9 lines
819 B
Markdown
9 lines
819 B
Markdown
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The factorial part is pretty easy - we cache the factorials from 1 to 9 and then we can calculate `facdigitsum(n)` in `O(log_10(n))`.
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The problemdescription tells us there are only seven numbers in a loop (`{169, 363601, 1454}`, `{871, 45361}`, `{872, 45362}`).
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So every other chain ends with a number mapping to itself. We manually insert these seven numbers in our grid and calculate the rest (where we only need to test if `f(n) == f(n-1)`).
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And we cache ever calculated value of `chainlength()` in our 1000000-element array. So as soon as we reach an already calculated number we can stop.
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This works because there are no loops (except the seven pre-inserted values) and every chain is strictly linear.
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Be sure to check out the pre-optimized version of this to see just how much more condensed this version is :)
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