<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(string &s,int idx,char prev,vector<vector<int>>&dp){
    if(idx==s.length()){
        return 0;
    }
char c;
if(idx==0){
     int a=solve(s,idx+1,s[idx],dp);
      
     if(s[0]=='0'){
        c='1';
     }
     else{
        c='0';
     }
     int b=1+solve(s,idx+1,c,dp);
     return min(a,b);
}
if(idx>=1)
 {
    int a=prev-48;
    if(dp[a][idx]!=-1){
    return dp[a][idx];
    }
}
if(prev=='0'){
if(s[idx]=='1'){
    int a=solve(s,idx+1,s[idx],dp);
    c='0';
    int b=1+solve(s,idx+1,c,dp);
      
    dp[0][idx]=min(a,b);
    return dp[0][idx];
}
else{
int a=solve(s,idx+1,s[idx],dp);
    c='1';
    int b=1+solve(s,idx+1,c,dp);
    dp[0][idx]=min(a,b);
    return dp[0][idx];

}
}
else{
if(s[idx]=='1'){
    dp[1][idx]=solve(s,idx+1,s[idx],dp);
    return dp[1][idx];
}
else{
    c='1';
    dp[1][idx]=1+solve(s,idx+1,c,dp);
    return dp[1][idx];
}

}




}
    int minFlipsMonoIncr(string s) {
        int n=s.length();
 vector<vector<int>>dp(2,vector<int>(n,-1));

int ans=solve(s,0,0,dp);
 

return ans;


 
 
 



        
    }
};
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