<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 Solution {
    vector<int> isPalindrome(string& s, bool inPrefix) {
        int n = s.length();
        
        string ss = "#";
        for (char ch: s) ss += ch, ss += '#';
        int m = 2*n + 1;

        vector<int> rd(m);
        int l = 0, r = 0;
        for (int i = 0; i < m; i++)
        {
            if (i <= r) rd[i] = min(r-i, rd[l + (r-i)]);
            int ll = i-rd[i]-1, rr = i+rd[i]+1;
            while ((ll >= 0 && rr < m) && (ss[ll] == ss[rr])) ll--, rr++, rd[i]++;
            l = i - rd[i], r = i + rd[i];
        }

        vector<int> dp(n);
        for (int i = 1; i < m-1; i ++)
        {
            l = i - rd[i], r = i + rd[i];
            if (inPrefix && l == 0) dp[r/2-1] = 1;
            if (!inPrefix && r == m-1) dp[l/2] = 1;
        }

        return dp;
    }

public:
    vector<vector<int>> palindromePairs(vector<string>& words) {
        vector<vector<int>> ans;
        int n = words.size();

        unordered_map<string, int> pMap, sMap;
        for (int i = 0; i < n; i++)
        {
            string word = words[i]; pMap[word] = i;
            reverse(word.begin(), word.end()); sMap[word] = i;
        }

        set<vector<int>> pp;
        for (int i = 0; i < n; i++) {
            string word = words[i];
            int len = word.length();

            vector<int> isPrePalindrome = isPalindrome(word, 1);
            vector<int> isSufPalindrome = isPalindrome(word, 0);
            
            string suf = "";
            for (int j = len; j >= 0; j--) {
                if (j < len) suf += word[j];
                if (pMap.find(suf) != pMap.end() && pMap[suf] != i && (j == 0 || isPrePalindrome[j-1])) {
                    pp.insert({pMap[suf], i});
                }
            }

            string pre = "";
            for (int j = -1; j < len; j++) {
                if (j >= 0) pre += word[j];
                if (sMap.find(pre) != sMap.end() && sMap[pre] != i && (j == len-1 || isSufPalindrome[j+1])) { 
                    pp.insert({i, sMap[pre]});
                }
            }
        }

        for (auto pr: pp) ans.push_back(pr);
        return ans;
    }
};
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