887. Super Egg Drop

You are given K eggs, and you have access to a building with N floors from 1 to N.

Each egg is identical in function, and if an egg breaks, you cannot drop it again.

You know that there exists a floor F with 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 egg (if you have an unbroken one) and drop it from any floor X (with 1 <= X <=
N).

Your goal is to know with certainty what the value of F is.

What is the minimum number of moves that you need to know with certainty what F is, regardless of the
initial value of F?



Example 1:

Input: K = 1, N = 2
Output: 2
Explanation:
Drop the egg from floor 1.  If it breaks, we know with certainty that F = 0.
Otherwise, drop the egg from floor 2.  If it breaks, we know with certainty that F = 1.
If it didn't break, then we know with certainty F = 2.
Hence, we needed 2 moves in the worst case to know what F is with certainty.

Example 2:

Input: K = 2, N = 6
Output: 3

Example 3:

Input: K = 3, N = 14
Output: 4



Note:

    1 <= K <= 100
    1 <= N <= 10000

public int superEggDrop(int K, int N) {
    if(K == 1 || N == 1) return N;
    int[][] dp = new int[N+1][K+1];
    int m = 0;
    while(dp[m][K] < N) {
        m++;
        for(int k = 1; k <= K; k++) {
            dp[m][k] = dp[m-1][k-1] + dp[m-1][k] + 1;
        }
    }
    return m;
}