Short Problem Definition:

A company has requested to streamline their product allocation strategy, and given n products, each of which has an associated value, you are required to arrange these products into segments for processing. There are infinite segments indexed as 1, 2, 3 and so on.

Link

Product Distribution

Complexity:

time complexity is O(N)

space complexity is O(1)

Execution:

There are a few things you need to keep in mind here:

• the buckets must all be the same size and can not be empty
• the last bucket can contain the remainder of the N/M elements
• sort the array so that the largest values are as far out as possible

Keep an eye out for the edge conditions.

Solution:

MODULO = 1000000007

def maxScore(a, m):
    n = len(a)
    bucket = 1
    result = 0
    
    a.sort()
    
    i = 0
    while i + (2*m) <= n:
        result += sum(a[i:i+m])*bucket
        i += m
        bucket += 1
        
        result %= MODULO
        
    result += sum(a[i:])*bucket
    
    return result % MODULO