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.
This is a more difficult version of problem 81, but still, as you can’t move left so we can still optimize one column at a time.
First, let’s read the input file into a 2D array:
and initialize another matrix with the same size to store the minimum sum to each of the cells:
In order to avoid miscalculations due to uninitialized cells (i.e. if we had initialized them with 0), I’ve initialized the cells by assuming that we have moved right all the way, hence this line:
else matrix.[row, 0..col] |> Array.sum
which adds up all the cells to the left of, and including, the (row, col) cell.
Next, we’ll add a couple of helper functions to work out the new minimum sum to the cell at (row, col) if we had moved up, down, or right:
We can now use these functions to optimize the columns one at a time.
The tricky thing here is that we might need a few passes to converge onto the true minimum sum path to each of the cells. For example, in order to work out the minimum sum at (row, col) we need to know the minimum sum at (row-1, col) and (row+1, col). But to work out the minimum sum at (row-1, col) we need to know the minimum sum at (row, col)!
So, instead, we’ll recursively try to optimize each cell in the column until it can’t be optimized anymore:
At the end of the snippet above, we optimized the columns one at a time from left to right. (I could have equally included this as part of the recursive function, but it would introduce another level of nesting which is why I opted against it)
And finally, look for the minimum sum on the right-most column in the sum matrix to answer the question:
This solution runs in 9ms on my laptop.
The source code for this solution is here.
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.
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. Enrol now and enjoy a special preorder price of £9.99 (~$13).
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!
Here is a complete list of all my posts on serverless and AWS Lambda. In the meantime, here are a few of my most popular blog posts.
- Lambda optimization tip – enable HTTP keep-alive
- You are thinking about serverless costs all wrong
- Many faced threats to Serverless security
- We can do better than percentile latencies
- I’m afraid you’re thinking about AWS Lambda cold starts all wrong
- Yubl’s road to Serverless
- AWS Lambda – should you have few monolithic functions or many single-purposed functions?
- AWS Lambda – compare coldstart time with different languages, memory and code sizes
- Guys, we’re doing pagination wrong