danhnguyen0902's blog

[SPOJ] LQDNUMS
By danhnguyen0902, 11 years ago, In English

Does anyone know how to solve this problem?

http://www.spoj.com/problems/LQDNUMS/

Or at least please give me the references for it. Thanks a lot in advance.

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11 years ago, # |
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I have some ideas to solve it in polynomial time, but it's too slow.
Let F(N) be the length of the result string. We have to find N, such that F(N) == M.
Use binary search to find N. F(N) can be calculated using DP and fast matrix exponentiation. I know how to do it with about 18-36 matrices of size K x K, K ~ 18 * 10 * 2.

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    11 years ago, # ^ |
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    No, i was wrong with matrix exponentiation. I think there is kind of dp, we have to divide iterval [1..N] into several ones with the same prefix. for example for N = 1234 ther will be
    [1..999] for all numbers with length < length(N)
    [1000..1199] — 1 234
    [1200..1229] — 12 34
    [1230..1234] — 123 4

    for each of these intervals we have to use this dp recursively.

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