96 lines
2.2 KiB
Python
96 lines
2.2 KiB
Python
MOD = 10**7
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SPACE = 10**7
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CACHE = [None for _ in range(SPACE * 2)]
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CACHE_TILL = [None for _ in range(SPACE)]
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CACHE_TILL_IS_TWO_EVEN = [None for _ in range(SPACE)]
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CACHE_TILL_IS_TWO_ODD = [None for _ in range(SPACE)]
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CACHE_T_FROM_ACC = [None for _ in range(SPACE * 2)]
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def t_from_acc(rem: int, is_two: bool) -> int:
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offset = rem + SPACE * is_two
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if (value := CACHE_T_FROM_ACC[offset]) is not None:
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return value
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if rem < 0:
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return 0
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s = t_from(rem, is_two) + t_from_acc(rem - 2, is_two)
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s %= MOD
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CACHE_T_FROM_ACC[offset] = s
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return s
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def t_from(rem: int, is_two: bool) -> int:
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offset = rem + SPACE * is_two
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if (value := CACHE[offset]) is not None:
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return value
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s = 0
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if rem < 0:
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s = 0
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elif rem == 1:
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s = 0
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elif rem == 0 and is_two:
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s = 1
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else:
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s += t_from(rem - 2, is_two) # d = 1
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s %= MOD
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s += t_from(rem - 4, True) # d = 2
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s %= MOD
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s += t_from_acc(rem - 6, is_two)
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s %= MOD
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# Naive (too slow):
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# for d in range(1, rem // 2 + 1):
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# s += t_from(rem - 2 * d, is_two or d == 2)
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# s %= MOD
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CACHE[offset] = s % MOD
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return s % MOD
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def t_old(n: int) -> int:
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# print(f"t({n}) = ", end="")
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s = 0
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for i in range(0, n + 1):
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rem = n - i
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s += t_from(rem, i == 2)
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return s % MOD
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def t(n: int) -> int:
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s = CACHE_TILL[n - 4]
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assert s is not None
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s += t_from(n - 3, False)
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CACHE_TILL[n - 3] = s % MOD
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s += t_from(n - 2, True)
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s %= MOD
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s += t_from(n - 1, False)
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s %= MOD
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s += t_from(n, False)
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s %= MOD
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return s
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def euler_710():
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for i in range(4):
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CACHE_TILL[i] = 0
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for n in range(4, 50):
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t(n)
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assert t(5) == 1
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assert t(6) == 4
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assert t(20) == 824
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assert t(42) == 1999923
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for n in range(10, SPACE):
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tn = t(n)
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if tn % 10**6 == 0:
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# print(f"t({n}) = {tn} <<<")
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return n
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# if tn % 10000 == 0:
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# print(f"t({n}) = {tn}")
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assert False, "Solution not found"
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if __name__ == "__main__":
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solution = euler_710()
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print(f"e710.py: {solution}")
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assert solution == 1275000
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