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
gaurav_2000: 2018-11-08 09:42:28

AC in 1 go!

sachinspoj: 2018-11-04 13:51:56

AC in one go :)
Easy Peasy!!

jmr99: 2018-09-27 21:33:53

****spoiler !!****
matrix chain multiplication.

supriyanta: 2018-08-23 23:26:19

before thinking learn matrix chain multiplication

ayushgupta1997: 2018-08-15 08:55:24

Awesome Problem :) That's why I love spoj :p

masterchef2209: 2018-08-10 08:02:44

good question, learning about MCM would be a great help.
(spoiler-read only if you are stuck even after trying for a long time)

use a array of pairs
for a subproblem from [i,j] try to find min(smoke[i,k]+smoke[k+1,j]+smoke_generated after mixing these two) over all i<=k<j. store it in dp[i][j].second. store new chemical in dp[i][j].first corresponding to min smoke.
print dp[0][n-1].second

yobro: 2018-06-26 23:20:27

ac in one go :D

castor21: 2018-06-17 08:06:58

dont use your brain it will give wrong answer

krp1999: 2018-06-06 12:19:02

How to handle such type of input in python3??

x0r19x91: 2018-03-31 23:27:18

AC in one go !

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