'''
Author: SJ2050
Date: 2021-10-10 23:34:50
LastEditTime: 2021-10-16 23:23:48
Version: v0.0.1
Description: Solution for homework 2.
Copyright © 2021 SJ2050
'''
from itertools import permutations

def combination(arr, n):
    if n == 0:
        return [[]]

    l =[]
    for i in range(0, len(arr)):
        m = arr[i]
        remLst = arr[i + 1:]

        for p in combination(remLst, n-1):
            l.append([m]+p)

    return l


def heapPermutation(arr, n, process):
    if n == 1:
        process(arr)
        return

    for i in range(n):
        heapPermutation(arr, n-1, process)
        if n & 1:
            arr[0], arr[n-1] = arr[n-1], arr[0]
        else:
            arr[i], arr[n-1] = arr[n-1], arr[i]



if __name__ == '__main__':
    nums = [1, 2, 3, 4]
    m = 3
    count = 0
    combs = combination(nums, m)

    def printAndCount(arr):
        global count
        count += 1

        for i in range(len(arr)):
            print(f'{arr[i]}', end='')

        print('')

    print('3-digit nums:')
    for c in combs:
        heapPermutation(c, m, printAndCount)
    print('-'*12)
    print(f'Total count: {count}')

    # 从一列数中取出三个元素组成三位数的算法复杂度分析:
    # 首先是组合分析，从一列数中取出三个数的组合个数为n*(n-1)*(n-2)/6，算法时间复杂度为O(n^3).
    # 接着，对每队组合进行排列，排列算法选用的是heap算法，其时间复杂度为O(n!).
    # 故总的时间复杂度为: O((n^3)*(3!)) --> O(n^3)