<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 solve(int i,string &s ,int prev,int n,vector<vector<int>>&dp)
{
  if(i>=n) return 0;
  if(dp[i][prev]!=-1) return dp[i][prev];
  int flip=INT_MAX;
  int notflip=INT_MAX;
  if(s[i]=='0'){
     if(prev==0){
      notflip=solve(i+1,s,0,n,dp);
      flip=1+solve(i+1,s,1,n,dp);
     }
     else {
      flip=1+solve(i+1,s,1,n,dp);
     }
  }
  else {
    if(prev==0){
       notflip=solve(i+1,s,1,n,dp);
      flip=1+solve(i+1,s,0,n,dp);
    }
    else {
      notflip=solve(i+1,s,1,n,dp);
    }
  }
  return dp[i][prev]= min(flip,notflip);
}
 
    int minFlipsMonoIncr(string s) {
        int n=s.size();
        vector<vector<int>>dp(n+1,vector<int>(2,-1));
        return solve(0,s,0,n,dp);
    }
};
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