堆算法 - Python 中的非递归方法生成排列

Question

我是编程新手。我正在研究堆算法，特别是非递归方法。互联网上没有太多关于该算法如何工作的解释。我从 Bernardo Sulzbach 找到了这篇文章，但他没有解释他的算法是如何工作的。几天来我一直坚持下去，尝试了一切都无法弄清楚。我在每一行之后添加了注释以使自己理解——这里发生了什么？但我仍然无法让它发挥作用。难道我做错了什么？请帮忙。

# Heap's Algorithm (Non Recursive)

# function to swap values in python
def swap(elements, i, j):
    elements[i], elements[j] = elements[j], elements[i]

# function to generate permutation
def generate_permutations(elements, n): 
    # Passing two parameters of elements and n to function "generate_permutations".
    c = [0] * n 
    # c is a new list and its value set to an array literal with value 0, n times.
    # Example - [a] * 3 ==> ['a', 'a', 'a', 'a']
    yield elements 
    # "yield" statement is used to define generators, while "return" statement causes a function to exit.
    # "yield" replacing the return of a function to provide a result to its caller without destroying
    # local variables. Unlike a function, where on each call it starts with new sets of variables, a generator
    # will resume the execution where it left off.
    i = 0
    # i is a new variable and its value is set to 0. It can also be used to count the number of loop runs.
    while i < n:
    # while loop ==> while i is less than n, do following:
        if c[i] < i:
        # if statement ==> while i is less than n and if any element from 'c' list is less than i, 
        # then do following:
            if i % 2 == 0:
            # if statement ==> while i is less than n, and if any element in 'c' list is less than i, and
            # i is an even number, then do following:
                swap(elements, 0, i)
                # calling swap function and passing following arguments: elements, '0' and 'i'
            else:
            # else, if all three conditions above are not true then do following:
                swap(elements, c[i], i)
                # calling swap funtions and passing following arguments: elements, an item from 'c' list and 'i'
            yield elements
            # ??? yield elements
            c[i] += 1
            # after that, increment c[i] by 1.
            i = 0
            # set the value of i to 0
        else:
            # else, if c[i] < i is not true the do the following.
            c[i] = 0
            # set the value of c[i] to 0
            i += 1
            # and increment i by 1

def permutations(elements):
    return generate_permutations(elements, len(elements))

# Driver Code
# c = ?
# n = ?
# i = ?
print(permutations(['abc']))

Answer 1

只是清理你的代码（评论太多）：

# Heap's Algorithm (Non Recursive)
# https://en.wikipedia.org/wiki/Heap%27s_algorithm

def swap(seq, i, j):
  seq[i], seq[j] = seq[j], seq[i]

def generate_permutations(seq, seqLen, resLen): 
  c = [0] * seqLen
  yield seq[:resLen]
  
  i = 0
  while i < seqLen:
    if c[i] < i:
      if i % 2 == 0:
        swap(seq, 0, i)
      else:
        swap(seq, c[i], i)
      yield seq[:resLen]
      c[i] += 1
      i = 0
    else:
      c[i] = 0
      i += 1

def permutations(seq, resLen=None):
  if not resLen: resLen = len(seq)
  return generate_permutations(seq, len(seq), resLen)

for p in permutations([1,2,3]): print(p)
for p in permutations([1,2,3],2): print(p)

堆算法 - Python 中的非递归方法生成排列

Heap's Algorithm - Non Recursive Method in Python to generate permutations

python

algorithm

permutation

heaps-algorithm