<p>You are given an <code>m x n</code> matrix <code>board</code>, representing the<strong> current </strong>state of a crossword puzzle. The crossword contains lowercase English letters (from solved words), <code>&#39; &#39;</code> to represent any <strong>empty </strong>cells, and <code>&#39;#&#39;</code> to represent any <strong>blocked</strong> cells.</p>

<p>A word can be placed<strong> horizontally</strong> (left to right <strong>or</strong> right to left) or <strong>vertically</strong> (top to bottom <strong>or</strong> bottom to top) in the board if:</p>

<ul>
	<li>It does not occupy a cell containing the character <code>&#39;#&#39;</code>.</li>
	<li>The cell each letter is placed in must either be <code>&#39; &#39;</code> (empty) or <strong>match</strong> the letter already on the <code>board</code>.</li>
	<li>There must not be any empty cells <code>&#39; &#39;</code> or other lowercase letters <strong>directly left or right</strong><strong> </strong>of the word if the word was placed <strong>horizontally</strong>.</li>
	<li>There must not be any empty cells <code>&#39; &#39;</code> or other lowercase letters <strong>directly above or below</strong> the word if the word was placed <strong>vertically</strong>.</li>
</ul>

<p>Given a string <code>word</code>, return <code>true</code><em> if </em><code>word</code><em> can be placed in </em><code>board</code><em>, or </em><code>false</code><em> <strong>otherwise</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/10/04/crossword-ex1-1.png" style="width: 478px; height: 180px;" />
<pre>
<strong>Input:</strong> board = [[&quot;#&quot;, &quot; &quot;, &quot;#&quot;], [&quot; &quot;, &quot; &quot;, &quot;#&quot;], [&quot;#&quot;, &quot;c&quot;, &quot; &quot;]], word = &quot;abc&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> The word &quot;abc&quot; can be placed as shown above (top to bottom).
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/10/04/crossword-ex2-1.png" style="width: 180px; height: 180px;" />
<pre>
<strong>Input:</strong> board = [[&quot; &quot;, &quot;#&quot;, &quot;a&quot;], [&quot; &quot;, &quot;#&quot;, &quot;c&quot;], [&quot; &quot;, &quot;#&quot;, &quot;a&quot;]], word = &quot;ac&quot;
<strong>Output:</strong> false
<strong>Explanation:</strong> It is impossible to place the word because there will always be a space/letter above or below it.</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/10/04/crossword-ex3-1.png" style="width: 478px; height: 180px;" />
<pre>
<strong>Input:</strong> board = [[&quot;#&quot;, &quot; &quot;, &quot;#&quot;], [&quot; &quot;, &quot; &quot;, &quot;#&quot;], [&quot;#&quot;, &quot; &quot;, &quot;c&quot;]], word = &quot;ca&quot;
<strong>Output:</strong> true
<strong>Explanation:</strong> The word &quot;ca&quot; can be placed as shown above (right to left). 
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == board.length</code></li>
	<li><code>n == board[i].length</code></li>
	<li><code>1 &lt;= m * n &lt;= 2 * 10<sup>5</sup></code></li>
	<li><code>board[i][j]</code> will be <code>&#39; &#39;</code>, <code>&#39;#&#39;</code>, or a lowercase English letter.</li>
	<li><code>1 &lt;= word.length &lt;= max(m, n)</code></li>
	<li><code>word</code> will contain only lowercase English letters.</li>
</ul>

class Solution:

    def kmp_modified(self, pattern, string, lps):
        i = 0
        j = 0
        while i < len(string):
            if string[i] == pattern[j] or (string[i] == ' ' and string[i] != '#' and pattern[j] != '#'):
                j += 1
                i += 1
                if j == len(pattern):
                    return True
            elif j != 0:
                j = lps[j - 1]
            else:
                i += 1
        return False
        
    def create_lps(self, pattern):
        pattern_len = len(pattern)
        lps = [0] * pattern_len
        i = 1
        prev_lps = 0
        while i < pattern_len:
            if pattern[i] == pattern[prev_lps]:
                lps[i] = prev_lps + 1
                prev_lps += 1
                i += 1
            elif prev_lps == 0:
                lps[i] = 0
                i += 1
            else:
                prev_lps = lps[prev_lps - 1]
        return lps

    def placeWordInCrossword(self, board: List[List[str]], word: str) -> bool:
        ROWS = len(board)
        COLS = len(board[0])

        word = '#' + word + '#'
        reverse_word = word[::-1]
        word_lps = self.create_lps(word)
        rev_lps = self.create_lps(reverse_word)

        for row in range(ROWS):
            row_string = '#' + "".join(board[row]) + '#'
            if self.kmp_modified(word, row_string, word_lps) or \
                    self.kmp_modified(reverse_word, row_string, rev_lps):
                return True
        
        for col_string in zip(*board):
            col_string = '#' + "".join(col_string) + '#'
            if self.kmp_modified(word, col_string, word_lps) or \
                    self.kmp_modified(reverse_word, col_string, rev_lps):
                return True
        return False
1289