<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 {
    vector<int> loc;
    string s;
    void kmp(const string &w,int l){
        string test = w + "#" + s;
        //lps Implemenation
        vector<int> lps(test.size());
        int i=0,j=i+1;
        while(j<test.size()){
            if(test[i]==test[j]){
                lps[j] = i+1;
                i++;
                j++;
            }else if(i==0)
                j++;
            else
                i = lps[i-1];
        }
        for(int i=w.size()+1;i<test.size();i++){
            if(lps[i]==w.size())
                loc[i-2*w.size()] = l;
        }
    }
public:
    vector<int> findSubstring(string s, vector<string>& words) {
        loc.resize(s.size());
        this->s = s;
        int ws = words[0].size();
        int tws = ws*words.size();

        if(tws>s.size())    return {};
        unordered_map<string,int> wrds;
        unordered_map<int,int> wrdsI;
        for(auto &w:words)
            wrds[w]++;
        
        int cnt = 1;
        for(auto &wp:wrds){
            kmp(wp.first,cnt);
            wrdsI[cnt] = wp.second;
            cnt++;
        }

        vector<int> ans;
        for(int i=0;i<=loc.size()-tws;i++){
            if(loc[i]==0)   continue;
            unordered_map<int,int> mp;
            bool flag = false;
            int cnt = 0;
            for(int j=i;j<loc.size();j+=ws){
                if(loc[j]==0)   break;
                mp[loc[j]]++;
                cnt++;
                if(mp[loc[j]]>wrdsI[loc[j]])    break;
                if(cnt==words.size()){
                    flag = true;
                    break;
                }
            }
            if(flag)
                ans.push_back(i);
        }
        return ans;
    }
};
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