<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>

struct Trie_t : public map<char,Trie_t> {
    int index = -1;
};

Trie_t root_rev, root_fwd;

void put_rev(string &s, int pos, int ndx, Trie_t& t)
{
    if(!pos)
        t[s[pos]].index=ndx;
    else
        put_rev(s,pos-1,ndx,t[s[pos]]);
}

void put_fwd(string &s, int pos, int ndx, Trie_t& t)
{
    if(pos==s.size()-1)
        t[s[pos]].index=ndx;
    else
        put_fwd(s,pos+1,ndx,t[s[pos]]);
}

bool isPaly(string &s, int l, int r)
{
    for(int i = (r-l+1)/2; i--;)
        if( s[l+i] != s[r-i])
            return false;
    return true;
}

void search_rev(string &s, int pos, Trie_t& t, int second_part, vector<vector<int>> &ret)
{
    if(t.index!=-1 && t.index!=second_part)
    {
        if(isPaly(s,pos,s.size()-1))
            ret.push_back({second_part,t.index});
    }
    if( pos < s.size() )
    {
        auto found = t.find(s[pos]);
        if ( found!=t.end() )
            search_rev(s,pos+1,found->second,second_part,ret);
    }
}

void search_fwd(string &s, int pos, Trie_t& t, int second_part, vector<vector<int>> &ret)
{
    if(t.index!=-1 && t.index!=second_part)
    {
        if(isPaly(s,0,pos))
            ret.push_back({t.index,second_part});
    }
    if( pos > 0 )
    {
        auto found = t.find(s[pos]);
        if ( found!=t.end() )
        {
            search_fwd(s,pos-1,found->second,second_part,ret);
        }
    }
}

class Solution {
public:
    vector<vector<int>> palindromePairs(vector<string>& words) {
        root_rev.clear();
        root_fwd.clear();
        vector<int> voids; // empty string indices
        vector<vector<int>> result;

        for(int i = words.size(); i--;)
        {
            if(words[i].size())
            {
                put_rev(words[i], words[i].size()-1, i, root_rev);
                put_fwd(words[i], 0, i, root_fwd);
            }
            else
                voids.push_back(i);
        }

        for(int i = words.size(); i--;)
        {
            if(!words[i].size())
                continue;
            if(isPaly(words[i],0,words[i].size()-1))
                for(auto v:voids)
                {
                    if(i!=v)
                    {
                        result.push_back({i,v});
                        result.push_back({v,i});
                    }
                }
            search_rev(words[i],0,root_rev,i,result);
            search_fwd(words[i],words[i].size()-1,root_fwd,i,result);
        }

        return result;
    }
};
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