<p>A binary string is monotone increasing if it consists of some number of <code>0</code>&#39;s (possibly none), followed by some number of <code>1</code>&#39;s (also possibly none).</p>

<p>You are given a binary string <code>s</code>. You can flip <code>s[i]</code> changing it from <code>0</code> to <code>1</code> or from <code>1</code> to <code>0</code>.</p>

<p>Return <em>the minimum number of flips to make </em><code>s</code><em> monotone increasing</em>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;00110&quot;
<strong>Output:</strong> 1
<strong>Explanation:</strong> We flip the last digit to get 00111.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;010110&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> We flip to get 011111, or alternatively 000111.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;00011000&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> We flip to get 00000000.
</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 either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
</ul>

class Solution {
public:
    int minFlipsMonoIncr(string s) {
        int n = s.length();
        vector<int> left(n,0), right(n,0);
        if(s[0] == '0') left[0] = 1;
        if(s[n-1] == '0') right[n-1] = 1;

        for(int i=1; i<n; ++i) {
            if(s[i] == '0') left[i] = left[i-1] + 1;
            else left[i] = left[i-1];
        }

        for(int i=n-2; i>=0; --i) {
            if(s[i] == '0') right[i] = right[i+1] + 1;
            else right[i] = right[i+1];
        }

        for(auto i: left) cout<<i<<" ";
        cout<<endl;
        for(auto i: right) cout<<i<<" ";
        cout<<endl;

        int minm = INT_MAX;
        for(int i=0; i<n; ++i) {
            int leftZero = left[i], rightZero = right[i];
            int leftFlips = (i+1) - leftZero, rightFlips = rightZero;
            int sum = leftFlips + rightFlips;
            minm = min(minm, sum);
        }
        
        return minm-1;
    }
};
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