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
Piyush Nirmal: 2015-07-31 05:03:41

a nice problem.

just_code21: 2015-07-29 19:21:40

very good ques for matrix multiplication

rk: 2015-07-11 15:46:01

my bad missed some states as was unknown to matrix chain algo but after that cakewalk :).

palash ahuja: 2015-06-27 14:20:30

dp solution should work

Last edit: 2015-06-27 14:29:51
:.Mohib.:: 2015-06-20 17:12:48

Matrix chain multiplication ;)

Sluggish_Fool: 2015-06-19 13:42:30

100th on a DP!! :D

Pagan Min: 2015-04-08 15:06:21

first question on matrix chain multiplication...nice one

Shubham Bansal: 2015-03-13 15:22:40

a very nice question for starters.. :-)

Sahil Sharma: 2015-01-04 10:47:15

The input file DOES NOT end with a \n and hence if you're following something like :
while( scanf("%d",&n) )
then it would fail since scanf on EOF returns EOF. It's better to use

while( scanf("%d",&n) > 0 )
in such cases.

Anne: 2015-01-04 04:17:04


Last edit: 2015-01-04 04:18:58

Added by:Tomek Czajka
Time limit:3s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET
Resource:Purdue Programming Contest Training