Pramp - Award Budget Cuts Solution - algorithm

I have a hard time wrapping my head around the solution given by Pramp for the problem:
Award Budget Cuts
https://www.pramp.com/challenge/r1Kw0vwG6OhK9AEGAyWV
I do not seem to be able to find some other explanations of what they are doing in their solution.
I kinda understand the other ways of solving it, suggested by other users here:
https://codereview.stackexchange.com/questions/194272/award-budget-cuts-implementation-in-java
But I am trying to understand the reasoning behind the:
surplus1 = surplus0 - 1*(grantsArray[0]-grantsArray[1])
surplus2 = surplus1 - 2*(grantsArray[1]-grantsArray[2])
surplus3 = surplus2 - 3*(grantsArray[2]-grantsArray[3])
Really don't understand that part...

Related

In a lua for loop what is a # used for?

I know how for loops work and I use them quite often but also seem to often come across a # in others' code and I want to know what it is for and how to use it. An example of this would be:
for i = 1, #npc do local v = npc[i]
I cant seem to find anything online regarding this, maybe my searches just aren't good but it would be nice if someone could explain it for me, thanks.
In Lua, # is the length operator. for i = 1, #npc essentially loops from 1 to the length of the npc array.
As was already pointed out, it gets the length of a list. However, there's another thing worth pointing out: that for loop is suboptimal and unidiomatic. It would be better written as for i, v in ipairs(npc) do. In general, using # in a for loop is almost always the wrong thing to do.

Algorithm design manual solution to 1-8

I'm currently reading through The Algorithm Design Manual by Steven S. Skiena. Some of the concepts in the book I haven't used in almost 7 years. Even while I was in college it was difficult for me to understand how some of my classmates came up with some of these proofs. Now, I'm completely stuck on one of the exercises. Please help.
Will you please answer this question and explain how you came up with what to use for your Base case and why each step proves why it is valid and correct. I know this might be asking a lot, but I really need help understanding how to do these.
Thank you in advance!
Proofs of Correctness
Question:
1-8. Proove the correctness of the following algorithm for evaluating a polynomial.
$$P(x) = a_nx_n+a_n−1x_n−1+⋯+a_1x+a_0$$
&function horner(A,x)
p=A_n
for i from n−1 to 0
p=p∗x+Ai
return p$
btw, off topic: Sorry guys, I'm not sure how to correctly add the mathematical formatting for the formula. I tried by addign '$' around each section. Not sure why that isn't working.
https://cs.stackexchange.com/ is probably better for this. Also I'm pretty sure that $$ formatting only works on some StackExchange sites. But anyways, think about what this algorithm is doing at each step.
We start with p = A_n.
Then we take p = p*x + A_{n-1}. So what is this doing? We now have p = x*A_n + A_{n-1}.
I'll try one more step. p = p*x + A_{n-2} so now p = (x^2)*A_n + x*A_{n-1} + A{n-2} (here x^2 means x to the power 2, of course).
You should be able to take it from here.

What is this prolog output trying to say?

Years ago in college,I tinkered with some prolog, but that's long forgotten, so I count as a complete beginnner again (humbling!)
Anyway, I was playing with some of Bruce Tate's code, and came up with what I thought was a sudoku solver for the full (9x9) game. But, when I run it, it generates some very odd output:
Solution = [_#3(2..3),_#24(2:7),_#45(2..3:5:7),_#66(2..3:8),_#87(2..3:5..6:8),4,_#121(2:5..6),1,9,6,8,_#194(2..5:7:9),_#215(1..3:9),_#236(2..3:5:9),_#257(1..2:5:9),_#278(2:4..5),_#299(4:7),_#320(5:7),_#341(1..2),_#362(2:4),_#383(2:4..5:9),_#404(1..2:9),_#425(2:5..6:9),7,3,_#472(4:6),8,4,1,_#532(2:8),_#553(2:8),7,3,9,5,6,7,5,_#689(6:8),_#710(4:8..9),_#731(4:6:8..9),_#752(6:8..9),1,2,3,_#828(2..3),9,_#862(2..3:6),5,1,_#909(2:6),7,8,4,8,_#990(2:4:7),1,6,_#1037(2..5:9),_#1058(2:5:9),_#1079(4..5),_#1100(3..4:7),_#1121(5:7),5,_#1163(4:6..7),_#1184(4:6..7),_#1205(1:3..4:8),_#1226(3..4:8),_#1247(1:8),_#1268(4:6:8),9,2,9,3,_#1341(2:4:6),7,_#1375(2:4..5:8),_#1396(1..2:5:8),_#1417(4..6:8),_#1438(4:6),_#1459(1:5)]
yes
I was expecting ... well, frankly I was half expecting total failure :) but I thought that only numbers could show up in this output. What's it trying to tell me with those #-tagged things, and stuff in parens that looks like ranges? Is it trying to say there are many possible solutions and it's telling me all at once (seems unlikely as it's very unhelpful if it is) or is this some kind of error state (in which case, why does it compile my code and say "yes" to this query?)
Any insight gratefully received!
I think it's the result of a set of constraints not sufficiently strong to determine a solution without search. For instance, _#3(2..3) could means that a variable named _#3 could assume values in range 2..3. You could try to label the variables, something like
..., labeling([], Solution).
Syntax details depend on your solver, of course...

LightsOut game solving method "reduced echolean ".Does it always gives correct result?

I am studing the algorithm given here, and
somewhere it is claimed that it is efficent and always give correct result.
But, I try to run the algorithm and it is not giving me correct or efficent output for the following patterns.
For 5 x 5 grid, where (n) is light number and 0/1 state whethere the light is on/off, 1 ON and 0 OFF.
(1)1 (2)0 (3)0 (4)0 (5)0 the output should be 1,7,13,19,25(Pressing this light will make the full grid OFF. But what I am getting is this
(6)0 (7)1 (8)0 (9)0 (10)0 3,5,6,7,8,10,13,16,18,19,20,21,23.
(11)0 (12)0 (13)1 (14)0 (15)0
(16)0 (17)0 (18)0 (19)1 (20)0
(21)0 (22)0 (23)0 (24)0 (25)1
While for some pattern it is giving me correct output as below.
(1)0 (2)0 (3)0 (4)0 (5)1 the output should be 5,9,13,17,21, and the algorithm is giving me correct result.
(6)0 (7)0 (8)0 (9)1 (10)0
(11)0 (12)0 (13)1 (14)0 (15)0
(16)0 (17)1 (18)0 (19)0 (20)0
(21)1 (22)0 (23)0 (24)0 (25)0
If somebody need a code let me know I can post it.
Can please somebody let me know if this methods will always give correct as well as efficient result or not ?
(I'm the author of the code you linked to.) To the best of my knowledge, the code is correct (and I'm sure that the high-level algorithm of using Gaussian elimination over GF(2) is correct). The solution it produces is guaranteed to solve the puzzle, though it's not necessarily the minimal number of button presses. The "efficiency" I was referring to in the writeup refers to the time complexity of solving the puzzle overall (it can solve a Lights Out grid in polynomial time, as opposed to the exponential-time brute-force solution of trying all possible combinations) rather than to the "efficiency" of the generated solution.
I actually don't know any efficient algorithms for finding a solution requiring the minimum number of button presses. Let me know if you find one!
Hope this helps!

Is it a bad practice writing long one-liner code?

I found myself keep writing pretty long one-liner code(influenced by shell pipe), like this:
def parseranges(ranges, n):
"""
Translate ":2,4:6,9:" to "0 1 3 4 5 8 9...n-1"
== === == === ===== =========
"""
def torange(x, n):
if len(x)==1:
(x0, ) = x
s = 1 if x0=='' else int(x0)
e = n if x0=='' else s
elif len(x)==2:
(x0, x1) = x
s = 1 if x0=='' else int(x0)
e = n if x1=='' else int(x1)
else:
raise ValueError
return range(s-1, e)
return sorted(reduce(lambda x, y:x.union(set(y)), map(lambda x:torange(x, n), map(lambda x:x.split(':'), ranges.split(','))), set()))
I felt ok when I written it.
I thought long one-liner code is a functional-programming style.
But, several hours later, I felt bad about it.
I'm afraid I would be criticized by people who may maintain it.
Sadly, I've get used to writing these kind of one-liner.
I really want to know others' opinion.
Please give me some advice. Thanks
I would say that it is bad practice if you're sacrificing readability.
It is common wisdom that source code is written once but read many times by different people. Therefore it is wise to optimize source code for the common case: being read, trying to understand.
My advice: Act according to this principle. Ask yourself: Can anybody understand any piece of my code more easily? When the answer is not a 100% "No, I can't even think of a better way to express the problem/solution." then follow your gut feeling and reformat or recode that part.
Unless performance is a major consideration, readability of the code should be given high major priority. Its really important for its maintainability.
A relevant quote from the book Structure and Interpretation of Computer Programs.
"Programs should be written for people to read, and only incidentally for machines to execute."
(Update 2022-03-25: My answer refers to a previous revision of the question.)
The first and third examples are acceptable to me. They are close enough to the application domain so that I can easily see the intention of the code.
The second example is much too clever. I don't even have an idea about its purpose. Can you rewrite it in maybe five lines, giving the variables longer names?

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