<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.remainingPalIndexes = []
        self.endIndex = -1
        import collections
        self.children = collections.defaultdict(Node)

class Trie:
    def __init__(self): self.root = Node()
    
    def insert(self, w, j):
        isPal = lambda x: x == x[::-1]
        n = self.root
        if isPal(w): n.remainingPalIndexes.append(j)
        for i in range(len(w)):
            c, suf = w[i], w[i+1:]
            n = n.children[c]
            if isPal(suf): n.remainingPalIndexes.append(j)
        n.endIndex = j

    def search(self, w):
        isPal = lambda x: x == x[::-1]
        n = self.root
        if not w: return n.remainingPalIndexes
        r = []
        for i in range(len(w)):
            c, suf = w[i], w[i+1:]
            if c not in n.children: return r
            n = n.children[c]
            if suf and isPal(suf) and n.endIndex > -1:
                r.append(n.endIndex)
        return r + n.remainingPalIndexes
        # return r.extend(n.remainingPalIndexes)

class Solution:
    def palindromePairs(self, words: List[str]) -> List[List[int]]:
        r = []
        trie = Trie()
        for i, w in enumerate(words):
            trie.insert(w[::-1], i)
        for i, w in enumerate(words):
            js = trie.search(w)
            if js: 
                r.extend([[i, j] for j in js if i != j])
                if not w: r.extend([[i, j][::-1] for j in js if i != j])
        return r
    

class Solution2:
    def palindromePairs(self, words: List[str]) -> List[List[int]]:
        d = {e: i for i, e in enumerate(words)}
        r = []
        isPal = lambda x: x == x[::-1]
        for j, w in enumerate(words):
            n = len(w)
            for i in range(n+1):
                pre, suf = w[:i], w[i:]
                if isPal(pre):
                    s = suf[::-1]
                    if s != w and s in d: r.append([d[s], j])
                if i != n and isPal(suf):
                    s = pre[::-1]
                    if s != w and s in d: r.append([d[s], j][::-1])
        return r
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