class Solution: def garbageCollection(self, garbage: List[str], travel: List[int]) -> int:

Problem Breakdown

1. We need to count the total time required to collect garbage from different houses.
2. Each type of garbage (represented in the garbage list) has a unique collection time based on the distance to travel from one house to another specified in the travel list.

Relevant Concepts

1. The time to collect garbage from houses is the sum of the lengths of the strings in garbage, which represent the amount of garbage at each house.
2. After collecting garbage, for each type of garbage (represented by different strings in garbage), we must account for the travel time only if there's more garbage of the same type beyond the last house that contains it.

Analysis and Detail

1. Calculate the time spent collecting garbage directly from each house.
2. Determine the travel time required for each type of garbage, summing the appropriate entries from the travel list.

Steps to Implement the Solution

1. Initialize total time to zero.
2. For each type of garbage:
   • Add the length of the string to total time.
   • If there are any subsequent houses with that type of garbage, add the corresponding travel time.
3. Since the travel is dependent only on houses up to the last occurrence of each type, we can keep track of the index of the last occurrence during the iteration.

Example Implementation

from typing import List

class Solution:
    def garbageCollection(self, garbage: List[str], travel: List[int]) -> int:
        total_time = 0
        last_index = {'M': -1, 'P': -1, 'G': -1}  # tracks the last index of each type
        
        # Calculate collection time and last index
        for i in range(len(garbage)):
            total_time += len(garbage[i])
            if garbage[i] in last_index:
                last_index[garbage[i]] = i
        
        # Add travel time based on last index of each garbage type
        for i in last_index.values():
            if i != -1 and i < len(travel):
                total_time += sum(travel[:i])  # sum travel times until the last index
        
        return total_time

# Example usage:
solution = Solution()
result = solution.garbageCollection(["G","P","G"], [2, 4, 3])
print(result)  # Outputs the total time needed

Final Answer

The garbageCollection function calculates the total time required to collect garbage and includes travel times efficiently, returning the required result in an optimal manner.