Floyd's Implementation

Here is Floyd's cycle detection:

function floydCycleDetection(f, start):
    slow = start
    fast = start

    // Phase 1: Detect if cycle exists
    while true:
        slow = f(slow)
        fast = f(f(fast))
        if slow == fast:
            break

    // Phase 2: Find cycle start
    slow = start
    while slow != fast:
        slow = f(slow)
        fast = f(fast)

    cycleStart = slow

    // Phase 3: Find cycle length
    length = 1
    fast = f(slow)
    while fast != slow:
        fast = f(fast)
        length = length + 1

    return (cycleStart, length)

Time: $O(n)$. Space: $O(1)$.