# GFG POTD: Egg dropping puzzle solution (Dynamic Programming)

## Problem Statement

You are given N identical eggs and you have access to a K-floored building from 1 to K.

There exists a floor f where 0 <= f <= such that any egg dropped at a floor higher than f will break, and any egg dropped at or below floor will not break. There are few rules given below.

• An egg that survives a fall can be used again.
• A broken egg must be discarded.
• The effect of a fall is the same for all eggs.
• If the egg doesn’t break at a certain floor, it will not break at any floor below.
• If the eggs breaks at a certain floor, it will break at any floor above.

Return the minimum number of moves that you need to determine with certainty what the value of f is.

Example 1:

```Input:
N = 1, K = 2
Output: 2
Explanation:
1. Drop the egg from floor 1. If it
breaks, we know that f = 0.
2. Otherwise, drop the egg from floor 2.
If it breaks, we know that f = 1.
3. If it does not break, then we know f = 2.
4. Hence, we need at minimum 2 moves to
determine with certainty what the value of f is.```

Example 2:

```Input:
N = 2, K = 10
Output: 4```

Complete the function eggDrop() which takes two positive integer N and K as input parameters and returns the minimum number of attempts you need in order to find the critical floor.

Expected Time Complexity : O(N*(K^2))
Expected Auxiliary Space: O(N*K)

Constraints:
1<=N<=200
1<=K<=200

## Solution

```int dp; //Creating matrix of size 202*202
class Solution
{
public:
//Function to find minimum number of attempts needed in
//order to find the critical floor.

//optimize the worst case
//best of worst case

int solve(int e, int f){

if(f==1||f==0||e==1)
return f;
if(dp[e][f]!=-1) return dp[e][f];
int minMoves=INT_MAX;

for(int k=1; k<=f; k++){
int broke=1+solve(e-1,k-1);
int unbroke=1+solve(e,f-k);

int temp=max(broke,unbroke);
minMoves = min(minMoves, temp);
}
return dp[e][f]=minMoves;

}

int eggDrop(int n, int k)
{
memset(dp,-1,sizeof(dp)); //initializing matrix with -1
return solve(n,k);
}
};```
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