Word Squares

Description

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

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

Example

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"]]

思路：字典树+dfs。
根据已添加单词确定下一个单词的前缀，利用dfs搜索。

public class Solution {
     class TrieNode {
        List<String> startWith;
        TrieNode[] children;

        TrieNode() {
            startWith = new ArrayList<>();
            children = new TrieNode[26];
        }
    }

    class Trie {
        TrieNode root;

        Trie(String[] words) {
            root = new TrieNode();
            for (String w : words) {
                TrieNode cur = root;
                for (char ch : w.toCharArray()) {
                    int idx = ch - 'a';
                    if (cur.children[idx] == null)
                        cur.children[idx] = new TrieNode();
                    cur.children[idx].startWith.add(w);
                    cur = cur.children[idx];
                }
            }
        }

        List<String> findByPrefix(String prefix) {
            List<String> ans = new ArrayList<>();
            TrieNode cur = root;
            for (char ch : prefix.toCharArray()) {
                int idx = ch - 'a';
                if (cur.children[idx] == null)
                    return ans;

                cur = cur.children[idx];
            }
            ans.addAll(cur.startWith);
            return ans;
        }
    }

    public List<List<String>> wordSquares(String[] words) {
        List<List<String>> ans = new ArrayList<>();
        if (words == null || words.length == 0)
            return ans;
        int len = words[0].length();
        Trie trie = new Trie(words);
        List<String> ansBuilder = new ArrayList<>();
        for (String w : words) {
            ansBuilder.add(w);
            search(len, trie, ans, ansBuilder);
            ansBuilder.remove(ansBuilder.size() - 1);
        }

        return ans;
    }

    private void search(int len, Trie tr, List<List<String>> ans,
            List<String> ansBuilder) {
        if (ansBuilder.size() == len) {
            ans.add(new ArrayList<>(ansBuilder));
            return;
        }

        int idx = ansBuilder.size();
        StringBuilder prefixBuilder = new StringBuilder();
        for (String s : ansBuilder)
            prefixBuilder.append(s.charAt(idx));
        List<String> startWith = tr.findByPrefix(prefixBuilder.toString());
        for (String sw : startWith) {
            ansBuilder.add(sw);
            search(len, tr, ans, ansBuilder);
            ansBuilder.remove(ansBuilder.size() - 1);
        }
    }
}