Dynamic Programming Optimization with Convex Hull Trick
Given an array a of N integers a1, a2, a3, … aN you have to find the longest alternating sub-sequence of this array .
An alternating sequence b1, b2 … bk, k>=1 is a sequence that has the 2 following properties:
-
b1 < b2 < b3 <…..< bk - The signs alternate between adjacent elements, i.e, if b1 > 0 then b2<0, b3 >0 and so on. Alternatively, if b1<0, then b2>0, b3<0 and so on.
A sub sequence of array a is a sequence obtained by dropping some elements of the array a.
Here is the formal definition.
It is guaranteed that the array a contains no element equal to 0.
Input:
The first line contains a single integer N, denoting the size of the array.
The next line contains N integers , denoting the array a.
Output:
Print a single integer - the length of the longest alternating sub-sequence.
Constraints:
1<=N<=5000
|ai|<=109, ai not equal to 0
