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
karlo_2107: 2020-10-18 11:45:29

WA in 1 go! :(

sandipan789: 2020-10-07 09:07:55

Tougher version of the same problem is
"Minimum Cost to Merge Stones" leetcode

gnomegeek: 2020-08-06 19:10:31

WTF !! Number of testcases not given. Use while(cin >> n) { ... }. Costed me 7 WA's. GG.

Last edit: 2020-08-06 19:10:52
anshumankr001: 2020-07-23 20:40:53

Number of test cases is not given. Keep that in mind, rest is just a slight modification of matrix chain multiplication. There are no wrong test cases.

indabhi_007: 2020-06-09 23:23:57

guys use matrix multiplication with some changes

coding_joshi26: 2020-05-30 13:58:14

**Wrong answer**
13 57 43
this will give 2451 not 2491

this_variable: 2020-05-22 07:38:37

People Writing AC in one go are HEREBY invited to NASA to go to mars..as earth have had enough of idiots

ayushpandia: 2020-04-28 20:00:01

Most comments be like AC in 1 go!! What on the earth you all wanna prove!

saquib_imam: 2020-04-26 00:26:15

ac in one go!!

ks1999: 2020-04-23 03:42:20

13 57 43 -> 2491
Just make sure that you covered all cases and used dp properly.
I had a lot of problems with tiny tiny bug

Added by:Tomek Czajka
Time limit:3s
Source limit:50000B
Memory limit:1536MB
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