<p>You are given a string <code>s</code> and an array of strings <code>words</code>. All the strings of <code>words</code> are of <strong>the same length</strong>.</p>

<p>A <strong>concatenated string</strong> is a string that exactly contains all the strings of any permutation of <code>words</code> concatenated.</p>

<ul>
	<li>For example, if <code>words = [&quot;ab&quot;,&quot;cd&quot;,&quot;ef&quot;]</code>, then <code>&quot;abcdef&quot;</code>, <code>&quot;abefcd&quot;</code>, <code>&quot;cdabef&quot;</code>, <code>&quot;cdefab&quot;</code>, <code>&quot;efabcd&quot;</code>, and <code>&quot;efcdab&quot;</code> are all concatenated strings. <code>&quot;acdbef&quot;</code> is not a concatenated string because it is not the concatenation of any permutation of <code>words</code>.</li>
</ul>

<p>Return an array of <em>the starting indices</em> of all the concatenated substrings in <code>s</code>. You can return the answer in <strong>any order</strong>.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;barfoothefoobarman&quot;, words = [&quot;foo&quot;,&quot;bar&quot;]</span></p>

<p><strong>Output:</strong> <span class="example-io">[0,9]</span></p>

<p><strong>Explanation:</strong></p>

<p>The substring starting at 0 is <code>&quot;barfoo&quot;</code>. It is the concatenation of <code>[&quot;bar&quot;,&quot;foo&quot;]</code> which is a permutation of <code>words</code>.<br />
The substring starting at 9 is <code>&quot;foobar&quot;</code>. It is the concatenation of <code>[&quot;foo&quot;,&quot;bar&quot;]</code> which is a permutation of <code>words</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;wordgoodgoodgoodbestword&quot;, words = [&quot;word&quot;,&quot;good&quot;,&quot;best&quot;,&quot;word&quot;]</span></p>

<p><strong>Output:</strong> <span class="example-io">[]</span></p>

<p><strong>Explanation:</strong></p>

<p>There is no concatenated substring.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">s = &quot;barfoofoobarthefoobarman&quot;, words = [&quot;bar&quot;,&quot;foo&quot;,&quot;the&quot;]</span></p>

<p><strong>Output:</strong> <span class="example-io">[6,9,12]</span></p>

<p><strong>Explanation:</strong></p>

<p>The substring starting at 6 is <code>&quot;foobarthe&quot;</code>. It is the concatenation of <code>[&quot;foo&quot;,&quot;bar&quot;,&quot;the&quot;]</code>.<br />
The substring starting at 9 is <code>&quot;barthefoo&quot;</code>. It is the concatenation of <code>[&quot;bar&quot;,&quot;the&quot;,&quot;foo&quot;]</code>.<br />
The substring starting at 12 is <code>&quot;thefoobar&quot;</code>. It is the concatenation of <code>[&quot;the&quot;,&quot;foo&quot;,&quot;bar&quot;]</code>.</p>
</div>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= words.length &lt;= 5000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 30</code></li>
	<li><code>s</code> and <code>words[i]</code> consist of lowercase English letters.</li>
</ul>

class Solution {
public:
    vector<int> findSubstring(string s, vector<string>& words) {
		std::vector<int> output;
		
		this->word_size = words[0].length();
		int end = s.length() - this->word_size * words.size();

		std::priority_queue<std::pair<int, std::string>, std::vector<std::pair<int, std::string>>,
			std::greater<std::pair<int, std::string>>> cache;
		
        for (int i = 0; i <= end; ++i) {
			if (!cache.empty() && cache.top().first == i - this->word_size) {
				if (s.substr(i + (words.size() - 1) * this->word_size, this->word_size) == cache.top().second) {
					output.push_back(i);
					cache.pop();
					cache.push(std::make_pair(i, s.substr(i, this->word_size)));
				} else {
					cache.pop();
				}
			} else if (check(s, words, i)) {
				output.push_back(i);
				cache.push(std::make_pair(i, s.substr(i, this->word_size)));
			}		   
		}

		return output;
    }

private:
	bool check(const std::string& s, const std::vector<string>& words, int idx) const {
	    std::unordered_map<std::string, int> mapping;
		for (const std::string& word : words) {
			if (mapping.find(word) == mapping.end())
				mapping.insert(std::make_pair(word, 1));
			else
				mapping.at(word)++;
		}
		
		for (int i = 0; i < words.size(); ++i, idx+= this->word_size) {
			if (!use_word(s.substr(idx, this->word_size), mapping)) {
				return false;
			}
		}
		return true;
	}

	bool use_word(const std::string& word,
				 std::unordered_map<std::string, int>& mapping) const {
		if (mapping.find(word) == mapping.end()
			|| mapping.at(word) == 0) {
			return false;
		} else {
			mapping.at(word)--;
			return true;
		}
	}

	size_t word_size;
};
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