Good Sequences(codeforces 264B)

最新推荐文章于 2021-02-24 22:29:56 发布

CatDsy

最新推荐文章于 2021-02-24 22:29:56 发布

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分类专栏：动态规划数论

本文链接：https://blog.youkuaiyun.com/CatDsy/article/details/77446888

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这是一道关于寻找最长递增子序列的问题，序列中相邻元素的最大公约数必须大于1。需要找到这样的序列并输出其长度。题解涉及动态规划和质因数分解，其中关键在于正确初始化ans的值和优化质因数分解的范围。

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题目：
Squirrel Liss is interested in sequences. She also has preferences of integers. She thinks n integers a1, a2, …, an are good.

Now she is interested in good sequences. A sequence x1, x2, …, xk is called good if it satisfies the following three conditions:

The sequence is strictly increasing, i.e. xi < xi + 1 for each i
(1 ≤ i ≤ k - 1).
No two adjacent elements are coprime, i.e. gcd(xi, xi + 1) > 1 for
each i (1 ≤ i ≤ k - 1) (where gcd(p, q) denotes the greatest
common divisor of the integers p and q).
All elements of the sequence are good integers.

Find the length of the longest good sequence.

input
The input consists of two lines. The first line contains a single integer n (1 ≤ n ≤ 10^5) — the number of good integers. The second line contains a single-space separated list of good integers a1, a2, …, an in strictly increasing order