<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 find_moves(const int&k,const int&n,vector<vector<int>>&dp){
        if(k==1 ){
            return n;
        }
        if(n==1 || n==0){
            return n;
        }
        if(dp[k][n]!=-1){
            return dp[k][n];
        }
        int ans=INT_MAX;
        int l=1;int r=n; int mid;
        // for(int i=1;i<=n;++i){
        //     int temp=1+max(find_moves(k-1,i-1,dp),find_moves(k,n-i,dp));
        //     ans=min(ans,temp);
        // }
        while(l<=r){
            mid=(l+r)/2;
            int a=find_moves(k-1,mid-1,dp);
            int b=find_moves(k,n-mid,dp);
            int temp=1+max(a,b);
            if(a<b){
                l=mid+1;
            }
            else{
                r=mid-1;
            }
            ans=min(ans,temp);
        }
        return dp[k][n]=ans;
    }
    int superEggDrop(int k, int n) {
        vector<vector<int>>dp(k+1,vector<int>(n+1,-1));
        return find_moves(k,n,dp);
        
    }
};
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