全排列

递归实现：把元素换到数组首位，剩下的部分做全排列

def constraint():
    return True

def bound():
    return True

def perm_backtracking(depth,lst):
    size = len(lst)
    
    if depth == size:
        print(lst)
    else:
        for i in range(depth,size):          
            if constraint() and bound():
                lst[depth],lst[i] = lst[i],lst[depth]
                perm_backtracking(depth+1,lst)
                lst[depth],lst[i] = lst[i],lst[depth]

迭代实现，可以参考完全ｎ叉树，这个应该是一个通用的迭代的处理方法，在这里：只要不在同一列就行了

def perm_backtracking_iteration(depth,lst):
    size = len(lst)
    Selected =[-1]*size
    # 排列数，列号不能重复
    def place(k):
        for i in range(k):
            if Selected[i] == Selected[k]:
                return False
        return True
    

    
    while depth >=0:
        
        Selected[depth] +=1
        #　直到选择一个可行的解
        while Selected[depth]<size and not place(depth):
            Selected[depth] +=1
       #　这个就是回溯条件，子集树不为空
        if Selected[depth] <= size-1:
            if depth == size-1:
# print Selected
					#　解码结果，Selected里面对应的是选择了哪一个数
                for i in Selected:
                    print lst[i],
                print ""
            else:
            #　到达下一层时，初始化下一层的子树的范围
                depth +=1
                Selected[depth] =-1
        #　回溯，还是从上一层的未选的的地方走
        else:
            depth -=1


        
      
A = ['A','B','C','D']
perm_backtracking(0,A)

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

还可以基于排列树的迭代方式：

def perm_backtracking_iteration2(depth,lst):
    size = len(lst)
    Selected =[i for i in range(size)]
    change = [-1]*size   
    count = 0
    
    while depth >=0:
        # range(Selected[depth],size)记录的是剩余的次数，这里面还不能表现到底是那几次？估计还可以改进
        if Selected[depth] < size:
            
            for i in range(Selected[depth],size):
                 # 交换且记录交换
                lst[depth],lst[i] = lst[i],lst[depth]
                change[depth] = i
                
                Selected[depth] +=1
                
                if depth == size-1:
                    count +=1
                    print lst
                    print count

                else:                    
                    depth +=1
                    Selected[depth] = depth
                    break
        else:
         # 子集树为空了，回溯到上一层,在最底部是没有交换动作的，因为change[depth]就是本身，
		# 所以需要先-1，再交换，可以自己先调试一遍
            depth -=1  
            lst[depth],lst[change[depth]] = lst[change[depth]],lst[depth]
            change[depth] = -1




A = ['A','B','C','D']
#perm_backtracking(0,A)
perm_backtracking_iteration2(0,A)


['A', 'B', 'C', 'D']
1
['A', 'B', 'D', 'C']
2
['A', 'C', 'B', 'D']
3
['A', 'C', 'D', 'B']
4
['A', 'D', 'C', 'B']
5
['A', 'D', 'B', 'C']
6
['B', 'A', 'C', 'D']
7
['B', 'A', 'D', 'C']
8
['B', 'C', 'A', 'D']
9
['B', 'C', 'D', 'A']
10
['B', 'D', 'C', 'A']
11
['B', 'D', 'A', 'C']
12
['C', 'B', 'A', 'D']
13
['C', 'B', 'D', 'A']
14
['C', 'A', 'B', 'D']
15
['C', 'A', 'D', 'B']
16
['C', 'D', 'A', 'B']
17
['C', 'D', 'B', 'A']
18
['D', 'B', 'C', 'A']
19
['D', 'B', 'A', 'C']
20
['D', 'C', 'B', 'A']
21
['D', 'C', 'A', 'B']
22
['D', 'A', 'C', 'B']
23
['D', 'A', 'B', 'C']
24