<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 {
    int f(int ind,int prev,string &s,vector<vector<int>>&dp){
        int n=s.size();
        if(ind==n){
            return 0;
        }
        if(dp[ind][prev]!=-1){
            return dp[ind][prev];
        }
        if(prev==0){
            if(s[ind]=='1'){
                return dp[ind][prev]=min(1+f(ind+1,0,s,dp),f(ind+1,1,s,dp));
            }
            else{
                return dp[ind][prev]=min(1+f(ind+1,1,s,dp),f(ind+1,0,s,dp));
            }
        }
        else{
            if(s[ind]=='1'){
                return dp[ind][prev]=f(ind+1,1,s,dp);
            }
            else{
                return dp[ind][prev]=1+f(ind+1,1,s,dp);
            }
        }
    }
public:
    int minFlipsMonoIncr(string s) {
        int n=s.size();
        vector<vector<int>> dp(n+1,vector<int>(2,-1));
        vector<int> ans;
        ans.push_back(s[0]);
        for(int i=1;i<s.size();i++){
            if(s[i]>=ans.back()){
                ans.push_back(s[i]);
            }else{
                int res=upper_bound(ans.begin(),ans.end(),s[i])-ans.begin();
                ans[res]=s[i];

            }
        }

        // for(auto i : ans){
        //     cout<<i<<" ";
        // }

        return n-ans.size();
        // return min(n-lis2.size(),n-lis.size());
        return f(0,0,s,dp);
    }
};
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