GCJ 2017 Round 1C. Problem C. Core Training

C.pi

import util, mip.

go(T, N, K, U, Xs) =>
	X = new_array(N),
	X :: 0.0..1.0,
	foreach(I in 1..N)
		X[I] #>= Xs[I],
		X[I] #<= Xs[I] + U
	end,
	sum(X) #<= sum(Xs) + U,
	S #= prod([1.0 - X[I] : I in 1..N]),
	solve($[max(S)], [S, X]),
	printf(stderr, "Case #%d: %f\n", T, S).

go2(T, N, K, U, Xs) =>
	X = new_array(N),
	X :: 0.0..1.0,
	Y = new_array(N),
	Y :: 0..1,
	foreach(I in 1..N)
		X[I] #>= Xs[I],
		X[I] #<= Xs[I] + U
	end,
	sum(X) #<= sum(Xs) + U,
	sum(Y) #= K,
	S #= prod([1.0 - (X[I] * Y[I]) : I in 1..N]),
	solve($[max(S)], [S, X, Y]),
	printf(stderr, "Case #%d: %f\n", T, S).

go3(T, N, K, U, Xs) =>
	X = new_array(N),
	X :: 0.0..1.0,
	foreach(I in 1..N)
		X[I] #>= Xs[I],
		X[I] #<= Xs[I] + U
	end,
	sum(X) #<= sum(Xs) + U,
	Z = new_array(N+1),
	Z :: 0.0..1.0,
	Z[1] = 1.0,
	foreach(I in 2..N+1)
		Z[I] #= Z[I - 1] * (1.0 - X[I-1])
	end,
	S #= Z[N+1],
	solve($[max(S)], [S, X, Z]),
	printf(stderr, "Case #%d: %f\n", T, S).

main() =>
	[T] = [X.to_number() : X in readln().split()],
	foreach(I in 1..T)
		[N, K] = [X.to_number() : X in readln().split()],
		[U] = [X.to_number() : X in readln().split()],
		Xs = [X.to_number() : X in readln().split()],
		go3(I, N, K, U, Xs)
	end.