<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:
// // Similar question: https://leetcode.com/problems/minimum-deletions-to-make-string-balanced/
// // Solution 1: Using stack
//     int minFlipsMonoIncr(string s) {
//         stack<char> stk;
//         int ans=0;
//         for(char ch: s){
//             if(!stk.empty() && ch<stk.top()){
//                 stk.pop();
//                 ans++;
//             }else stk.push(ch);
//         }
//         return ans;
//     }

// Solution 2: Memoziation/DP:
int solve(string& s,int i, bool prevOne,vector<vector<int>>& dp){
    if(i==s.size()) return 0;
    if(dp[i][prevOne]!=-1) return dp[i][prevOne];
    if(prevOne){
        return dp[i][prevOne] = s[i]=='0' ? 1+solve(s,i+1, true,dp) : solve(s,i+1,true,dp);
    }
        return dp[i][prevOne]=min(solve(s,i+1, s[i]=='1',dp), 1+solve(s,i+1, !(s[i]=='1'),dp));
}

int minFlipsMonoIncr(string s) {
    vector<vector<int>> dp(s.size(), vector<int>(2,-1));
    return min(solve(s,1, s[0]=='1',dp), 1+solve(s,1, !(s[0]=='1'),dp));
}
};
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