Given a set of words (without duplicates), find all word squares you can build from them.

A sequence of words forms a valid word square if the kth row and column read the exact same string, where 0 ≤ k < max(numRows, numColumns).

For example, the word sequence ["ball","area","lead","lady"] forms a word square because each word reads the same both horizontally and vertically.

b a l l
a r e a
l e a d
l a d y

Note:

1. There are at least 1 and at most 1000 words.
2. All words will have the exact same length.
3. Word length is at least 1 and at most 5.
4. Each word contains only lowercase English alphabet a-z.

Example 1:

Input:
["area","lead","wall","lady","ball"]

Output:
[
  [ "wall",
    "area",
    "lead",
    "lady"
  ],
  [ "ball",
    "area",
    "lead",
    "lady"
  ]
]

Explanation:
The output consists of two word squares. The order of output does not matter (just the order of words in each word square matters).

Example 2:

Input:
["abat","baba","atan","atal"]

Output:
[
  [ "baba",
    "abat",
    "baba",
    "atan"
  ],
  [ "baba",
    "abat",
    "baba",
    "atal"
  ]
]

Explanation:
The output consists of two word squares. The order of output does not matter (just the order of words in each word square matters).

class Solution {
public:
    vector<vector<string>> wordSquares(vector<string>& words) {
        vector<vector<string>> res;
        unordered_map<string, set<string>> m;
        int n = words[0].size();
        for (string word : words) {
            for (int i = 0; i < n; ++i) {
                string key = word.substr(0, i);
                m[key].insert(word);
            }
        }
        vector<vector<char>> mat(n, vector<char>(n));
        helper(0, n, mat, m, res);
        return res;
    }
      void helper(int i, int n, vector<vector<char>>& mat, unordered_map<string, set<string>>& m, vector<vector<string>>& res) {
            if (i == n) {
                vector<string> out;
                for (int j = 0; j < n; ++j) out.push_back(string(mat[j].begin(), mat[j].end()));
                res.push_back(out);
                return;
            }
            string key = string(mat[i].begin(), mat[i].begin() + i);
        for (string str : m[key]) { 
            mat[i][i] = str[i];
            int j = i + 1;
            for (; j < n; ++j) {
                mat[i][j] = str[j];
                mat[j][i] = str[j];
                if (!m.count(string(mat[j].begin(), mat[j].begin() + i + 1))) break;
            }
            if (j == n) helper(i + 1, n, mat, m, res);
        }
    }
};

LC 425 word squares