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.
Input
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.
Output
For each test case, output the minimum amount of smoke.
Example
Input: 2 18 19 3 40 60 20 Output: 342 2400
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
kushal_singh:
20230224 11:38:37
great question!!! 

fizz_05:
20230120 06:25:17
awesome problem.


old_monk1:
20220731 21:32:43
For C++ users getting RTE, don't use > ios_base::sync_with_stdio(false) as well as cin.tie(NULL) 

cloverr20:
20220407 20:58:59
@tommy_trash dude your comment saved me, thanks a lot!! 

siba_tripathy:
20211225 19:44:12
how to input no of testcases is not clearly mentioned in question. use while(cin>>n); 

yasser1110:
20210716 11:29:04
Maybe its more useful to think of this problem as a divide and conquer recursion problem. 

Waseem Ahmed:
20210704 04:32:15
Got an AC only after


atultyagi:
20210527 23:48:36
Modified version of Matrix Chain multiplication, good problem but keep in mind ,number of test cases are not given use while(cin >> n ) Last edit: 20210527 23:49:05 

anurag_20:
20210221 06:46:19
Awesome use of Matrix chain multiplication concept


shubham7811:
20210123 23:50:01
ikd why it is showing worng answer

Added by:  Tomek Czajka 
Date:  20050503 
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 