LintCode 634: Word Square (搜索经典题！！！)

Word Squares
中文English
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
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”]]
Notice
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.

这题关键是要能根据字符串的前缀找到与之相匹配的字符串们。方法有两个: hashmap (prefix vs matches_strings) 和 Trie。

解法1：用hashmap。虽然知道思路，可是还是感觉很难。参考的网上的答案。
举例如下：
words = [“area”,“lead”,“wall”,“lady”,“ball”]
我们先让prefix[""]=words, 然后将所有字符串的的前缀和对应字符串都放到prefix 这个hash table里面。
squares[][]这个里面是放已经找好的words，当已经找到了wordLen个字符串之后就是一个可行解了，放到results里面。
checkPrefix(index, nextWord)这个函数是在第index+1到wordLen的列中，找第0到index - 1行中找到pre前缀。

比如说squares = [wall, area, lead]
index = 3，此时pre遍历squares，把每个字符串的第3个字符拼起来，即lad，然后再与还不在squares中的字符串(lady, ball)的第3个字符挨个拼起来，看是不是在prefix里面。这里先处理lady, lad+y=lady，在prefix里面，所以squares=[wall, area, lead, lady]是一个可行解，放入results。

注意：

dfs里面每次循环都必须从0开始。

代码如下：

class Solution {
public:
  /**
   * @param words a set of words without duplicates
   * @return all word squares
   */
  
  void initPrefix(vector<string> & words) {
      int n = words.size();
      prefix[""] = words;
      for (int i = 0; i < n; ++i) {
          int m = words[i].size();
          for (int j = 0; j < m; ++j) {
              prefix[words[i].substr(0, j + 1)].push_back(words[i]);
          }
      }
  }
  
  bool checkPrefix(int index, string nextWord) {
     for (int i = index + 1; i < wordLen; ++i) {
         string pre;
         for (int j = 0; j < index; ++j) {
             pre += squares[j][i];
         }
         pre += nextWord[i];
     
         if (prefix.find(pre) == prefix.end()) {
             return false;
         }
     }
     
     return true;
  }
  
  void dfs(int index) {
    if (index == wordLen) {
        results.push_back(squares);
        return;
    }
    string pre;
    for (int i = 0; i < index; ++i) {
        pre += squares[i][index];
    }
    
    vector<string> matchedWords = prefix[pre];
    int m = matchedWords.size();
    for (int i = 0; i < m; ++i) {
        if (!checkPrefix(index, matchedWords[i])) {
            continue;
        }
        squares.push_back(matchedWords[i]);
        dfs(index + 1);
        squares.pop_back();
    }
  }
  
  vector<vector<string>> wordSquares(vector<string>& words) {
      if (words.size() == 0) return results;
      initPrefix(words);
      wordLen = words[0].size();
      dfs(0);
      return results;
  }
  
private:
    int wordLen;
    unordered_map<string, vector<string>> prefix;
    vector<string> squares;
    vector<vector<string>> results;
};

解法2： Trie
TBD

LintCode 634: Word Square (搜索经典题！！！)

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