<p>You are given a <strong>0-indexed</strong> string <code>s</code> and a dictionary of words <code>dictionary</code>. You have to break <code>s</code> into one or more <strong>non-overlapping</strong> substrings such that each substring is present in <code>dictionary</code>. There may be some <strong>extra characters</strong> in <code>s</code> which are not present in any of the substrings.</p>

<p>Return <em>the <strong>minimum</strong> number of extra characters left over if you break up </em><code>s</code><em> optimally.</em></p>

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

<pre>
<strong>Input:</strong> s = &quot;leetscode&quot;, dictionary = [&quot;leet&quot;,&quot;code&quot;,&quot;leetcode&quot;]
<strong>Output:</strong> 1
<strong>Explanation:</strong> We can break s in two substrings: &quot;leet&quot; from index 0 to 3 and &quot;code&quot; from index 5 to 8. There is only 1 unused character (at index 4), so we return 1.

</pre>

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

<pre>
<strong>Input:</strong> s = &quot;sayhelloworld&quot;, dictionary = [&quot;hello&quot;,&quot;world&quot;]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can break s in two substrings: &quot;hello&quot; from index 3 to 7 and &quot;world&quot; from index 8 to 12. The characters at indices 0, 1, 2 are not used in any substring and thus are considered as extra characters. Hence, we return 3.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 50</code></li>
	<li><code>1 &lt;= dictionary.length &lt;= 50</code></li>
	<li><code>1 &lt;= dictionary[i].length &lt;= 50</code></li>
	<li><code>dictionary[i]</code>&nbsp;and <code>s</code> consists of only lowercase English letters</li>
	<li><code>dictionary</code> contains distinct words</li>
</ul>

struct Node
{
    Node *links[26];
    bool flag;
    Node()
    {
        for(int i=0;i<26;i++) links[i]=NULL;
        flag=false;
    }
    void put(char ch,Node *node)
    {
        links[ch-'a'] = node;
    }
    Node *get(char ch)
    {
        return links[ch-'a'];
    }
    bool containsKey(char ch)
    {
        return links[ch-'a']!=NULL;
    }
    void setEnd()
    {
        flag = true;
    }
    bool isEnd()
    {
        return flag;
    }
};
class Trie
{
    private:
        Node *root;
    public:
        Trie()
        {
            root = new Node();
        }
        void insert(string word)
        {
            Node *node = root;
            for(int i=0;i<word.length();i++)
            {
                if(node->containsKey(word[i])==false)
                {
                    node->put(word[i],new Node());
                }
                node = node->get(word[i]);
            }
            node->setEnd();
        }
        bool checkPrefix(string prefix)
        {
            Node *node = root;
            for(int i=0;i<prefix.length();i++)
            {
                if(node->containsKey(prefix[i])==false)
                {
                    return false;
                }
                node = node->get(prefix[i]);
            }
            return true;
        }
        bool checkWord(string word)
        {
            Node *node = root;
            for(int i=0;i<word.length();i++)
            {
                if(node->containsKey(word[i])==false)
                {
                    return false;
                }
                node = node->get(word[i]);
            }
            return node->isEnd();
        }
};
int f(int ind,string &s,Trie &t,vector<int> &dp)
{
    if(ind==s.length())
    {
        return 0;
    }
    if(dp[ind]!=-1)
    {
        return dp[ind];
    }
    // Case-1: ind is the extra character
    int extra = 1 + f(ind+1,s,t,dp);
    int noExtra = INT_MAX;
    // Case-2: ind is not the extra character
    for(int j=ind;j<s.length();j++)
    {
        string str1 = s.substr(ind,j-ind+1);
        if(t.checkWord(str1))
        {
            noExtra = min(noExtra,f(j+1,s,t,dp));
        }
    }
    return dp[ind] =min(extra,noExtra);
}
class Solution 
{
    public:
    int minExtraChar(string s, vector<string>& dictionary)
    {
        Trie t;
        for(int i=0;i<dictionary.size();i++)
        {
            t.insert(dictionary[i]);
        }      
        vector<int> dp(s.length()+1,-1);
        int ans = f(0,s,t,dp);
        return ans;
    }
};
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