Synthesis: merge and mutate

The merge pattern — ArrayList's most exam-typical synthesis task:

"Merge two sorted lists into one sorted result (duplicates allowed)."

public static ArrayList<Integer> merge(ArrayList<Integer> a, ArrayList<Integer> b) {
    ArrayList<Integer> out = new ArrayList<Integer>();
    int i = 0, j = 0;
    while (i < a.size() && j < b.size()) {
        if (a.get(i) <= b.get(j)) { out.add(a.get(i)); i++; }
        else { out.add(b.get(j)); j++; }
    }
    while (i < a.size()) { out.add(a.get(i)); i++; }
    while (j < b.size()) { out.add(b.get(j)); j++; }
    return out;
}

Reading it as machines: a two-pointer comparison while both lists have material, then two "drain the remainder" sentinel loops. The <= matters for stability — with <=, ties take from a first; a student writing < is still correct here, but in exam variants asking for stable merge of records, that one character is the difference.

Second synthesis: positional operations. "Swap the halves of list in place" or "insert value after every even element" (backward insert loop! insertion shifts right just like removal shifts left). Whenever an ArrayList problem mutates, ask: forward or backward? Removal from the front region, insertion, and anything touching consecutive elements → backward. Pure reading or end-appending → forward is fine.