http://codeforces.com/contest/566/problem/F
F. Clique in the Divisibility Graph
time limit per test
memory limit per test
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output
As you must know, the maximum clique problem in an arbitrary graph is NP-hard. Nevertheless, for some graphs of specific kinds it can be solved effectively.
Just in case, let us remind you that a clique in a non-directed graph is a subset of the vertices of a graph, such that any two vertices of this subset are connected by an edge. In particular, an empty set of vertexes and a set consisting of a single vertex, are cliques.
Let's define a divisibility graph for a set of positive integers A = {a1, a2, ..., an} as follows. The vertices of the given graph are numbers from set A, and two numbers ai and aj (i ≠ j) are connected by an edge if and only if either ai is divisible by aj, or aj is divisible by ai.
You are given a set of non-negative integers A. Determine the size of a maximum clique in a divisibility graph for set A.
Input
The first line contains integer n (1 ≤ n ≤ 106), that sets the size of set A.
The second line contains n distinct positive integers a1, a2, ..., an (1 ≤ ai ≤ 106) — elements of subset A. The numbers in the line follow in the ascending order.
Output
Print a single number — the maximum size of a clique in a divisibility graph for set A.
Examples
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output
Note
In the first sample test a clique of size 3 is, for example, a subset of vertexes {3, 6, 18}. A clique of a larger size doesn't exist in this graph.
设DP[i]表示第i个数字结尾的最大合法情况。
那么递推过来的话,要在前i - 1个数字中,是a[i]约数的,才能递推过来dp[i],那么需要把a[i]分解因子。这样要sqrtn复杂度。超时。
可以考虑以第a[i]个数递推去后面,就是去更新[i + 1,以后的数字。
那么只有k * a[i]的才能递推过去。
但是有些会重复,
3 4 24这样,24既可以从3递推过来,也可以从4递推过来。那么娶个max即可。
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