<p>You are given a <strong>0-indexed</strong> array of <strong>unique</strong> strings <code>words</code>.</p>

<p>A <strong>palindrome pair</strong> is a pair of integers <code>(i, j)</code> such that:</p>

<ul>
	<li><code>0 &lt;= i, j &lt; words.length</code>,</li>
	<li><code>i != j</code>, and</li>
	<li><code>words[i] + words[j]</code> (the concatenation of the two strings) is a <span data-keyword="palindrome-string">palindrome</span>.</li>
</ul>

<p>Return <em>an array of all the <strong>palindrome pairs</strong> of </em><code>words</code>.</p>

<p>You must write an algorithm with&nbsp;<code>O(sum of words[i].length)</code>&nbsp;runtime complexity.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;abcd&quot;,&quot;dcba&quot;,&quot;lls&quot;,&quot;s&quot;,&quot;sssll&quot;]
<strong>Output:</strong> [[0,1],[1,0],[3,2],[2,4]]
<strong>Explanation:</strong> The palindromes are [&quot;abcddcba&quot;,&quot;dcbaabcd&quot;,&quot;slls&quot;,&quot;llssssll&quot;]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;bat&quot;,&quot;tab&quot;,&quot;cat&quot;]
<strong>Output:</strong> [[0,1],[1,0]]
<strong>Explanation:</strong> The palindromes are [&quot;battab&quot;,&quot;tabbat&quot;]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;a&quot;,&quot;&quot;]
<strong>Output:</strong> [[0,1],[1,0]]
<strong>Explanation:</strong> The palindromes are [&quot;a&quot;,&quot;a&quot;]
</pre>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 5000</code></li>
	<li><code>0 &lt;= words[i].length &lt;= 300</code></li>
	<li><code>words[i]</code> consists of lowercase English letters.</li>
</ul>

class Node:
    def __init__(self):
        self.idx = -1 
        self.children = {}
        self.palindrome_indexes = []
        self.end = False

class Solution:
    def __init__(self):
        self.root = Node() 

    
    def palindromePairs(self, words: List[str]) -> List[List[int]]:

        def is_palindrome(s):
            return s == s[::-1]

        def search(word, idx, ret):
            curr = self.root

            # long word short trie
            for i in range(len(word)):
                if curr.end and is_palindrome(word[i:]):
                    ret.append([idx, curr.idx])
                # traverse
                if word[i] not in curr.children:
                    return 
                curr = curr.children[word[i]]
            
            # exact match
            if curr.end and curr.idx != idx:
                ret.append([curr.idx, idx])

            # long trie short word
            for i in curr.palindrome_indexes:
                ret.append([idx, i])

            return 

        ret = []

        # build trie
        for i, word in enumerate(words):
            curr = self.root 
            reversed_word = word[::-1]
            for j in range(len(reversed_word)):
                if is_palindrome(reversed_word[j:]):
                    curr.palindrome_indexes.append(i)
                
                # traverse
                if reversed_word[j] not in curr.children:
                    curr.children[reversed_word[j]] = Node()
                curr = curr.children[reversed_word[j]]

            curr.end = True
            curr.idx = i

        # search
        for i, word in enumerate(words):
            search(word, i, ret)

        return ret



            
        
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