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1ca0407 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | """Block stacking (overhang) problem, closed form of the constraints; checked in exact rational arithmetic.
Upstream (block_stacking_problem.ipynb) used a float tolerance of 100*eps on every constraint, which lets a
submission exceed the true optimum H_n/2 by accumulated slack; here all constraints are exact (non-strict).
"""
from fractions import Fraction
from run import Invalid, float_list
def check(inst, ans):
n = inst["n"]
x = [Fraction(v) for v in float_list(ans.get("x"), n, "x")]
xs = [Fraction(0)] + x # x_0 = 0
for i in range(n):
if xs[i + 1] < xs[i]:
raise Invalid(f"need x_{i} <= x_{i + 1}")
tail = Fraction(0)
for i in range(n - 1, -1, -1): # tail = x_{i+1} + ... + x_n
tail += xs[i + 1]
if tail > (n - i) * (xs[i] + Fraction(1, 2)):
raise Invalid(f"stability constraint violated at i = {i}")
return float(xs[n]), {}
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