all_permutations 所有排列

all_permutations 所有排列

将n个元素组成的序列进行排列，其序列由数字、字符串 组成，列出其所有的全排列，
其排列数为 $ P_n^n $

算法

在这个问题中，我们要确定所有可能的排列
对于给定序列的。 我们使用回溯来解决这个问题。

范例：

由$ ['A', 'B', 'C'] $ 3个字符组成的序列，其排列共有 $ P_3^3 = 3 \times 2 \times 1 = 6 $
其排列如下：

\[ ['A', 'B', 'C'] \\ ['A', 'C', 'B'] \\ ['B', 'A', 'C'] \\ ['B', 'C', 'A'] \\ ['C', 'A', 'B'] \\ ['C', 'B', 'A'] \]

代码

[all_permutations.py]{..\src\backtracking\all_permutations.py}

"""
Prepare
   1. sys.path 中增加 TheAlgorithms\src 子模块

"""
import sys
sys.path.append('E:\dev\AI\TheAlgorithms\src')

案例一：

由$ ['A', 'B', 'C'] $ 组成的所有排列,其排列共有 $ P_3^3 = 3 \times 2 \times 1 = 6 $

from backtracking.all_permutations import generate_all_permutations
from typing import List, Union
"""
"""
sequence: List[Union[int, str]] = ["A", "B", "C"]
generate_all_permutations(sequence)

['A', 'B', 'C']
['A', 'C', 'B']
['B', 'A', 'C']
['B', 'C', 'A']
['C', 'A', 'B']
['C', 'B', 'A']

案例二：

由$ [3,2,1,4,"C"] $ 组成的所有排列,其排列共有 $ P_5^5 = 5 \times 4 \times 3 \times 2 \times 1 = 120 $

from backtracking.all_permutations import generate_all_permutations
from typing import List, Union
"""
"""
sequence: List[Union[int, str]] = [3,2,1,4,"C"]
generate_all_permutations(sequence)

[3, 2, 1, 4, 'C']
[3, 2, 1, 'C', 4]
[3, 2, 4, 1, 'C']
[3, 2, 4, 'C', 1]
[3, 2, 'C', 1, 4]
[3, 2, 'C', 4, 1]
[3, 1, 2, 4, 'C']
[3, 1, 2, 'C', 4]
[3, 1, 4, 2, 'C']
[3, 1, 4, 'C', 2]
[3, 1, 'C', 2, 4]
[3, 1, 'C', 4, 2]
[3, 4, 2, 1, 'C']
[3, 4, 2, 'C', 1]
[3, 4, 1, 2, 'C']
[3, 4, 1, 'C', 2]
[3, 4, 'C', 2, 1]
[3, 4, 'C', 1, 2]
[3, 'C', 2, 1, 4]
[3, 'C', 2, 4, 1]
[3, 'C', 1, 2, 4]
[3, 'C', 1, 4, 2]
[3, 'C', 4, 2, 1]
[3, 'C', 4, 1, 2]
[2, 3, 1, 4, 'C']
[2, 3, 1, 'C', 4]
[2, 3, 4, 1, 'C']
[2, 3, 4, 'C', 1]
[2, 3, 'C', 1, 4]
[2, 3, 'C', 4, 1]
[2, 1, 3, 4, 'C']
[2, 1, 3, 'C', 4]
[2, 1, 4, 3, 'C']
[2, 1, 4, 'C', 3]
[2, 1, 'C', 3, 4]
[2, 1, 'C', 4, 3]
[2, 4, 3, 1, 'C']
[2, 4, 3, 'C', 1]
[2, 4, 1, 3, 'C']
[2, 4, 1, 'C', 3]
[2, 4, 'C', 3, 1]
[2, 4, 'C', 1, 3]
[2, 'C', 3, 1, 4]
[2, 'C', 3, 4, 1]
[2, 'C', 1, 3, 4]
[2, 'C', 1, 4, 3]
[2, 'C', 4, 3, 1]
[2, 'C', 4, 1, 3]
[1, 3, 2, 4, 'C']
[1, 3, 2, 'C', 4]
[1, 3, 4, 2, 'C']
[1, 3, 4, 'C', 2]
[1, 3, 'C', 2, 4]
[1, 3, 'C', 4, 2]
[1, 2, 3, 4, 'C']
[1, 2, 3, 'C', 4]
[1, 2, 4, 3, 'C']
[1, 2, 4, 'C', 3]
[1, 2, 'C', 3, 4]
[1, 2, 'C', 4, 3]
[1, 4, 3, 2, 'C']
[1, 4, 3, 'C', 2]
[1, 4, 2, 3, 'C']
[1, 4, 2, 'C', 3]
[1, 4, 'C', 3, 2]
[1, 4, 'C', 2, 3]
[1, 'C', 3, 2, 4]
[1, 'C', 3, 4, 2]
[1, 'C', 2, 3, 4]
[1, 'C', 2, 4, 3]
[1, 'C', 4, 3, 2]
[1, 'C', 4, 2, 3]
[4, 3, 2, 1, 'C']
[4, 3, 2, 'C', 1]
[4, 3, 1, 2, 'C']
[4, 3, 1, 'C', 2]
[4, 3, 'C', 2, 1]
[4, 3, 'C', 1, 2]
[4, 2, 3, 1, 'C']
[4, 2, 3, 'C', 1]
[4, 2, 1, 3, 'C']
[4, 2, 1, 'C', 3]
[4, 2, 'C', 3, 1]
[4, 2, 'C', 1, 3]
[4, 1, 3, 2, 'C']
[4, 1, 3, 'C', 2]
[4, 1, 2, 3, 'C']
[4, 1, 2, 'C', 3]
[4, 1, 'C', 3, 2]
[4, 1, 'C', 2, 3]
[4, 'C', 3, 2, 1]
[4, 'C', 3, 1, 2]
[4, 'C', 2, 3, 1]
[4, 'C', 2, 1, 3]
[4, 'C', 1, 3, 2]
[4, 'C', 1, 2, 3]
['C', 3, 2, 1, 4]
['C', 3, 2, 4, 1]
['C', 3, 1, 2, 4]
['C', 3, 1, 4, 2]
['C', 3, 4, 2, 1]
['C', 3, 4, 1, 2]
['C', 2, 3, 1, 4]
['C', 2, 3, 4, 1]
['C', 2, 1, 3, 4]
['C', 2, 1, 4, 3]
['C', 2, 4, 3, 1]
['C', 2, 4, 1, 3]
['C', 1, 3, 2, 4]
['C', 1, 3, 4, 2]
['C', 1, 2, 3, 4]
['C', 1, 2, 4, 3]
['C', 1, 4, 3, 2]
['C', 1, 4, 2, 3]
['C', 4, 3, 2, 1]
['C', 4, 3, 1, 2]
['C', 4, 2, 3, 1]
['C', 4, 2, 1, 3]
['C', 4, 1, 3, 2]
['C', 4, 1, 2, 3]