Golden Pyramid
Our Robo-Trio need to train for future journeys and treasure hunts. Stephan has built a special flat model of a pyramid. Now the robots can train for speed gold running. They start at the top of the pyramid and must collect gold in each room, choose to take the left or right path and continue down to the next level. To optimize their gold runs, Stephan need to know the maximum amount of gold that can be collected in one run.
Consider a list of lists in which the first list has one integer and each consecutive list has one more integer then the last. Such a list of lists would look like a pyramid. You should write a program that will help Stephan find the highest possible sum on the most profitable route down the pyramid. All routes down the pyramid involve stepping down and to the left or down and to the right.
Tips: Think of each step down to the left as moving to the same index location or to the right as one index location higher. Be very careful if you plan to use recursion here.
Input: A pyramid as a list of lists of integers.
Output: The maximum possible sum as an integer.
Examples:
assert (
count_gold(
[
[1],
[2, 3],
[3, 3, 1],
[3, 1, 5, 4],
[3, 1, 3, 1, 3],
[2, 2, 2, 2, 2, 2],
[5, 6, 4, 5, 6, 4, 3],
]
)
== 23
)
assert (
count_gold(
[
[1],
[2, 1],
[1, 2, 1],
[1, 2, 1, 1],
[1, 2, 1, 1, 1],
[1, 2, 1, 1, 1, 1],
[1, 2, 1, 1, 1, 1, 9],
]
)
== 15
)
assert count_gold([[9], [2, 2], [3, 3, 3], [4, 4, 4, 4]]) == 18
assert (
count_gold(
[[2], [7, 9], [0, 8, 6], [4, 7, 6, 8], [0, 5, 5, 4, 1], [9, 1, 0, 1, 6, 9]]
)
== 35
)
How it is used: this is a classical problem which shows you how to use dynamic programming. This concept is a core component of many optimizations tasks.
Preconditions:
- 0 < len(pyramid) ≤ 20;
- all(all(0 < x < 10 for x in row) for row in pyramid).
CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.
In order to install CheckiO client you'll need installed Python (version at least 3.8)
Install CheckiO Client first:
pip3 install checkio_client
Configure your tool
checkio --domain=py config --key=
Sync solutions into your local folder
checkio sync
(in beta testing) Launch local server so your browser can use it and sync solution between local file end extension on the fly. (doesn't work for safari)
checkio serv -d
Alternatevly, you can install Chrome extension or FF addon
checkio install-plugin
checkio install-plugin --ff
checkio install-plugin --chromium
Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.
