LeetCode #1752 — EASY

Check if Array Is Sorted and Rotated

Build confidence with an intuition-first walkthrough focused on array fundamentals.

The Problem

Problem Statement

Given an array nums, return true if the array was originally sorted in non-decreasing order, then rotated some number of positions (including zero). Otherwise, return false.

There may be duplicates in the original array.

Note: An array A rotated by x positions results in an array B of the same length such that B[i] == A[(i+x) % A.length] for every valid index i.

Example 1:

Input: nums = [3,4,5,1,2]
Output: true
Explanation: [1,2,3,4,5] is the original sorted array.
You can rotate the array by x = 2 positions to begin on the element of value 3: [3,4,5,1,2].

Example 2:

Input: nums = [2,1,3,4]
Output: false
Explanation: There is no sorted array once rotated that can make nums.

Example 3:

Input: nums = [1,2,3]
Output: true
Explanation: [1,2,3] is the original sorted array.
You can rotate the array by x = 0 positions (i.e. no rotation) to make nums.

Constraints:

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

Step 01

Brute Force Baseline

Problem summary: Given an array nums, return true if the array was originally sorted in non-decreasing order, then rotated some number of positions (including zero). Otherwise, return false. There may be duplicates in the original array. Note: An array A rotated by x positions results in an array B of the same length such that B[i] == A[(i+x) % A.length] for every valid index i.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array

Example 1

[3,4,5,1,2]

Example 2

[2,1,3,4]

Example 3

[1,2,3]

Core Insight

What unlocks the optimal approach

Brute force and check if it is possible for a sorted array to start from each position.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1752: Check if Array Is Sorted and Rotated
class Solution {
    public boolean check(int[] nums) {
        int cnt = 0;
        for (int i = 0, n = nums.length; i < n; ++i) {
            if (nums[i] > nums[(i + 1) % n]) {
                ++cnt;
            }
        }
        return cnt <= 1;
    }
}

// Accepted solution for LeetCode #1752: Check if Array Is Sorted and Rotated
func check(nums []int) bool {
	cnt := 0
	for i, v := range nums {
		if v > nums[(i+1)%len(nums)] {
			cnt++
		}
	}
	return cnt <= 1
}

# Accepted solution for LeetCode #1752: Check if Array Is Sorted and Rotated
class Solution:
    def check(self, nums: List[int]) -> bool:
        return sum(nums[i - 1] > v for i, v in enumerate(nums)) <= 1

// Accepted solution for LeetCode #1752: Check if Array Is Sorted and Rotated
impl Solution {
    pub fn check(nums: Vec<i32>) -> bool {
        let n = nums.len();
        let mut count = 0;
        for i in 0..n {
            if nums[i] > nums[(i + 1) % n] {
                count += 1;
            }
        }
        count <= 1
    }
}

// Accepted solution for LeetCode #1752: Check if Array Is Sorted and Rotated
function check(nums: number[]): boolean {
    const n = nums.length;
    return nums.reduce((r, v, i) => r + (v > nums[(i + 1) % n] ? 1 : 0), 0) <= 1;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(1)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.