Maximum Difference Between Adjacent Elements in a Circular Array — Easy Problem & Solution

Problem statement

The array nums is circular: the element after the last one is the first one again.

Return the maximum absolute difference between any two adjacent elements.

Example 1

Input: nums = [1,2,4]
Output: 3
Explanation: The wrap-around pair (4, 1) differs by 3, more than any straight neighbour.

Example 2

Input: nums = [-5,-10,-5]
Output: 5
Explanation: |-5 - (-10)| = 5.

Example 3

Input: nums = [7]
Output: 0
Explanation: A single element is its own neighbour.

Constraints

• 1 <= nums.length <= 100
• -100 <= nums[i] <= 100

How to solve Maximum Difference Between Adjacent Elements in a Circular Array

The circular neighbour of index i is (i + 1) % n, so one loop over every index covers all n adjacent pairs, wrap included.

Approach

1. Start best at 0.
2. For each i, compute |nums[i] - nums[(i + 1) % n]|.
3. Keep the largest value seen.

Why it works

In a circle of n elements there are exactly n adjacent pairs, one per starting index, and (i + 1) % n enumerates each exactly once.

Complexity

• Time — O(n)
• Space — O(1)

Pitfalls

• Looping only to n - 2 misses the wrap-around pair, which is often the answer.
• Forgetting the absolute value reports a negative difference as small.

Reference solution

Python

from typing import List

def maxAdjacentDistance(nums: List[int]) -> int:
    n = len(nums)
    return max(abs(nums[i] - nums[(i + 1) % n]) for i in range(n))

JavaScript

var maxAdjacentDistance = function(nums) {
    var n = nums.length, best = 0;
    for (var i = 0; i < n; i++) {
        var d = Math.abs(nums[i] - nums[(i + 1) % n]);
        if (d > best) best = d;
    }
    return best;
};

Also on the editorial tab: C, C#, C++, Go, Java, Kotlin, PHP, Ruby, Rust, Swift, TypeScript.

More arrays problems

• Special Array I Easy
• Type of Triangle Easy
• Find the Losers of the Circular Game Easy
• Form Smallest Number From Two Digit Arrays Easy
• Delete Greatest Value in Each Row Easy
• The Employee That Worked on the Longest Task Easy