Visa Interview Question has me stomped for a while

I have been trying to resolve this interview question but so far I have not been able to. Please help.

Question

There are factories in an area which produce a pollutive gas and filters are to be installed at each factory to reduce pollution.

Each filter installed would half the pollution in that factory. Each factory can have multiple filters.
There is a list of N integers representing the level of pollution in each of the N factories in the area.

Find the minimum number of filters needed to half the overall pollution.

E.g. - Let [3, 5, 6, 1, 18] be the list of pollution levels in 5 factories.
Overall pollution = 3+5+6+1+18 = 33 (target is 33/2 = 16.5)

Install a filter in factory given by index=4 -- > pollution levels will be [3, 5, 6, 1, 9] --> 24
Install a filter in factory given by index=4 -- > pollution levels will be [3, 5, 6, 1, 4.5] --> 19.5
Install a filter in factory given by index=2 -- > pollution levels will be [3, 5, 3, 1, 4.5] --> 16.5

Need 3 filters minimum to half the overall pollution.

N is an integer within the range [1....30,000]. Each element in the list is an integer within the range [0....70,000]

I am not being lazy, here's my incorrect attempt:

public static int getMinimumFilters(double[] pollutionLevels) {
    double totalPollution = Arrays.stream(pollutionLevels).sum();
    double targetPollution = totalPollution / 2.0;
    int numFilters = 0;
    double currentPollution = 0;
    double tempPollution = 0;

    Arrays.sort(pollutionLevels);

    for (double i = pollutionLevels.length -1; i >= 0; i--) {
        currentPollution = (totalPollution - pollutionLevels[(int) i]) + pollutionLevels[(int) i]/2;
        numFilters++;
        if (currentPollution <= targetPollution) {
            break;
        }

    }

    return numFilters;
}

public static void main(String[] args) {
    double[] pollutionLevels = {3, 5, 6, 1, 18};
    System.out.println("Minimum number of filters needed: " + getMinimumFilters(pollutionLevels));
}

My next line of thought was to sum the array and then use the difference between the sum and the targetPollution value to somehow check which array values should be halved to achieve the target.

Any help is appreciated.

This is a classic heap problem where you need to keep the elements sorted while insertion and deletion, in this case we remove max pollution from heap and insert half it's value and pull the next max value right from top of the heap, we could use PriorityQueue in java

public static int getMinimumFilters(double[] pollutionLevels) {
    double currentPollution = Arrays.stream(pollutionLevels).sum();
    double targetPollution = currentPollution / 2.0;
    PriorityQueue<Double> queue = new PriorityQueue<>(10, Collections.reverseOrder());
    for(double level : pollutionLevels) {
        queue.offer(level);
    }
    int numFilters = 0;
    while(currentPollution > targetPollution) {
        double maxPollution = queue.poll(); 
        double pollutionAfterFilter = maxPollution/2.0;
        queue.offer(pollutionAfterFilter); 
        currentPollution -= pollutionAfterFilter;
        numFilters++;
    }
    return numFilters;
}

public static void main(String[] args) {
    double[] pollutionLevels = {3, 5, 6, 1, 18};
    System.out.println("Minimum number of filters needed: " + getMinimumFilters(pollutionLevels));
}