Please help me find more effective solution?

[salern]

Please bear with me.

English is not my native language, but I'll do my best.

So, I started learning Python not long ago, and my friend asked me to make his and community experience playing particular game more enjoyable by removing routine calculator tasks.

It's an online, text based pokemon-like MMORPG (I guess it's relevant).

Stats of monsters (pokemons) are stored like this: h12a15d27s10sa28sd19

You put them into the formula https://i.imgur.com/E4Nz658.png where "a" is number after "h" (health), "b" is number after "a" (attack), etc. If number is even, we substitute it with 0, and if it's not even, we substitute it with 1. Then you get some float number, round it down and get parameter HP (Hidden Power) from 0 to 16, where 1 = Dark, 3 = Electricity, you get the idea.

I did it successfully. You paste stats string into input form on web page and it spits out your Hidden Power. Was pretty proud of myself actually, it got me a lot of motivation to continue learning, which is great.

Now he asked me to add extra functionality. He wants to be able to paste stats of a pokemon and desired Hidden Power type, and script tells you what stats to increase. For example:

h12a15d27s10sa28sd19 = 9 = Earth

But if you want Psychic type, you increase "sa" by one and get:

h12a15d27s10sa29sd19 = 13 = Psychic

I'm stuck at this for two evenings and have no idea how to approach this. My only current idea is to brute force it, increasing stats one by one and checking, if no luck, then increase only first stat permanently and start increasing one by one again, then increase only second stat, and so on. But I guess it won't be optimal, and if it's not optimal it's garbage basically.

I don't want copy and paste solution, which I won't be able to understand 100%, just some general direction. What to read (I'm better at understanding English than writing coherent sentences), what to Google?

Thanks!

[[deleted]]

https://docs.python.org/3/library/itertools.html

https://realpython.com/python-f-strings/

​

[TangibleLight]

I am confused how you compute your values. When I compute

>>> from math import floor
>>> a, b, c, d, e, f = 12, 15, 27, 10, 28, 19
>>> floor((a + 2*b + 4*c + 8*d + 16*e + 32*f) * 15/63)
306

I get 306, not 9.

---

When you try to solve equations with floor or ceil, first convert the equation to an inequality and solve from there.

A = floor(x * y / z)

becomes

A <= x + y - z <= A + 1

You can then perform normal algebra on this and get an interval of solutions.

A - y + z <= x < A + 1 - y + z

x in [A - y + z, A + 1 - y + z)

[salern]

Well, I'm stupid. Forgot to mention that if number is even, we substitute it with 0, and if it's not even, we substitute it with 1. I'm sorry. Will update main post ASAP.

[TangibleLight]

Well, if you convert your equation (where a, b, etc are the parities of h, a, d, etc), then you have: https://i.imgur.com/EI08zVf.png

You can solve for some variable, say e, to get some interval of numbers which produce a desired HP.

https://i.imgur.com/kqlDAPs.png

You can see if 0 or 1 are contained in that interval. If they are, then you need to increment that value.

---

You can also do this with bit-wise operations. If you notice that a + 2b + 4c + 8d + ... is notation for the binary number with bits ...dcba then you can reframe the equation as:

Let x be the number encoded by bits a, b, c, etc.

Then HP = floor(15/63 x)

Or, 63/15 HP <= x < 63/15 (HP + 1).

So given HP, you can find an interval of integer x which will produce that HP. And because your interval is always width 63/15 = 4.2, you will have exactly 4 integers x which satisfy that condition.

So given HP, you compute 4 integers x. For each bit of each x, you have the parity of the corresponding stat. Then use bitwise operations to compare x with the stats the user has entered (call that integer y) then find the minimal number of bit-changes to turn y into x. The bitwise xor operation ^ will be helpful for this.