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Classic House Robber linear DP:
dp[i] = max(dp[i-2] + houses[i], dp[i-1])
For [2; 7; 9; 3; 1; 5; 8; 6]:
dp = [2, 7, 11, 11, 12, 16, 20, 22]
max sum = 22
Optimal pick is {indices 0, 2, 5, 7}: 2 + 9 + 5 + 6 = 22 (all
non-adjacent).
Tests linear DP with early-return edge cases for n=0 and n=1,
inline-if rhs for max-of-two, dual look-back into dp[i-2] and
dp[i-1].
189 baseline programs total.
20 lines
465 B
OCaml
20 lines
465 B
OCaml
let rob houses =
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let n = Array.length houses in
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if n = 0 then 0
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else if n = 1 then houses.(0)
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else begin
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let dp = Array.make n 0 in
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dp.(0) <- houses.(0);
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dp.(1) <- if houses.(0) > houses.(1) then houses.(0) else houses.(1);
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for i = 2 to n - 1 do
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let take = dp.(i - 2) + houses.(i) in
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let skip = dp.(i - 1) in
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dp.(i) <- if take > skip then take else skip
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done;
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dp.(n - 1)
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end
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;;
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rob [| 2; 7; 9; 3; 1; 5; 8; 6 |]
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