Pure Java

Recursive function with a global bit index. I used BiFunctions to list the mathematical operations so I didn't have to use an ugly switch statement. Be aware that this type of code is not thread-safe, I was going for conciseness.

For part 2 I got all the examples correct, but got a 'too low' answer on the real data. It turned out that you shouldn't use == on two Integer objects. I thought they would be auto-unboxed but I guess not? Anyway, lesson learned. Thank goodness IntelliJ warned me of the issue because I would have been searching forever.

https://github.com/arjanIng/advent2021/blob/main/src/advent/Day16.java

List<BiFunction<Long, Long, Long>> operations = new ArrayList<>();

public void day16(String filename) throws IOException {
    String input = Files.lines(Paths.get(filename)).collect(Collectors.toList()).get(0);

    operations.add(Long::sum);
    operations.add((a, b) -> a * b);
    operations.add((a, b) -> a < b ? a : b);
    operations.add((a, b) -> a > b ? a : b);
    operations.add((a, b) -> null);
    operations.add((a, b) -> a > b ? 1L : 0L);
    operations.add((a, b) -> a < b ? 1L : 0L);
    operations.add((a, b) -> a.equals(b) ? 1L : 0L);

    StringBuilder sbuilder = new StringBuilder(new BigInteger(input, 16).toString(2));
    if (input.startsWith("0")) {
        sbuilder.insert(0, "0000");
    }
    if (sbuilder.length() % 4 != 0) {
        int add = (sbuilder.length() / 4 + 1) * 4 - sbuilder.length();
        for (int i = 0; i < add; i++) sbuilder.insert(0, "0");
    }

    long result = calculate(sbuilder.toString());
    System.out.printf("Part 1: %d%n", versionSum);
    System.out.printf("Part 2: %d%n", result);
}

int versionSum = 0;
int pos = 0; // not thread safe!
public long calculate(String sbits) {
    int version = Integer.parseInt(sbits.substring(pos, pos + 3), 2);
    int typeId = Integer.parseInt(sbits.substring(pos + 3, pos + 6), 2);
    versionSum += version;
    pos += 6;
    if (typeId == 4) {
        boolean last = false;
        StringBuilder data = new StringBuilder();
        while (!last) {
            String part = sbits.substring(pos, pos + 5);
            if (part.startsWith("0")) last = true;
            data.append(part.substring(1));
            pos += 5;
        }
        return Long.parseLong(data.toString(), 2);
    } else {
        int lengthTypeId = Integer.parseInt(sbits.substring(pos, pos + 1), 2);
        int l = lengthTypeId == 0 ? 15 : 11;
        int length = Integer.parseInt(sbits.substring(pos + 1, pos + 1 + l), 2);
        pos += l + 1;
        List<Long> results = new ArrayList<>();
        if (lengthTypeId == 0) {
            while (length > 0) {
                int start = pos;
                results.add(calculate(sbits));
                length -= (pos - start);
            }
        } else {
            for (int i = 0; i < length; i++) {
                results.add(calculate(sbits));
            }
        }
        return results.stream().reduce((a, b) -> operations.get(typeId).apply(a, b)).orElseThrow();
    }
}