python - 排列 : producing cycle notation

Question

请考虑以下问题:我有一定的排列西格玛:

sigma = [4,1,6,2,3,5]

期望的结果是产生如下循环符号:

my_cycles_perm = [[4,2,1],[6,5,3]]

我的尝试按照下面的代码进行，但是似乎我只达到了第一个周期，但似乎无法重新进入第二个周期:

my_row_cycle 函数背后的想法是采用一定的排列西格玛，设置一种称为标记的断路器(当标记 == 0 时 crcuit 关闭)，并迭代排列直到我完成一个循环，一旦循环完成后我将其存储到列表中。

然后，我通过再次迭代 sigma 来验证是否还有其他循环可以从排列中提取，直到在 sigma 中找到不在之前提取的循环中的数字。如果找到这样的数字，我将重新启动该过程。如果不是，我会触发断路器，标记 == 1 来结束整个过程并输出西格玛排列的循环符号。

但这对我来说似乎仍然是乌托邦。 :)

def my_row_cycle(sigma):
    aux_sigma = list(sigma)
    init_ref = aux_sigma.index(aux_sigma[0]) +1       #First antecedent of aux_sigma
    init_image = aux_sigma[init_ref-1]                #Image of the antecedent
    jumper_image = init_image
    row_cycle = []
    row_cycle.append(init_image)
    my_cycles_perm = []

    marker = 0

    while marker == 0:                                 #Circuit breaker
        while jumper_image != init_ref:                #establishes if cycle complete
            for x in aux_sigma:                     #iterates sigma while cycle incomplete
                jumper_ref = aux_sigma.index(x) + 1
                if jumper_ref == jumper_image:         #Condition to append to cycle
                    row_cycle.append(x)
                    jumper_image = x                   #Changing the while loop condition
        my_cycles_perm.append(row_cycle)

        for a in aux_sigma:
            for a in my_cycles_perm:
                cycle = a
                for a in cycle:                  #looking for match in aux_sigma and cycle
                    if a not in cycle:
                        row_cycle = []
                        init_image = a
                        init_ref = aux_sigma.index(init_image) + 1
                        marker = 0
                        break

                    else:
                        marker = 1

return init_ref, init_image, jumper_image, jumper_ref, row_cycle, marker, my_cycles_perm

评估后:

(1, 4, 1, 6, [4, 2, 1], 1, [[4, 2, 1]])

我似乎无法理解为什么我的标记会跳到值“1”，但我的循环符号不完整。如果您有任何建议和或更正，我先谢谢您。

Answer 1

我相信这个函数可以满足您的要求:

def to_cycles(perm):
    pi = {i+1: perm[i] for i in range(len(perm))}
    cycles = []

    while pi:
        elem0 = next(iter(pi)) # arbitrary starting element
        this_elem = pi[elem0]
        next_item = pi[this_elem]

        cycle = []
        while True:
            cycle.append(this_elem)
            del pi[this_elem]
            this_elem = next_item
            if next_item in pi:
                next_item = pi[next_item]
            else:
                break

        cycles.append(cycle)

    return cycles

print(to_cycles([]))
# []

print(to_cycles([1]))
# [[1]]

print(to_cycles([4,1,6,2,3,5]))
# [[4, 2, 1], [6, 5, 3]]