [i for i in list[1:] if i > pivot]
        return qSort(less) + [pivot] + qSort(greater)


listA = [40, 30, 20, 25, 60, 10]
print(qSort(listA))

快速排序

分而治之的典型演算法，在遞迴過程中要明確基線條件和遞迴條件

# 遞迴法快速排序實現2
def qSort2(list, left, right):
    if left >= right:
        return None
    else:
        bound = getBound(list, left, right)

        qSort2(list, left, bound - 1)  # 對基準值左側進行排序
        qSort2(list, bound + 1, right)  # 對基準值右側進行排序


def getBound(list, left, right):  # 使用雙指標，參考基準值從兩頭開始挑揀元素
    povit = list[left]
    while (left < right):
        while (left < right and list[right] >= povit):
            right -= 1

        list[left] = list[right]
        while (left < right and list[left] <= povit):
            left += 1

        list[right] = list[left]

    list[left] = povit
    return left


print(listA)
qSort2(listA, 0, len(listA) - 1)
print(listA)