The four loop machines

Almost every AP loop is one of four machines. Name the machine, and the code writes itself.

Accumulator — collapse a collection to one number.

int total = 0;
for (int i = 0; i < arr.length; i++) {
    total += arr[i];
}

Initialize to the identity of the operation: 0 for sums, 1 for products, arr[0] for max/min, "" for building a String.

Counter — count events, return the count.

int hits = 0;
for (int v : arr) {
    if (meets(v)) {
        hits++;
    }
}

A counter is an accumulator whose addition is + 1. Same identity rule (0), same shape.

Flag — did anything ever fire?

boolean found = false;
for (int v : arr) {
    if (v == target) {
        found = true;
    }
}
return found;

The default comes from the vacuous case (nothing fired → false). The early-exit form — return true; inside, return false; after — is the same machine with the exit moved.

Sentinel scan — find where, not whether.

int at = -1;
for (int i = 0; i < arr.length && at == -1; i++) {
    if (arr[i] == target) {
        at = i;
    }
}
return at;

-1 means "absent" by exam convention. The && at == -1 stops scanning at the first hit — without it you return the last occurrence (Module 1's bug, promoted to a pattern).