Jimmy owns a garden in which he has planted N trees in a row. After a few years, the trees have grown up and now they have different heights.
Jimmy pays much attention to the aesthetics of his garden. He finds his trees aesthetically pleasing if they alternately increase and decrease in height (..., shorter, taller, shorter, taller, ...).
These are examples of aesthetically pleasing trees:
Graphical representation of the example
These are examples of trees that are not aesthetically pleasing:
Graphical representation of the example
Note that two adjacent trees cannot have equal heights. It may turn out that some trees have to be shortened in order to keep the look of the garden aesthetically pleasing. Jimmy is a lazy type, so he wants to put as little energy as possible into obtaining the desired look for his garden. What is the minimum number of trees that should be shortened so that Jimmy would find his garden aesthetically pleasing?
Write a function:
class Solution { public int solution(int[] A); }
that, given an array A consisting of N integers, where A[K] denotes the height of the K-th tree, returns the minimum number of trees that should be shortened so that the garden looks aesthetically pleasing.
Examples:
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Given A = [5, 4, 3, 2, 6] your function should return 1. Jimmy can obtain the desired pattern by decreasing the height of the second tree to 2.
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Given A = [3, 7, 4, 5] your function should return 0, since the garden already looks aesthetically pleasing.-
Write an efficient algorithm for the following assumptions:
N is an integer within the range [1..100,000]; each element of array A is an integer within the range [2..1,000].