Codeforces 586F - Lizard Era: Beginning

Problem Statement:
586F - Lizard Era : Beginning

Solution:
This problem has a very cool hashing and look-up idea. (This method is described in the official editorial as well)

First break the array of l[i], m[i], and w[i] into two halves, namely the upper half and the lower half. This helps to reduce down the \(O(3^n)\) component to \(O(3^{n/2})\), which actually allows us to solve the problem given \(n \leq 25\).

Suppose the upper part gives us (a, b, c) as the sum of the chosen configuration of l[i], m[i], and w[i]. Similarly, we suppose (a', b', c') are the sum for the lower part. Hence our job is actually to find such (a', b', c') that \(a+a' = b+b' = c+c' \).