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