78 lines
1.8 KiB
Python
Executable File
78 lines
1.8 KiB
Python
Executable File
#!/usr/bin/env python3
|
|
|
|
import sys
|
|
from typing import Optional
|
|
|
|
def magnitude(x : int) -> int:
|
|
assert x >= 0
|
|
return len(str(x))
|
|
|
|
def delta(order : int) -> int:
|
|
return 10**order + 1
|
|
|
|
def sum_1_to_excl(x : int) -> int:
|
|
return x * (x - 1) // 2
|
|
|
|
def sum_1_to_incl(x : int) -> int:
|
|
return x * (x + 1) // 2
|
|
|
|
# incl. both bounds
|
|
def sum_from_to_incl(lo : int, hi : int) -> int:
|
|
if lo > hi:
|
|
return 0
|
|
|
|
return sum_1_to_incl(hi) - sum_1_to_excl(lo)
|
|
|
|
def div2(x : int) -> Optional[int]:
|
|
if x % 2:
|
|
return None
|
|
else:
|
|
return x // 2
|
|
|
|
# inclusive both bounds
|
|
def sum_invalid_ids(lo : int, hi : int) -> int:
|
|
total = 0
|
|
|
|
while True:
|
|
magnitude_lo = magnitude(lo)
|
|
order_lo = div2(magnitude_lo)
|
|
if order_lo is None:
|
|
# no invalid IDs in that order of magnitude
|
|
lo = 10**magnitude_lo
|
|
continue
|
|
|
|
magnitude_hi = magnitude(hi)
|
|
d = delta(order_lo)
|
|
|
|
if magnitude_lo > magnitude_hi:
|
|
# this can happen with odd magnitude_hi
|
|
break
|
|
|
|
elif magnitude_lo == magnitude_hi:
|
|
assert lo <= hi, f"{lo} <= {hi}"
|
|
total += d * sum_from_to_incl((lo-1)//d + 1, hi // d)
|
|
break
|
|
|
|
assert magnitude_lo < magnitude_hi
|
|
surrogate_hi = 10**magnitude_lo - 1
|
|
assert lo <= surrogate_hi, f"{lo} <= {surrogate_hi}"
|
|
total += d * sum_from_to_incl((lo-1)//d + 1, surrogate_hi // d)
|
|
lo = surrogate_hi + 1
|
|
|
|
return total
|
|
|
|
if __name__ == '__main__':
|
|
ranges = [
|
|
(int(lo_s), int(hi_s))
|
|
for lo_s, hi_s in (
|
|
rng.split('-')
|
|
for rng in sys.stdin.read().strip().split(',')
|
|
)
|
|
]
|
|
|
|
total = 0
|
|
for lo, hi in ranges:
|
|
total += sum_invalid_ids(lo, hi)
|
|
|
|
print(total)
|