[LintCode] Permutations II

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

For example,
[1,1,2] have the following unique permutations:
[1,1,2], [1,2,1], and [2,1,1].

class Solution {

public:

    vector<vector<int>> permuteUnique(vector<int>& nums) {

        vector<vector<int>> paths;

        if (nums.empty()) {

            return paths;

        }

        

        vector<int> index;

        vector<int> path;

        permuteUniqueHelper(nums, index, path, paths);

        return paths;

        

    }

    

private:

    void permuteUniqueHelper(const vector<int> &nums,

                             vector<int> &index,

                             vector<int> &path,

                             vector<vector<int>> &paths) {

        if (path.size() == nums.size()) {

            paths.push_back(path);

            return;

        }

        

        // 保证相同的数不在同一位置出现两次以上

        unordered_set<int> hashset;

        for (int ix = 0; ix < nums.size(); ix++) {

            if (find(index.begin(), index.end(), ix) == index.end() && hashset.count(nums[ix]) == 0) {

                hashset.insert(nums[ix]);

                

                index.push_back(ix);

                path.push_back(nums[ix]);

                permuteUniqueHelper(nums, index, path, paths);

                index.pop_back();

                path.pop_back();

            }

        } 

    }

};

能否对空间复杂度做进一步的优化？

class Solution {

public:

    /**

     * @param nums: A list of integers.

     * @return: A list of unique permutations.

     */

    vector<vector<int> > permuteUnique(vector<int> &nums) {

        // write your code here

        vector<vector<int>> paths;

        if (nums.empty()) {

            return paths;

        }

        

        sort(nums.begin(), nums.end());

        bool *visited = new bool[nums.size()]();

        vector<int> path;

        permuteUniqueHelper(nums, visited, path, paths);

        return paths;

    }

    

private:

    void permuteUniqueHelper(const vector<int> &nums,

                             bool visited[],

                             vector<int> &path,

                             vector<vector<int>> &paths) {

        if (path.size() == nums.size()) {

            paths.push_back(path);

            return;

        } 

        

        for (int ix = 0; ix < nums.size(); ix++) {

            if (visited[ix] == true || ix > 0 && nums[ix - 1] == nums[ix] && visited[ix - 1] == false) {

                continue;    

            }

            

            visited[ix] = true;

            path.push_back(nums[ix]);

            permuteUniqueHelper(nums, visited, path, paths);

            visited[ix] = false;

            path.pop_back();

        }

    }

};