My Tangle with Number 494
Alright, let’s talk about this thing, number 494. Popped up recently, looked like some kind of coding challenge people pass around. So, I decided to give it a whirl myself, see what it was all about.
First off, I had to figure out what the actual task was. Looked like you get a list of numbers, positive ones, and a target number. The goal? Slap either a plus or a minus sign in front of each number in the list. Then, add ’em all up. You gotta find out how many different ways you can assign those pluses and minuses to make the final sum equal the target number.
My first gut feeling? Just try everything. For the first number, you can add it or subtract it. Then for the second number, add or subtract. Keep going down the line. Sounds like a branching path, right? So, recursion seemed like the obvious first thing to try.
I started coding up a recursive function. Something like: take the current position in the number list and the sum accumulated so far.
- If you’re past the end of the list, check if the current sum equals the target. If yes, you found one way, return 1. If no, return 0.
- Otherwise, call the function again for the next position (index + 1). Make two calls: one where you add the current number `nums[index]` to the sum, and another where you subtract `nums[index]` from the sum. Add the results of these two calls together. That’s how many ways you can get the target from the current point.
Seemed logical. I wrote it down, ran it with a small example list. Worked fine. Felt pretty good. Then, I tried it with a slightly longer list of numbers… and boom. It took forever. Like, ages. The computer was just churning away. Clearly, this simple recursive approach was way too slow for anything non-trivial. It was trying the same calculations over and over again down different branches.
Hitting the Wall and Finding a Fix
Okay, plan A wasn’t cutting it. This performance issue was a big wall. I realized the problem: I was recalculating the number of ways to get a certain sum from a certain index multiple times. For example, getting a sum of 5 by the third number might happen through `+1+2+2` or `+1-2+6` (just making up numbers), but from that point onwards (say, index 3 with sum 5), the remaining calculation is identical regardless of how you got there.
This screamed “optimization needed”. The classic fix for this kind of overlapping subproblem in recursion is memoization. Basically, caching the results.
So, I tweaked my recursive function. I added a simple dictionary or map, let’s call it `memo`. The key would be something representing the state, like `(index, current_sum)`. Before doing any recursive calls, I’d check: is `(index, current_sum)` already in my `memo`?
- If yes, great! Just return the stored value right away. No need to compute again.
- If no, then go ahead, do the recursive calls like before. But! Before returning the result, store it in the `memo` with the key `(index, current_sum)`.
Implemented this change. It wasn’t too much extra code. Ran the same ‘long’ list that choked the previous version. Night and day difference! It finished super quick. The cache was doing its job, avoiding all that repeated work.
Could also think about this using dynamic programming from the bottom up, building a table of possibilities. It’s kinda the same idea, just structured differently. Sometimes DP feels a bit cleaner if you can map out the states properly, but memoization on the recursion often feels more natural to code up first when you see the overlapping parts.
So, that’s the story of me wrestling with number 494. Started with a simple idea, hit a performance snag, and used a standard trick (memoization) to make it efficient. A good reminder that the first approach isn’t always the best, and sometimes you gotta look for those repeating patterns to speed things up. Just part of the process, you know?
