The Unique Permutations Algorithm with Duplicate Elements

  • 时间:2020-09-17 14:26:24
  • 分类:网络文摘
  • 阅读:80 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:
有位置随便坐作文650字  不一样的端午节作文  读《为了妹妹》有感  灯光下的父爱作文  门  写人作文描写班长的作文300字  振兴中华,匹夫有责作文1200字  乡村让我陶醉  诗词名句鉴赏:愿得一心人,白头不相离。  里革断罟匡君原文及翻译 
评论列表
添加评论