<p>You are given a string <code>s</code> consisting only of characters <code>&#39;a&#39;</code> and <code>&#39;b&#39;</code>​​​​.</p>

<p>You can delete any number of characters in <code>s</code> to make <code>s</code> <strong>balanced</strong>. <code>s</code> is <strong>balanced</strong> if there is no pair of indices <code>(i,j)</code> such that <code>i &lt; j</code> and <code>s[i] = &#39;b&#39;</code> and <code>s[j]= &#39;a&#39;</code>.</p>

<p>Return <em>the <strong>minimum</strong> number of deletions needed to make </em><code>s</code><em> <strong>balanced</strong></em>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;aababbab&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> You can either:
Delete the characters at 0-indexed positions 2 and 6 (&quot;aa<u>b</u>abb<u>a</u>b&quot; -&gt; &quot;aaabbb&quot;), or
Delete the characters at 0-indexed positions 3 and 6 (&quot;aab<u>a</u>bb<u>a</u>b&quot; -&gt; &quot;aabbbb&quot;).
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;bbaaaaabb&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> The only solution is to delete the first two characters.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s[i]</code> is&nbsp;<code>&#39;a&#39;</code> or <code>&#39;b&#39;</code>​​.</li>
</ul>

class Solution 
{
    vector<pair<int,int>> preprocess(string const & s)
    {
        vector<pair<int,int>> excludes;
        int idx = 0;
        while (idx<s.size() && s[idx]=='a')
        {
            ++idx;
        }
        pair<int,int> exclude;
        while(idx<s.size())
        {
            while (idx < s.size() && s[idx]=='b')
            {
                exclude.first++;
                ++idx;
            }
            while (idx < s.size() && s[idx]=='a')
            {
                exclude.second++;
                ++idx;
            }   
            excludes.push_back(exclude);  
            exclude = {0,0};
        }
        if (!excludes.empty() && excludes.back().second==0)
            excludes.pop_back();
        return excludes;
    }
public:
    int minimumDeletions(string s) 
    {
        auto excludes = preprocess(s);
        if (excludes.empty())
            return 0;
        int n = excludes.size(), opt = INT_MAX;
        vector<pair<int, int>> prefix(excludes.size()+1);
        for (int i = 0; i<n; ++i)
        {
            prefix[i+1].first = prefix[i].first + excludes[i].first;
        }
        opt = prefix.back().first;
        for (int i = n-1; i>=0; --i)
        {
            prefix[i].second = prefix[i+1].second + excludes[i].second;
            opt = min(opt, prefix[i].first + prefix[i].second);
        }
        return opt;
    }
};
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