基础算法——BFPRT

def partition(arr, pivot_index):
    index = 0
    r = len(arr) - 1
    pivot_value = arr[pivot_index]
    arr[pivot_index], arr[r] = arr[r], arr[pivot_index]
    for i in range(0, r + 1):
        if arr[i] > pivot_value:
            arr[index], arr[i] = arr[i], arr[index]
            index += 1
    arr[index], arr[r] = arr[r], arr[index]
    return index

#找到数组中的中位数并返回
def pivot_mid(arr):
    n = len(arr)
    while n > 5:
        cols = (n // 5) + 1
        m = []  # 存储中位数
        for i in range(cols):
            s = sorted(arr[5 * i:(5 * i + 5)])
            s_mid = (len(s) - 1) // 2
            # print(s_mid)
            m.append(s[s_mid])
        arr = m
        n = len(arr)
        print(n)
    arr.sort()
    return arr[n // 2]


def bfprt(arr, k):
    pivot = pivot_mid(arr)
    pivot_index = arr.index(pivot)
    index = partition(arr, pivot_index)
    n = len(arr)
    if k < n - index:
        return bfprt(arr[index + 1:n], k)
    elif k == n - index:
        return pivot
    elif k > n - index:
        return bfprt(arr[0:index], k - (n - index))


array = [2, 3, 8, 5, 6, 7, 9, 0, 4, 1, 11, 12]
print(sorted(array))
print(bfprt(array, 5))