The Unique Permutations Algorithm with Duplicate Elements

  • 时间：2020-09-17 14:26:24
  • 分类：网络文摘
  • 阅读：138 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：
饮食健康与胃病食疗（二）：慢性胃炎的饮食调理　 饮食健康与胃病食疗（三）：这样饮食降低胃癌风险　 冬至时节，常吃这几种传统美食可补阳、防寒！　 只有这样吃大蒜才能杀菌防癌，以前你吃对了吗　 丝瓜营养丰富，其对人体的保健功效如此之多　 患有胃病的人常吃这些食物，可以帮助调理好胃　 山药营养丰富食疗价值高，助爱美女性吃出好身材　 糖尿病患者常有这些饮食误区，朋友们注意啦！　 网络上流传甚广的垃圾食品方便面有毒、致癌的传闻是真的吗？　 经常吃核桃仁可以补脑是真的吗 一天吃多少核桃才健康　
评论列表
添加评论