The Unique Permutations Algorithm with Duplicate Elements

  • 时间：2020-09-17 14:26:24
  • 分类：网络文摘
  • 阅读：76 次

Given a collection of numbers that might contain duplicates, return all possible unique permutations.

Example:

Input: [1,1,2]
Output:

1
2
3
4
5

[
  [1,1,2],
  [1,2,1],
  [2,1,1]
]
[
  [1,1,2],
  [1,2,1],
  [2,1,1]
]

How to Get Unique Permuations in C++?

In fact, the C++ STL algorithm header provides the std::next_permutation() which deals with the duplicate elements in the candidate array. We just need to sort the array, then start permutating until the next_permutation() returns false.

1
2
3
4
5
6
7
8
9
10
11
12

class Solution {
public:
    vector<vector<int>> permuteUnique(vector<int>& nums) {
        vector<vector<int>> r;
        sort(begin(nums), end(nums));
        r.push_back(nums);
        while (next_permutation(begin(nums), end(nums))) {
            r.push_back(nums);
        }
        return r;
    }
};
class Solution {
public:
    vector<vector<int>> permuteUnique(vector<int>& nums) {
        vector<vector<int>> r;
        sort(begin(nums), end(nums));
        r.push_back(nums);
        while (next_permutation(begin(nums), end(nums))) {
            r.push_back(nums);
        }
        return r;
    }
};

Recursive Permutation Algorithm without Duplicate Result

Similar to The Permutation Algorithm for Arrays using Recursion, we can do this recursively by swapping two elements at each position. However, we need to keep tracking of the solution that has also been in the permutation result using a hash set.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

class Solution {
public:
    vector<vector<int>> permuteUnique(vector<int>& nums) {
        vector<vector<int>> r;
        dfs(nums, 0, r, "");
        return r;
    }
    
private:
    unordered_set<string> used;
    void dfs(vector<int>& nums, int index, vector<vector<int>> &r, string key) {
        if (index == nums.size()) {
            if (!used.count(key)) {
                r.push_back(nums);
                used.insert(key);
            }            
        } else {
            for (int i = index; i < nums.size(); ++ i) {
                swap(nums[i], nums[index]);
                dfs(nums, index + 1, r, key + std::to_string(nums[index]));
                swap(nums[i], nums[index]);
            }
        }
    }
};
class Solution {
public:
    vector<vector<int>> permuteUnique(vector<int>& nums) {
        vector<vector<int>> r;
        dfs(nums, 0, r, "");
        return r;
    }
    
private:
    unordered_set<string> used;
    void dfs(vector<int>& nums, int index, vector<vector<int>> &r, string key) {
        if (index == nums.size()) {
            if (!used.count(key)) {
                r.push_back(nums);
                used.insert(key);
            }            
        } else {
            for (int i = index; i < nums.size(); ++ i) {
                swap(nums[i], nums[index]);
                dfs(nums, index + 1, r, key + std::to_string(nums[index]));
                swap(nums[i], nums[index]);
            }
        }
    }
};

In the worst cases, both implementations are O(N!) as N! is the total number of permutation results for N-size elements.

–EOF (The Ultimate Computing & Technology Blog) —

推荐阅读：
How to Delete N Nodes After M Nodes of a Linked List?　 Bruteforce Algorithm to Find the Unique Positive Integer Whose S　 Clone (Deep Copy) Binary Tree With Random Pointer using Hash Map　 How to Compute Running Sum of 1d Array using std::partial_sum in　 How to Renew the Free SSL Certificates (Nginx Server)?　 Design: How to Solve 503 Error of API when Resources are not ava　 SteemJs Programming: What Happens on the Steem Blockchain in the　 How to Set Up Your On-Call Duty when Your Steem Witness is Missi　 Common Mistakes You Can Face With Trying to switch Your Hosting 　 Recursive Algorithm to Construct Binary Tree from Preorder and P　
评论列表
添加评论