All Permutations of Subsets without duplication
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题目
Given a string with no duplicate characters, return a list with all permutations of the string and all its subsets.
Examples
Set = “abc”, all permutations are [“”, “a”, “ab”, “abc”, “ac”, “acb”, “b”, “ba”, “bac”, “bc”, “bca”, “c”, “cb”, “cba”, “ca”, “cab”].
Set = “”, all permutations are [“”].
Set = null, all permutations are [].
思想
DFS
有n个action就有n个position要遍历
在每个position选择一个action到该位置,剩下的action放到后面,即把选择后的action和前面pos位置的action交换,然后DFS进入下一个位置时pos+=1 就可以选择剩下的没选的action
在用“”来不选择action时有可能会出现重复的情况,比如["", b,""] 和["", "", b] 虽然在不同位置选择b,但是最后join的string是一样的,所以要用set进行对result list除重
Time: O(B*H), B= tree branch, H= height of tree = number of actions to use
Space: O(H) for recursion, O(n) for storing result so O(H + n)
Coding
class Solution(object):
def allPermutationsOfSubsets(self, s):
"""
input: string set
return: string[]
"""
# write your solution here
# tree level = the position we need to fill
# [, , , ]
# [a, , ,] [b, , ,] [c, , ,] [c, , ,]
# [a,b,,], [a,c,,] [a,,,] [b, a, ,], [b,c, ,]...
#
#
action = list(s)
sol = []
sols = set()
self.bt(sol, sols, action, 0)
return sols
def bt(self,sol, sols, action, pos):
if pos == len(action):
res = "".join(sol[:])
# if res not in sols:
# sols.append(res)
sols.add(res)
return
# add one action
for i in range(pos, len(action)):
sol.append(action[i])
# swap the selected action to the begin of the selectable array
# so that we will not select the action that already picked
action[pos], action[i] = action[i], action[pos]
self.bt(sol, sols, action, pos+1)
# swap it back
action[pos], action[i] = action[i], action[pos]
sol.pop(-1)
# don't add anything
self.bt(sol, sols, action, pos+1)
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