Problem 44787. What can you get for exactly amount of money(harder)

Created by li haitao

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Inspired by "Problem 42996. what can you get for exactly amount of money" https://ww2.mathworks.cn/matlabcentral/cody/problems/42996-what-can-you-get-for-exactly-amount-of-money Problem 42996 is a good problem, but the test suit is too weak.

You go to store, where each product has price. Prices are in vector

v = [ 195 125 260 440 395 290] and you have amount of money s=570

Question is what can you buy, if you want to use whole amount of money

For this data answer is

res=[ 125 125 125 195]

The answer may not be unique, return any feasible answer. Do not cheat please.

In this hard version, 1 <= length(v) <= 50 1 <= s <= 10000000019 (1e10 + 19)

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Last Solution submitted on Oct 29, 2023

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Binbin Qi on 21 Nov 2018

Because memory, some solution will not be allowed.

Karl Ezra Pilario on 4 Jun 2020

This problem merely requires a fast search heuristic that works only for the given test cases but not necessarily for the general case. For instance, the accepted solutions here will not pass for v = (1:50)+1e8 and s = 1e10+19. Also, the memory limit would be exceeded for v = 1:50 and s = 1e10+19.

Rafael S.T. Vieira on 22 Jul 2020

The tip here is that numbers must be the same order of magnitude. For instance, if I have to add the integers 6 and 4 until they add to 1e20, it will take forever. However, the numbers 6e19 and 4e19 (multiples of 6 and 4) will find the sum 1e20 with one iteration.

Rafael S.T. Vieira on 22 Jul 2020

And, I don't agree with Karl, my code finds a solution for v=1:50 and s=1e10+19 within 4 seconds. And for v = 1:50+1e8 within 12 seconds (at an i5-3230M CPU @ 2.60GHz). I am not sure there is a solution for (1:50)+1e8. It seems unlikely since 19 will be hard to appear from a magnitude of 1e8 within the range of s=1e10+19. In order words, we are trying to find the prime number 10000000019, and the smallest number that we are adding is 100000001 from (1:50)+1e8. If we add 100000001 one hundred times, the smallest number with the same order of 10000000019 is 10000000100.

Karl Ezra Pilario on 28 Jan 2021

Apparently, my solution worked faster when I sorted the vector "v" in descending order before doing anything else. Thanks Rafael S.T. Vieira. Now, I can find a solution for v=1:50 and s=1e10+19 within a few seconds as well.

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Problem 44787. What can you get for exactly amount of money(harder)

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Problem 44787. What can you get for exactly amount of money(harder)

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