MIXTURES - Mixtures

Harry Potter has n mixtures in front of him, arranged in a row. Each mixture has one of 100 different colors (colors have numbers from 0 to 99).

He wants to mix all these mixtures together. At each step, he is going to take two mixtures that stand next to each other and mix them together, and put the resulting mixture in their place.

When mixing two mixtures of colors a and b, the resulting mixture will have the color (a+b) mod 100.

Also, there will be some smoke in the process. The amount of smoke generated when mixing two mixtures of colors a and b is a*b.

Find out what is the minimum amount of smoke that Harry can get when mixing all the mixtures together.


There will be a number of test cases in the input.

The first line of each test case will contain n, the number of mixtures, 1 <= n <= 100.

The second line will contain n integers between 0 and 99 - the initial colors of the mixtures.


For each test case, output the minimum amount of smoke.


18 19
40 60 20


In the second test case, there are two possibilities:

  • first mix 40 and 60 (smoke: 2400), getting 0, then mix 0 and 20 (smoke: 0); total amount of smoke is 2400
  • first mix 60 and 20 (smoke: 1200), getting 80, then mix 40 and 80 (smoke: 3200); total amount of smoke is 4400

The first scenario is a much better way to proceed.

hide comments
bani_raheja: 2018-03-28 22:14:39

@kmkhan_014 Kaleem Placed!

ameyanator: 2018-02-22 22:22:44

Awesome problem! It was fun to find the dp. However I couldn't code a clean implementation of the top-down approach. The comments pointed towards MCM. Read it,studied it ACed it :D

kmkhan_014: 2018-02-12 09:46:49

@blame the range of co
lors is from 0-99. you have included 100 in your test case.

amulyagaur: 2017-12-21 16:30:35

Took some time... but the outcome was joyful !!
@atharva_sarage: You got it right :)

atharva_sarage: 2017-12-19 05:52:48

what should be the answer for test case
10 80 50 23 14
I am getting 6102

mix 80 and 50
smoke-4000 new colour-30
mix 30 and 10
smoke 4300 new colour 40
mix 40 and 23
smoke 5220 new colour 63
mix 63 and 14
6102 new colour 77

Last edit: 2017-12-19 05:58:00
Muhammad Faishol Amirul Mukminin: 2017-10-01 11:17:44

The first line of the input is not the number of testcases. But you must read until EOF.

Last edit: 2017-10-01 11:24:59
tommy_trash: 2017-08-20 23:37:35

don't use //ios_base::sync_with_stdio(false);//cin.tie(NULL); it will give WA

heisenberg0820: 2017-06-23 10:27:21

Read Till EOF...costed me 3 WA's :(

leafbebop: 2017-06-03 15:17:44

for popat's test case ("100\n1 2 ... 100" one), 120175 or 120675 differs because, I suppose, the last mixture of 100. Note that the problem states colour being from 0 to 99, so it is an invalid input. One deal 100 as colour 0 would get 120175 and others would have 120675. It is hard to say which is correct, for the data case is wrong anyway.

saurabhrathi12: 2017-05-23 20:28:59

Input format mentioned wrong in the question (no of test cases not given). It is correct in example.

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