<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>

import queue

def is_pair(w1, w2):
    concat = w1 + w2
    return concat == concat[::-1]

class TrieNode:
    def __init__(self, key=None, val=None):
        self.key = key
        self.val = val
        self.children = {}

class Trie:
    def __init__(self):
        self.root = TrieNode("", None)
    
    def insert(self, key, word):
        curr = self.root
        if word == "":
            curr.children[""] = TrieNode(key=key, val="")
        for i in range(len(word)-1, -1, -1):
            if word[i] not in curr.children:
                curr.children[word[i]] = TrieNode(key=None, val=None)
            if i == 0:
                curr.children[word[i]].key = key
                curr.children[word[i]].val = word
            curr = curr.children[word[i]]
    
    def search_right(self, key, word):
        prefixes = []
        i, curr = 0, self.root
        if "" in curr.children:
            prefixes.append(curr.children[""])
        while i < len(word):
            if word[i] not in curr.children:
                break
            if curr.children[word[i]].val is not None:
                prefixes.append(curr.children[word[i]])
            curr = curr.children[word[i]]
            i += 1
        
        if i == len(word):
            prefixes.extend(self.words(curr))

        pairs = set()
        for prefix in prefixes:
            if is_pair(word, prefix.val) and key != prefix.key:
                pairs.add((key, prefix.key))
        
        return pairs

    def words(self, root):
        if not root:
            return []

        result = []
        q = queue.Queue()
        q.put(root)
        while not q.empty():
            curr = q.get()
            if len(curr.children) == 0:
                continue
            for k, v in curr.children.items():
                if v is not None and v.val is not None:
                    result.append(v)
                q.put(curr.children[k])
        
        return result

class Solution:
    def palindromePairs(self, words: List[str]) -> List[List[int]]:
        if len(words) == 0:
            return []

        trie = Trie()
        for i, word in enumerate(words):
            trie.insert(i, word)

        pairs = set()
        for i, word in enumerate(words):
            for pair in trie.search_right(i, word):
                pairs.add(pair)
        
        return list(map(list, pairs))
        
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