Yan Cui

I help clients go faster for less using serverless technologies.

**This article is brought to you by**

I never fully recovered my workspace setup when I upgraded my laptop two years ago, and I still miss things today. If only I had known about Gitpod back then…

#### Problem

In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, byonly moving to the right and down, is indicated in bold red and is equal to 2427.

Find the minimal path sum, in matrix.txt (right click and ‘Save Link/Target As…’), a 31K text file containing a 80 by 80 matrix, from the top left to the bottom right by only moving right and down.

#### Solution

I took a similar approach to the one I used for problem 18 and iteratively work out what’s the shortest path sum leading up to each of the cells in the matrix.

Considering that a brute force approach will need to walk through the 80 x 80 matrix a total of 92045125813734238026462263037378063990076729140 times…so that’s clearly not an option! So instead, for each cell *(x, y)* in the matrix, we consider the two possibilities:

- the path has traversed down from cell
*(x-1, y)* -
the path has traversed right from cell

*(x, y-1)*

the shortest path sum from top left to *(x, y)*, let’s call it *sps(x, y)* will be equal to the lesser of *sps(x-1, y) + (x, y)* and *sps(x, y-1) + (x, y)*. Obviously there are some special cases, such as when *x = 0* and when *y = 0*, as you can see the different handling in the match pattern.

**Whenever you’re ready, here are 3 ways I can help you:**

**Production-Ready Serverless**: Join 20+ AWS Heroes & Community Builders and 1000+ other students in levelling up your serverless game. This is your one-stop shop for**quickly levelling up your serverless skills**.- I help clients
**launch product ideas**,**improve their development processes**and**upskill their teams**. If you’d like to work together, then let’s**get in touch**. **Join my community on Discord**, ask questions, and join the discussion on all things AWS and Serverless.

Pingback: Project Euler - Problem 82 Solution | theburningmonk.com