The completed trace table is:
- Row 1: a=0, b=1, c=1
- Row 2: a=1, b=1, c=2
- Row 3: a=1, b=2, c=3
- Row 4: a=2, b=3, c=5
This algorithm generates the Fibonacci sequence (1, 1, 2, 3, 5, ...) and stops when a number greater than 4 is generated. A trace table helps track the state of variables through each step of the algorithm.
- **Initialisation:** `a` = 0, `b` = 1.
- **Iteration 1:**
- `c` = `a` + `b` = 0 + 1 = 1.
- Is `c > 4`? No.
- `a` becomes `b` (so `a` = 1).
- `b` becomes `c` (so `b` = 1).
- *Table state: a=1, b=1, c=1* (The question implies recording the state when c is calculated)
- **Iteration 2:**
- `c` = `a` + `b` = 1 + 1 = 2.
- Is `c > 4`? No.
- `a` becomes `b` (so `a` = 1).
- `b` becomes `c` (so `b` = 2).
- *Table state: a=1, b=2, c=2*
- **Iteration 3:**
- `c` = `a` + `b` = 1 + 2 = 3.
- Is `c > 4`? No.
- `a` becomes `b` (so `a` = 2).
- `b` becomes `c` (so `b` = 3).
- *Table state: a=2, b=3, c=3*
- **Iteration 4:**
- `c` = `a` + `b` = 2 + 3 = 5.
- Is `c > 4`? Yes.
- The loop terminates.
- *Table state: a=2, b=3, c=5*
The trace table should reflect the values of a, b, and c at the point `c` is calculated in each loop iteration.