<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, int n, string &s, int prev, vector<vector<int>>&dp)
    {
        if(i>=n)
        return 0;

        if(dp[i][prev] != -1)
        return dp[i][prev];

        int a = INT_MAX, b = INT_MAX, c =INT_MAX, d = INT_MAX, e = INT_MAX;
        if(prev == 0 && s[i] == '0')
        {
            a = solve(i+1, n, s, prev, dp);
        }

        if(prev == 0 && s[i] == '1')
        {
            b = 1 + solve(i+1, n, s, prev, dp);
            c = solve(i+1, n, s, 1, dp);
        }
        if(prev == 1 && s[i] == '1')
        {
            d = solve(i+1, n, s, 1, dp);
        }
        if(prev == 1 && s[i] == '0')
        {
            e = 1 + solve(i+1, n, s, 1, dp);
        }

        return dp[i][prev] = min({a, b, c, d, e});
    }
    int minFlipsMonoIncr(string s) {
        int n = s.size();
        vector<vector<int>>dp(n+1, vector<int>(2, 0));
        //return solve(0, n, s, 0, dp);
        dp[n][0] = 0;
        dp[n][1] = 0;

        for(int i = n-1; i >=0; i--)
        {
            for(int prev = 0; prev<2; prev++)
            {
                int a = INT_MAX, b = INT_MAX, c =INT_MAX, d = INT_MAX, e = INT_MAX;
                if(prev == 0 && s[i] == '0')
                {
                    a = dp[i+1][prev];
                }

                if(prev == 0 && s[i] == '1')
                {
                    b = 1 + solve(i+1, n, s, prev, dp);
                    c = dp[i+1][1];
                }
                if(prev == 1 && s[i] == '1')
                {
                    d = dp[i+1][prev];
                }
                if(prev == 1 && s[i] == '0')
                {
                    e = 1 + dp[i+1][prev];
                }

                dp[i][prev] = min({a, b, c, d, e});

            }
        }

        return dp[0][0];

    }
};
46533