Part 1

We are in a lobby with elevators offline and the escalator needs power. Power comes from batteries labeled 1-9 that are arranged in banks. Each bank is represented as a sequence of digits in our input. Turning on a subset of batteries in a bank produces a number which is the digits of the battery you choose in order.

The goal is to maximize the output from each bank and sum them all

• Turn on exactly two batteries per bank
• The number that is formed by the two digits (in order) is the joltage for the bank
• Sum the maximum joltage from each bank for the total output

Approach

Each bank is a sequence of digits Think 987654321111111

In order to maximize the two digit number: - We need the largest first digit that occurs before the largest second digit - Since the sequence is not very long, we can try all possible pairs of positions (i, j) with i < j - Compute the number formed by that pair and track the maximum

Repeat for all banks and sum the results.

Part 2

• Turn on exactly 12 batteries per bank
• The number formed by the 12 digits is the bank’s joltage
• Sum these maximal numbers across all banks

This could be done by using a greedy stack approach Essentially:

• Brute force all combinations is infeasible
• Get the largest 12 digit number while respecting the order
  • Scan left to right in the bank
  • Keep a stack of chosen digits forming the current sequence
• Repeat for each bank and sum the outputs

Solution

You can find the Github code for this problem here