Homework: Collatz Steps

作业: Collatz 步数

≈ 30 min · python-loops python-conditionals · Open in WolfCode

The textbook's own §7.3 example as a graded problem. The math is unsolved; the program is straightforward.

The rule

Start with a positive integer n. Each step:

If n is even → n = n // 2
If n is odd → n = 3 * n + 1

Stop when n == 1. Count steps.

Worked trace — `n = 3`

Python · runnable

# step 0: n = 3  (odd)  → 3*3 + 1 = 10
# step 1: n = 10 (even) → 10 // 2  = 5
# step 2: n = 5  (odd)  → 3*5 + 1 = 16
# step 3: n = 16 (even) → 16 // 2  = 8
# step 4: n = 8  (even) → 8  // 2  = 4
# step 5: n = 4  (even) → 4  // 2  = 2
# step 6: n = 2  (even) → 2  // 2  = 1
# step 7: n = 1  STOP

# Let's verify with code:
def collatz_steps(n):
    steps = 0
    while n != 1:
        if n % 2 == 0:
            n = n // 2
        else:
            n = 3 * n + 1
        steps += 1
    return steps

print(collatz_steps(3))     # → 7
print(collatz_steps(27))    # → 111   (the famous case)

Loading Python runtime (~5 MB, one-time)…

The integer-vs-float trap

Why // matters

# Wrong:
n = 4
n = n / 2          # n is now 2.0 (a float)
print(n, type(n))

# Right:
n = 4
n = n // 2         # n is now 2 (an int)
print(n, type(n))

Loading Python runtime (~5 MB, one-time)…

Why n = 27 is famous

The sequence takes 111 steps and reaches a peak of 9232 before coming down. Yet 27 isn't special — the sequence is just chaotic. From Think Python §7.3: "So far, no one has been able to prove [it terminates for all positive n] or disprove it."

Acceptance criteria

All 7 tests pass
Uses a while loop (not recursion)
Uses // for the even step (not /)
Returns an int

Homework: Collatz Steps

The rule

Worked trace — n = 3

The integer-vs-float trap

Why n = 27 is famous

Acceptance criteria

Worked trace — `n = 3`