giles
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Standard 2D DP for min-cost path with right/down moves only:
dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + cost[i][j]
cost: dp:
1 3 1 2 1 4 5 7
1 5 1 3 2 7 6 9
4 2 1 4 6 8 7 11
1 6 2 3 7 13 9 12
Optimal cost from (0,0) to (3,3) = 12.
Tests nested 2D arrays via Array.init + Array.make, double-nested
for-loops with branched edges (first row, first column, general),
mixed .(i-1).(j) read + .(i).(j)<- write on the same DP array.
161 baseline programs total.
32 lines
618 B
OCaml
32 lines
618 B
OCaml
let h = 4
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let w = 4
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let cost = [|
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[| 1; 3; 1; 2 |];
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[| 1; 5; 1; 3 |];
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[| 4; 2; 1; 4 |];
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[| 1; 6; 2; 3 |]
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|]
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let min_cost_path () =
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let dp = Array.init h (fun _ -> Array.make w 0) in
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dp.(0).(0) <- cost.(0).(0);
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for j = 1 to w - 1 do
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dp.(0).(j) <- dp.(0).(j - 1) + cost.(0).(j)
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done;
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for i = 1 to h - 1 do
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dp.(i).(0) <- dp.(i - 1).(0) + cost.(i).(0)
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done;
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for i = 1 to h - 1 do
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for j = 1 to w - 1 do
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let a = dp.(i - 1).(j) in
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let b = dp.(i).(j - 1) in
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dp.(i).(j) <- (if a < b then a else b) + cost.(i).(j)
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done
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done;
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dp.(h - 1).(w - 1)
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;;
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min_cost_path ()
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