Leetcode 457 - Circular Array Loop

Note:

  • DFS
    • choose an i, start from it and document the path in a set. Also mark the direction with a bool.
    • If next index appears in path, check if the path is length > 1.
    • If curr index is in visited[], then it must be false.
    • If nums[i] is positive but direction is false, then it means the curr path is false.
    • Move to next start index in the for loop.
    • Note that nums[i] might be bigger than length, so we need nums[i] % length sometimes.
    • Note that i + nums[i] might be bigger than length or smaller than 0, we need to map that to an index within the length of nums.

Question:

You are playing a game involving a circular array of non-zero integers nums. Each nums[i] denotes the number of indices forward/backward you must move if you are located at index i:

  • If nums[i] is positive, move nums[i] steps forward, and
  • If nums[i] is negative, move nums[i] steps backward.

Since the array is circular, you may assume that moving forward from the last element puts you on the first element, and moving backwards from the first element puts you on the last element.

A cycle in the array consists of a sequence of indices seq of length k where:

  • Following the movement rules above results in the repeating index sequence seq[0] -> seq[1] -> ... -> seq[k - 1] -> seq[0] -> ...
  • Every nums[seq[j]] is either all positive or all negative.
  • k > 1

Return true if there is a cycle in nums, or false otherwise.

Example:

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Input: nums = [2,-1,1,2,2]
Output: true
Explanation:
There is a cycle from index 0 -> 2 -> 3 -> 0 -> ...
The cycle's length is 3.

Input: nums = [-2,1,-1,-2,-2]
Output: false
Explanation:
The sequence from index 1 -> 2 -> 1 -> ... is not a cycle because nums[1] is positive, but nums[2] is negative.
Every nums[seq[j]] must be either all positive or all negative.

Input: nums = [-1,2]
Output: false
Explanation:
The sequence from index 1 -> 1 -> 1 -> ... is not a cycle because the sequence's length is 1.
By definition the sequence's length must be strictly greater than 1 to be a cycle.

Code:

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/**
* @param {number[]} nums
* @return {boolean}
*/
var circularArrayLoop = function(nums) {
const path = new Set();
let visited = {};
for (let i = 0; i < nums.length; i++) {
path.clear();
if (dfs(i, path, nums[i] > 0)) return true;
}
return false;

function dfs(startIndex, path, isForward) {
const nextStep = isForward ? startIndex : -startIndex;
if (path.has(nextStep)) {
let arr = Array.from(path);
const index = arr.indexOf(nextStep);
return arr.length - index > 1;
}
if (visited[startIndex] !== undefined) return visited[startIndex];
path.add(nextStep);
if (isForward && nums[startIndex] < 0 || !isForward && nums[startIndex] > 0) {
return false;
}
visited[startIndex] = false;
startIndex += nums[startIndex] % nums.length;
if (startIndex >= nums.length) startIndex -= nums.length;
if (startIndex < 0) startIndex += nums.length;
const ans = dfs(startIndex, path, isForward);
return ans;
}
};