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
try2catch: 2016-01-20 10:38:45

Spoiler Alert! - "Solution"
//read about matrix chain multiplication
//follow 4 basic steps of DP of bottom-up or top-down (as per your choice).

abhishekrahul: 2016-01-16 08:13:24

getting tle, why??

saketj: 2015-12-22 11:16:04

[code removed]
can anyone please help which cases am I missing ,I am getting WA but checked some test cases and got correct answers..

Last edit: 2015-12-22 15:42:19
rajesh1995: 2015-12-18 13:21:09

can we pick any two consecutive mixtures?

n_bukuri: 2015-12-16 12:43:59

Finally AC :) trying to solve for 2 days...output should be 0 for N=1

irbis9: 2015-11-20 21:09:16

My second dp on my own, confidence level is increasing.

Jian Luo: 2015-10-18 03:23:54

my first DP, it took me 1 week to do it correctly. But it worth the time. :-)

Harsh Vardhan Ladha: 2015-09-07 13:15:36

Top-Down DP

rahverma: 2015-09-07 07:40:08

kripya gyani na bane. apna gyan apne paas rakhe (don't spoil the party)

Surbhi Jain: 2015-07-31 07:05:07

Given link not working..pls see

Added by:Tomek Czajka
Time limit:3s
Source limit:50000B
Memory limit:1536MB
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Resource:Purdue Programming Contest Training