Project Euler – Problem 83 Solution

Check out my new course Learn you some Lambda best practice for great good! and learn the best practices for performance, cost, security, resilience, observability and scalability.

The problem description is here, and click here to see all my other Euler solutions in F#.

 

This is a more difficult version of problem 82, and now you can move in all four directions!

As before, we start by loading the input data into a 2D array:

Prob83_01

and initialize another matrix of the same size to hold the minimum sum leading to each cell:

Prob83_02v2

What we have done differently this time though, is to choose initial defaults:

  • for the top-left corner (0, 0) the minimum sum is itself
  • for all other cells at (row, col) we’ll always traverse right and then down
    • if row = 0, then this equates to only move right until we reach col
    • if col = 0, then this equates to only move down until we reach row

e.g.

Prob83_03

Next, as we did for the problem 82, we’ll add a couple of helper to help us traverse both matrices:

Prob83_04

and we’ll find the new minimum sum to each cell by taking the minimum from the four directions:

Prob83_05

Unlike before, we can’t isolate to optimizing one column at a time, and instead we’ll need to traverse the whole matrix. For better cache locality, we’ll traverse row first and recursively optimize the whole matrix until no more optimization is possible:

Prob83_06

Finally, find the final value for the bottom-right corner of the sum matrix:

Prob83_07

This solution runs in 73ms on my laptop.

 

The source code for this solution is here.

Liked this article? Support me on Patreon and get direct help from me via a private Slack channel or 1-2-1 mentoring.
Subscribe to my newsletter


Hi, I’m Yan. I’m an AWS Serverless Hero and the author of Production-Ready Serverless.

I specialise in rapidly transitioning teams to serverless and building production-ready services on AWS.

Are you struggling with serverless or need guidance on best practices? Do you want someone to review your architecture and help you avoid costly mistakes down the line? Whatever the case, I’m here to help.

Hire me.


Check out my new podcast Real-World Serverless where I talk with engineers who are building amazing things with serverless technologies and discuss the real-world use cases and challenges they face. If you’re interested in what people are actually doing with serverless and what it’s really like to be working with serverless day-to-day, then this is the podcast for you.


Check out my new course, Learn you some Lambda best practice for great good! In this course, you will learn best practices for working with AWS Lambda in terms of performance, cost, security, scalability, resilience and observability. We will also cover latest features from re:Invent 2019 such as Provisioned Concurrency and Lambda Destinations. Enrol now and start learning!


Check out my video course, Complete Guide to AWS Step Functions. In this course, we’ll cover everything you need to know to use AWS Step Functions service effectively. There is something for everyone from beginners to more advanced users looking for design patterns and best practices. Enrol now and start learning!


Are you working with Serverless and looking for expert training to level-up your skills? Or are you looking for a solid foundation to start from? Look no further, register for my Production-Ready Serverless workshop to learn how to build production-grade Serverless applications!

Find a workshop near you