LeetCode 457: Circular Array Loop (Explained, With Video)

The problem: you get a circular array of non-zero integers. From index i you move nums[i] steps (forward if positive, backward if negative, wrapping around). Return true if there is a cycle that

1. has more than one element, and
2. moves in only one direction (all positive or all negative).

The idea: fast and slow pointers

This is cycle detection, like Linked List Cycle (LeetCode 141), with two extra rules. From each start index:

• Move slow one step and fast two steps.
• Stop the walk as soon as a step would change direction or land on itself (a one-element loop).
• If slow and fast meet, there is a valid cycle.

To keep it O(n), once a start fails, walk its path again and set those entries to 0. Any later walk that reaches a 0 can stop immediately, so every index is visited a constant number of times.

Python solution

def circularArrayLoop(nums: list[int]) -> bool:
    n = len(nums)

    def nxt(i):
        return (i + nums[i]) % n

    for i in range(n):
        if nums[i] == 0:
            continue
        forward = nums[i] > 0

        def ok(j):  # same direction, not visited, not a 1-element loop
            return nums[j] != 0 and (nums[j] > 0) == forward and nxt(j) != j

        slow = fast = i
        while ok(fast) and ok(nxt(fast)):
            slow, fast = nxt(slow), nxt(nxt(fast))
            if slow == fast:
                return True

        j = i  # mark this failed path so it is never walked again
        while nums[j] != 0 and (nums[j] > 0) == forward:
            k = nxt(j)
            nums[j] = 0
            j = k
    return False

Python’s % always returns a non-negative result, so backward moves wrap correctly. In Java or C++ use ((i + nums[i]) % n + n) % n.

Test cases

Video walkthrough

Worked live in an SDE Skills daily coding session (6,000+ views).

Practice problems like this with others, free

SDE Skills is a volunteer-run 501(c)(3) nonprofit with free daily LeetCode practice on Zoom. See the schedule, the free DSA practice sheet and LeetCode 564: Find the Closest Palindrome.

Join a session on Zoom Join our free Discord