<p>You are given <code>k</code> identical eggs and you have access to a building with <code>n</code> floors labeled from <code>1</code> to <code>n</code>.</p>

<p>You know that there exists a floor <code>f</code> where <code>0 &lt;= f &lt;= n</code> such that any egg dropped at a floor <strong>higher</strong> than <code>f</code> will <strong>break</strong>, and any egg dropped <strong>at or below</strong> floor <code>f</code> will <strong>not break</strong>.</p>

<p>Each move, you may take an unbroken egg and drop it from any floor <code>x</code> (where <code>1 &lt;= x &lt;= n</code>). If the egg breaks, you can no longer use it. However, if the egg does not break, you may <strong>reuse</strong> it in future moves.</p>

<p>Return <em>the <strong>minimum number of moves</strong> that you need to determine <strong>with certainty</strong> what the value of </em><code>f</code> is.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> k = 1, n = 2
<strong>Output:</strong> 2
<strong>Explanation: </strong>
Drop the egg from floor 1. If it breaks, we know that f = 0.
Otherwise, drop the egg from floor 2. If it breaks, we know that f = 1.
If it does not break, then we know f = 2.
Hence, we need at minimum 2 moves to determine with certainty what the value of f is.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> k = 2, n = 6
<strong>Output:</strong> 3
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> k = 3, n = 14
<strong>Output:</strong> 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= 100</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:

    int eggDrop(int k, int n,vector<vector<int>>& dp) {
        if(k<=0||n==0)return 0;
        if(k==1)return n;
        if(dp[k-1][n-1]!=INT_MAX)return dp[k-1][n-1];
        long long minm=LLONG_MAX;
        int left=1, right=n;
        while(left<=right)
        {
            int floor  = (left+right)/2;
            int notBreak = eggDrop(k,n-floor,dp);
            int Break = eggDrop(k-1,floor-1,dp);
            long long moves =max(Break,notBreak)+1;
            minm=min(minm,moves);

            if (Break > notBreak) {
                right = floor - 1;
            } else {
                left = floor + 1;
            }
        }
        dp[k-1][n-1]=minm;
        return minm;
    }

    //recursive, memoized
    int eggDropx(int k, int n,vector<vector<int>>& dp) {
        if(k<=0||n==0)return 0;
        if(k==1)return n;
        if(dp[k-1][n-1]!=INT_MAX)return dp[k-1][n-1];
        long long minm=LLONG_MAX;
        for(int floor=n;floor>=1;floor--)
        {
            long long moves =max(eggDrop(k,n-floor,dp),eggDrop(k-1,floor-1,dp))+1;
            minm=min(minm,moves);
        }
        dp[k-1][n-1]=minm;
        return minm;
    }

     int superEggDrop(int k, int n) {
        if(k==1)return n;
        vector<vector<int>> dp(k,vector<int>(n,INT_MAX));

        return eggDrop(k,n,dp);
     }
};
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