Super Egg Drop

You have k eggs and n floors. Find the minimum number of moves to determine the critical floor (highest floor from which an egg won't break). Rules: A broken egg is lost. An unbroken egg can be reused. You may assume floor 0 always safe. Example 1: k=1, n=2 → 2 Example 2: k=2, n=6 → 3 Example 3: k=3, n=14 → 4 DE Shaw Tier 1 — LC 887. Naive DP: dp[k][n] = 1 + min over floor f of max(dp[k-1][f-1], dp[k][n-f]). O(kn^2). Optimal: Reframe — dp[m][k] = max floors checkable with m moves and k eggs. dp[m][k] = dp[m-1][k-1] + dp[m-1][k] + 1. Find smallest m where dp[m][k] >= n. O(k log n).