## Algorithm

Problem Name: 887. Super Egg Drop

You are given `k` identical eggs and you have access to a building with `n` floors labeled from `1` to `n`.

You know that there exists a floor `f` where `0 <= f <= n` such that any egg dropped at a floor higher than `f` will break, and any egg dropped at or below floor `f` will not break.

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

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

Example 1:

```Input: k = 1, n = 2
Output: 2
Explanation:
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.
```

Example 2:

```Input: k = 2, n = 6
Output: 3
```

Example 3:

```Input: k = 3, n = 14
Output: 4
```

Constraints:

• `1 <= k <= 100`
• `1 <= n <= 104`

## Code Examples

### #1 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const superEggDrop = function(K, N) {
let lo = 1,
hi = N,
mi
while (lo < hi) {
mi = ((lo + hi) / 2) >> 0
if (f(mi, K, N)  <  N) lo = mi + 1
else hi = mi
}
return lo
}

function f(x, K, N) {
let ans = 0,
r = 1,
i = 1
for (let i = 1; i <= K; ++i) {
r = ((r * (x - i + 1)) / i) >> 0
ans += r
if (ans >= N) break
}
return ans
}
``````
Copy The Code &

Input

cmd
k = 1, n = 2

Output

cmd
2

### #2 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def superEggDrop(self, K, N):
drops = 0                           # the number of eggs dropped
floors = [0 for _ in range(K + 1)]  # floors[i] is the number of floors that can be checked with i eggs

while floors[K] < N:                # until we can reach N floors with K eggs

for eggs in range(K, 0, -1):
floors[eggs] += 1 + floors[eggs - 1]
drops += 1

return drops
``````
Copy The Code &

Input

cmd
k = 1, n = 2

Output

cmd
2

### #3 Code Example with C# Programming

```Code - C# Programming```

``start coding...``
Copy The Code &