<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 solve1(int ind, string& s){
        int ans=0;
        for(int i=ind;i<s.length();i++){
            if(s[i]=='0') ans++;
        }
        // cout<<ind<<' '<<ans<<endl;
        return ans;
    }

    int solve(int ind, string &s, vector<int>& dp, vector<int>& solve1){
        // cout<<ind<<' ';

        if(ind==s.length()){
            return 0;
        }
        if(dp[ind]!=-1) return dp[ind];

        while(ind<s.length() && s[ind]=='0'){
            ind++;
        }
        if(ind==s.length()) return 0;

        return dp[ind] = min(1+solve(ind+1, s, dp, solve1), solve1[ind]);
    }

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

        vector<int>solve1(n,0);
        int curr=0;
        for(int i=n-1;i>=0;i--){
            if(s[i]=='0') curr++;
            solve1[i]=curr;
        }
        
        return solve(0, s, dp, solve1);
                
    }
};
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