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https://github.com/priyanshujain/messageboardbench.git
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55 lines
1.8 KiB
Python
55 lines
1.8 KiB
Python
from functools import lru_cache
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def count_beautiful_integers(low: int, high: int, k: int) -> int:
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""" Count the number of beautiful integers in the range [low, high].
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A number is beautiful if it meets both conditions:
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1. The count of even digits equals the count of odd digits
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2. The number is divisible by k
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Args:
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low: Lower bound of the range (inclusive), 0 < low <= high <= 10^9
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high: Upper bound of the range (inclusive)
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k: Divisor to check, 0 < k <= 20
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Returns:
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The count of beautiful integers in the given range
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>>> count_beautiful_integers(10, 20, 3)
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2
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>>> count_beautiful_integers(1, 10, 1)
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1
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>>> count_beautiful_integers(5, 5, 2)
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0
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"""
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def count_upto(n: int) -> int:
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if n <= 0:
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return 0
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s = str(n)
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L = len(s)
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@lru_cache(maxsize=None)
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def dp(pos: int, started: bool, diff: int, mod: int, tight: bool) -> int:
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if pos == L:
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return 1 if (started and diff == 0 and mod == 0) else 0
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limit = int(s[pos]) if tight else 9
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total = 0
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for d in range(limit + 1):
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ntight = tight and (d == limit)
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if not started:
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if d == 0:
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total += dp(pos + 1, False, diff, mod, ntight)
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else:
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ndiff = diff + (1 if d % 2 == 0 else -1)
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total += dp(pos + 1, True, ndiff, (mod * 10 + d) % k, ntight)
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else:
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ndiff = diff + (1 if d % 2 == 0 else -1)
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total += dp(pos + 1, True, ndiff, (mod * 10 + d) % k, ntight)
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return total
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return dp(0, False, 0, 0, True)
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return count_upto(high) - count_upto(low - 1)
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