95-monotone-travel.md

Problem:

Story

Peter lives on a hill, and he always moans about the way to his home. "It's always just up. I never get a rest". But you're pretty sure that at least at one point Peter's altitude doesn't rise, but fall. To get him, you use a nefarious plan: you attach an altimeter to his backpack and you read the data from his way back at the next day.

Task

You're given a list of compareable elements:

Ord a => [a]

heights = [Integers or Floats]

heights = [Integers or Floats]

heights = [h1, h2, h3, …, hn]

heights = new int[0 ... 100]

Your job is to check whether for any x all successors are greater or equal to x.

isMonotone [1,2,3] == True
isMonotone [1,1,2] == True
isMonotone [1]     == True
isMonotone [3,2,2] == False

is_monotone([1,2,3]) == True
is_monotone([1,1,2]) == True
is_monotone([1])     == True
is_monotone([3,2,1]) == False
is_monotone([3,2,2]) == False

is_monotone([1,2,3]) == True
is_monotone([1,1,2]) == True
is_monotone([1])     == True
is_monotone([3,2,1]) == False
is_monotone([3,2,2]) == False

isMonotone([1,2,3]) == true
isMonotone([1,1,2]) == true
isMonotone([1])     == true
isMonotone([3,2,1]) == false
isMonotone([3,2,2]) == false

Kata.IsMonotone(new int[] {1,2,3}) => true
Kata.IsMonotone(new int[] {1,1,2}) => true
Kata.IsMonotone(new int[] {1})     => true
Kata.IsMonotone(new int[] {3,2,1}) => false
Kata.IsMonotone(new int[] {3,2,2}) => false

If the list is empty, Peter has probably removed your altimeter, so we cannot prove him wrong and he's still right:

isMonotone []      == True

isMonotone([])     == True

is_monotone([])     == True

isMonotone([])     == True

Kata.IsMonotone(new int[] {}) => true

Such a sequence is also called monotone or monotonic sequence, hence the name isMonotone.

Solution