Editorial for COCI '15 Contest 5 #3 Perica
Submitting an official solution before solving the problem yourself is a bannable offence.
We need to calculate how many times each number from the input appears as the largest of numbers in every combination. If we sort the numbers in ascending order, we can see that this number is going to be maximal in an array of numbers if all other numbers are located to its left. Therefore, the number is maximal the exact number of times as the number of ways to choose numbers out of the first numbers. If we denote the number of ways to choose numbers out of numbers as , then it is easy to see that .
Using this relation, we can calculate each .
The solution is therefore the sum of the product of the corresponding and , where is the value on that location.