Head Meets Tail

Open Data Structures implements ArrayQueue with three fields: the backing array a, a head index j, and a count n. add(x) writes a[(j + n) % a.length] then increments n; remove() reads a[j], advances j, and decrements n.

An engineer drops n to save a word and tracks a tail index instead:

int a[8];
int head = 0, tail = 0;

bool empty(void) { return head == tail; }
void push(int x)  { a[tail] = x; tail = (tail + 1) % 8; }
int  pop(void)    { int x = a[head]; head = (head + 1) % 8; return x; }

Eight push calls run with no pop. What is the state?

The buffer works correctly but can never hold more than seven values, since the eighth push is rejected

All eight values are stored, but head == tail == 0, so empty() now reports true on a completely full buffer

The eighth push overwrites a[0], so the oldest value is silently lost

Nothing breaks: the modulo keeps every index in range, and head == tail is reachable only when the queue is empty