File size: 2,801 Bytes
848d4b7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 | #!/usr/bin/env python3
"""
Validator for schur_6: Maximum 6-Coloring with No Monochromatic x+y=z
Expected input: a list `colors` of length N+1 where
colors[0] = 0 (sentinel)
colors[i] in {0,1,2,3,4,5} for i = 1..N
Validity: for every color c and all x,y with 1<=x<=y<=N,
if colors[x] = colors[y] = c and x+y <= N, then colors[x+y] != c.
Metric: N (maximize).
"""
import argparse
from typing import Any
from . import ValidationResult, load_solution, output_result, success, failure
# Hard safety cap: proven upper bound S(6) <= 1836, so 10000 is generous.
MAX_N = 10000
def validate(sol: Any) -> ValidationResult:
try:
if not isinstance(sol, list):
return failure(f"Expected a list, got {type(sol).__name__}.")
if len(sol) < 2:
return failure("colors must have length at least 2 (N >= 1).")
N = len(sol) - 1
if N > MAX_N:
return failure(f"N={N} exceeds safety cap MAX_N={MAX_N}.")
if sol[0] != 0:
return failure("colors[0] must be 0.")
# Validate entries and collect positions per color.
pos = [[] for _ in range(6)]
for i in range(1, N + 1):
ci = sol[i]
if not isinstance(ci, int):
return failure(f"colors[{i}] is not an int (got {type(ci).__name__}).")
if ci < 0 or ci > 5:
return failure(f"colors[{i}]={ci} is out of range; must be in {{0,...,5}}.")
pos[ci].append(i)
# Check sum-free constraint: for each color c, for all x<=y in that color,
# if x+y<=N then colors[x+y] must not equal c.
for c in range(6):
lst = pos[c]
m = len(lst)
for a in range(m):
x = lst[a]
for b in range(a, m):
y = lst[b]
s = x + y
if s > N:
break
if sol[s] == c:
return failure(
f"Monochromatic violation in color {c}: "
f"{x} + {y} = {s} and all have color {c}."
)
return success(
f"Valid 6-coloring of {{1,...,{N}}} with no monochromatic x+y=z.",
N=N,
color_sizes=[len(pos[c]) for c in range(6)],
)
except Exception as e:
return failure(f"Exception during validation: {e}")
def main():
parser = argparse.ArgumentParser(description="Validate a 6-coloring for Schur number S(6)")
parser.add_argument("solution", help="Solution as JSON string or path to JSON file")
args = parser.parse_args()
sol = load_solution(args.solution)
result = validate(sol)
output_result(result)
if __name__ == "__main__":
main()
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