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Classic egg-drop puzzle DP:
dp[e][f] = 1 + min over k in [1, f] of
max(dp[e-1][k-1], dp[e][f-k])
For 2 eggs over 36 floors, the optimal worst-case is 8 trials
(closed form: triangular number bound).
Tests 2D DP with triple-nested for-loops, max-of-two via inline
if, large sentinel constant (100000000), mixed shifted indexing
(e-1) and (f-k) where both shift independently.
163 baseline programs total.
27 lines
605 B
OCaml
27 lines
605 B
OCaml
let egg_drop eggs floors =
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let dp = Array.init (eggs + 1) (fun _ -> Array.make (floors + 1) 0) in
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for f = 1 to floors do
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dp.(1).(f) <- f
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done;
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for e = 1 to eggs do
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dp.(e).(0) <- 0;
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dp.(e).(1) <- 1
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done;
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for e = 2 to eggs do
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for f = 2 to floors do
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let best = ref 100000000 in
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for k = 1 to f do
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let bre = dp.(e - 1).(k - 1) in
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let sur = dp.(e).(f - k) in
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let cand = 1 + (if bre > sur then bre else sur) in
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if cand < !best then best := cand
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done;
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dp.(e).(f) <- !best
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done
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done;
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dp.(eggs).(floors)
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;;
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egg_drop 2 36
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