Minimum Amount of Time to Collect Garbage

Problem Description

Ah, the joys of garbage collection! You know, that delightful chore we all love to avoid until the last possible moment. Imagine living in a neighborhood where everyone has their own unique way of disposing of trash. Some folks are meticulous, while others treat their garbage like a game of hide-and-seek. The problem at hand is to figure out how much time it takes to collect all that lovely refuse.

In this LeetCode problem, you are given a list of strings representing the garbage produced by different houses and a list of integers representing the travel time between these houses. Your task is to calculate the minimum amount of time required to collect all the garbage. Spoiler alert: it’s not as easy as it sounds!

Code Solution


class Solution:
    def garbageCollection(self, garbage: list[str], travel: list[int]) -> int:
        prefix = list(itertools.accumulate(travel))

        def getTime(c: str) -> int:
            characterCount = 0
            lastIndex = -1
            for i, s in enumerate(garbage):
                if any(g == c for g in s):
                    lastIndex = i
                characterCount += s.count(c)
            return characterCount + (0 if lastIndex <= 0 else prefix[lastIndex - 1])

        return getTime('M') + getTime('P') + getTime('G')

Approach

The approach taken in this solution is quite clever. It involves calculating the total time required to collect each type of garbage ('M', 'P', and 'G'). The function getTime counts the number of each type of garbage and determines the last index where that type appears. It then adds the travel time to the total time based on the last index found. The final result is the sum of the times for all three types of garbage.

Time and Space Complexity

Time Complexity: O(n), where n is the number of houses. We traverse the garbage list and the travel list a couple of times, leading to a linear time complexity.
Space Complexity: O(n) for storing the prefix sums of the travel times.

Real-World Example

Imagine you’re the neighborhood’s garbage collector, and you have to pick up trash from three different types of houses: those that produce metal, paper, and glass waste. You start at the first house and make your way to the last, but you can’t just run around aimlessly! You need to plan your route based on where the last piece of garbage is located. Just like in this problem, you need to account for the time it takes to travel between houses while ensuring you collect every last bit of trash.