Minimum Amount of Time to Collect Garbage

class Solution {
public:
    int totalCollection(vector<string>& trash, vector<int>& distances) {
        int metal = 0, paper = 0, glass = 0;
        int total = trash[0].size();
    
        for (int i = trash.size() - 1; i > 0; i--) {
            for (char item : trash[i]) {
                if (item == 'M') {
                    metal = 1;
                } else if (item == 'P') {
                    paper = 1;
                } else {
                    glass = 1;
                }
            }
    
            total += distances[i - 1] * (metal + paper + glass) + trash[i].size();
        }
    
        return total;
    }
};

In the problem titled "Minimum Amount of Time to Collect Garbage," you work with a C++ solution that calculates the amount of time needed to pick up different types of garbage, segregated as metal, paper, and glass. Also, the provided code involves tracking how far collectors must travel.

• Initialize three counters (metal, paper, glass) to track the presence of each type of garbage on the route.
• Start with counting the garbage items at the first location (index 0), setting the initial total time to the number of items at this location.
• From the second location onwards, loop through the trash collection in reverse, effectively evaluating from the last location back to the first. This approach helps in adding up the distances moved between locations efficiently.

For every house visited:

1. Check each trash item, categorizing it as 'M' for metal, 'P' for paper, and 'G' for glass.
2. Adjust the respective counters to 1 whenever an item type is detected thus indicating if subsequent locations also need to collect that type of trash.
3. Calculate the travel time to the next location based on whether collectors need to collect metal, glass, or paper trash there. Multiply this need by the respective distances.
4. Add the items at that location to the total collection time.

The function returns the total time spent collecting trash across all locations, combined with the time spent traveling between the locations based on the requirements to pick up each type of trash.

This algorithm is efficient, leveraging simple accumulation and condition checking for each type of garbage, ensuring that all items are picked up in minimal time while adjusting for travel distances appropriately.

class Solution {
    
    public int collectGarbage(String[] bins, int[] roads) {
        Boolean hasMetal = false, hasPaper = false, hasGlass = false;
        int totalTime = bins[0].length();
    
        for (int index = bins.length - 1; index > 0; index--) {
            hasMetal |= bins[index].contains("M");
            hasPaper |= bins[index].contains("P");
            hasGlass |= bins[index].contains("G");
            totalTime +=
            roads[index - 1] * ((hasMetal ? 1 : 0) + (hasPaper ? 1 : 0) + (hasGlass ? 1 : 0)) +
            bins[index].length();
        }
    
        return totalTime;
    }
}

This Java solution addresses the problem of calculating the minimum amount of time needed to collect garbage from multiple bins distributed along a road. Each bin can contain three types of garbage: Metal (M), Paper (P), and Glass (G), and the travel time between bins is given by an array of road times.

• Start by initializing three boolean flags (hasMetal, hasPaper, hasGlass) to track the presence of each type of garbage as false.

• The initial total time is set to the contents of the first bin since there's no travel needed to reach the first bin.

• Loop through each bin from the end to the beginning (except the first one):

  • Update each garbage type flag if the current bin contains that type of garbage using the contains method of the string.
  • Calculate the travel time to the current bin by checking the presence of each type of garbage flagged true. Multiply the presence flags (converted to integers) by the road time to the current bin. This logic thus only adds road time if there is still relevant garbage to collect moving forward in the list.
  • Update the total time by adding both the travel time (if any) and the time taken to collect garbage at the current bin (i.e., the length of the bin string).

• Finally, return the accumulated totalTime, which represents the minimum time required to collect all types of garbage from all bins effectively. This solution ensures that the garbage truck only travels as needed based on the remaining garbage types to be collected, optimizing the collection process.

class Solution:
    def collectGarbage(self, trash, roads):
        hasMetal, hasPaper, hasGlass = False, False, False
        result = len(trash[0])
    
        for idx in range(len(trash) - 1, 0, -1):
            hasMetal |= "M" in trash[idx]
            hasPaper |= "P" in trash[idx]
            hasGlass |= "G" in trash[idx]
            result += roads[idx - 1] * (int(hasMetal) + int(hasPaper) + int(hasGlass)) + len(trash[idx])
    
        return result

The given Python script defines a class Solution with a method collectGarbage that calculates the minimum time required to collect garbage. Here is a concise breakdown of how the solution achieves this:

• The method accepts two arguments: trash, a list where each element represents the garbage present at each house (using 'M' for metal, 'P' for paper, and 'G' for glass), and roads, a list of integers where each value represents the time to travel between two adjacent houses.

• The method initializes three boolean variables hasMetal, hasPaper, and hasGlass to track whether metal, paper, or glass is needed to be collected as the garbage truck moves through the houses.

• The first house's garbage pickup time is directly added to the total time, calculated by the length of the string in trash[0].

• The solution iterates from the last house back to the second, updating if metal, paper, or glass is present at each house. For each house, if that type of garbage is needed (as determined by the cumulative presence of that garbage type in the houses visited so far), the time to travel via the roads from the previous location to the current one is added to the result. This time is multiplied by the sum of booleans converted to integers (1 if true, 0 if false) for hasMetal, hasPaper, and hasGlass, indicating which types of garbage are required based on past observations.

• The garbage collection time at each house (as the length of the garbage string) is also added to the result.

• Finally, the total minimum time required to collect all garbage is returned.

This method efficiently calculates the time by ensuring the truck only stops for necessary garbage types as it progresses from the last house back to the first, optimizing travel and collection times.