Loop State and Tuple Assignment

Intuition

Each Fibonacci number is the sum of the previous two: 0, 1, 1, 2, 3, 5, 8, … To generate them you only need to remember the last two values — a sliding window of state.

Precise explanation

$F_0 = 0,\; F_1 = 1,\; F_k = F_{k-1} + F_{k-2}$ for $k \ge 2$.

Tuple assignment evaluates the whole right-hand side first, then assigns:

a, b = 0, 1
for _ in range(n):
    out.append(a)
    a, b = b, a + b    # new a = old b, new b = old a + old b

Without tuple assignment you would need a temporary variable (t = a + b; a = b; b = t). Writing a = b then b = a + b is a bug: a has already changed.

_ is a conventional name for a loop variable you don't use.

Worked example (n = 6)

Result: [0, 1, 1, 2, 3, 5].

Common mistakes

• Naive recursion fib(k-1) + fib(k-2) — exponential time; n = 40 takes seconds.
• Special-casing n = 1 and n = 2 with hard-coded lists and getting n = 0 wrong.
• Sequential (not simultaneous) assignment, as described above.

Why this matters

Carrying a small amount of state through a loop is the core of running averages, momentum in optimizers (DL-14) and discounted returns in RL (RL-01).

References

• The Python Tutorial (Python 3.15.1 docs) — Python Software Foundation (S001)