Solution 1

Python3

class Solution:
    def generatePalindromes(self, s: str) -> List[str]:
        def dfs(t):
            if len(t) == len(s):
                ans.append(t)
                return
            for c, v in cnt.items():
                if v > 1:
                    cnt[c] -= 2
                    dfs(c + t + c)
                    cnt[c] += 2

        cnt = Counter(s)
        mid = ''
        for c, v in cnt.items():
            if v & 1:
                if mid:
                    return []
                mid = c
                cnt[c] -= 1
        ans = []
        dfs(mid)
        return ans

Java

class Solution {
    private List<String> ans = new ArrayList<>();
    private int[] cnt = new int[26];
    private int n;

    public List<String> generatePalindromes(String s) {
        n = s.length();
        for (char c : s.toCharArray()) {
            ++cnt[c - 'a'];
        }
        String mid = "";
        for (int i = 0; i < 26; ++i) {
            if (cnt[i] % 2 == 1) {
                if (!"".equals(mid)) {
                    return ans;
                }
                mid = String.valueOf((char) (i + 'a'));
            }
        }
        dfs(mid);
        return ans;
    }

    private void dfs(String t) {
        if (t.length() == n) {
            ans.add(t);
            return;
        }
        for (int i = 0; i < 26; ++i) {
            if (cnt[i] > 1) {
                String c = String.valueOf((char) (i + 'a'));
                cnt[i] -= 2;
                dfs(c + t + c);
                cnt[i] += 2;
            }
        }
    }
}

C++

class Solution {
public:
    int n;
    vector<string> ans;
    unordered_map<char, int> cnt;

    vector<string> generatePalindromes(string s) {
        n = s.size();
        for (char c : s) ++cnt[c];
        string mid = "";
        for (auto& [k, v] : cnt) {
            if (v & 1) {
                if (mid != "") {
                    return ans;
                }
                mid += k;
            }
        }
        dfs(mid);
        return ans;
    }

    void dfs(string t) {
        if (t.size() == n) {
            ans.push_back(t);
            return;
        }
        for (auto& [k, v] : cnt) {
            if (v > 1) {
                v -= 2;
                dfs(k + t + k);
                v += 2;
            }
        }
    }
};

Go

func generatePalindromes(s string) []string {
    cnt := map[byte]int{}
    for i := range s {
        cnt[s[i]]++
    }
    mid := ""
    ans := []string{}
    for k, v := range cnt {
        if v%2 == 1 {
            if mid != "" {
                return ans
            }
            mid = string(k)
        }
    }
    var dfs func(t string)
    dfs = func(t string) {
        if len(t) == len(s) {
            ans = append(ans, t)
            return
        }
        for k, v := range cnt {
            if v > 1 {
                cnt[k] -= 2
                c := string(k)
                dfs(c + t + c)
                cnt[k] += 2
            }
        }
    }
    dfs(mid)
    return ans
}

Problem