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315.py
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315.py
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from utils import primes_in_range
from dataclasses import dataclass
@dataclass
class Number:
top: int
top_left: int
top_right: int
middle: int
bottom_left: int
bottom_right: int
bottom: int
def __iter__(self):
return (self.top, self.top_left, self.top_right, self.middle, self.bottom_left, self.bottom_right, self.bottom)
def sum(self):
return sum(self.__iter__())
def diff(self, other: "Number") -> int:
return sum([int(s1 != s2) for s1, s2 in zip(self.__iter__(), other.__iter__())])
numbers = {
0: Number(1, 1, 1, 0, 1, 1, 1),
1: Number(0, 0, 1, 0, 0, 1, 0),
2: Number(1, 0, 1, 1, 1, 0, 1),
3: Number(1, 0, 1, 1, 0, 1, 1),
4: Number(0, 1, 1, 1, 0, 1, 0),
5: Number(1, 1, 0, 1, 0, 1, 1),
6: Number(1, 1, 0, 1, 1, 1, 1),
7: Number(1, 1, 1, 0, 0, 1, 0),
8: Number(1, 1, 1, 1, 1, 1, 1),
9: Number(1, 1, 1, 1, 0, 1, 1),
}
def segments(num: int) -> int:
return sum(numbers[int(c)].sum() for c in str(num))
def sam_count(nums: list[int]) -> int:
return sum(2*segments(num) for num in nums)
def max_count(nums: list[int]) -> int:
res = segments(nums[0]) + segments(nums[-1])
prev = nums[0]
for num in nums[1:]:
# turn off / on non-overlap, then compute overlap
to_trim = len(str(prev)) - len(str(num))
if to_trim:
res += segments(int(str(prev)[:to_trim]))
for c1, c2 in zip(str(prev)[to_trim:], str(num)):
res += numbers[int(c1)].diff(numbers[int(c2)])
prev = num
return res
def root_seq(num: int) -> list[int]:
curr = num
res = [num]
while curr > 9:
curr = sum(int(c) for c in str(curr))
res.append(curr)
return res
assert root_seq(137) == [137, 11, 2]
assert sam_count([137, 11, 2]) == 40
assert max_count([137, 11, 2]) == 30
assert sam_count(root_seq(1999993)) == 116
assert max_count(root_seq(1999993)) == 78
max_res = sam_res = 0
primes = primes_in_range(10**7, 2*10**7)
for p in primes:
seq = root_seq(p)
max_res += max_count(seq)
sam_res += sam_count(seq)
print(sam_res - max_res)