Check if an Array Was Sorted and Rotated

easy Searching and Sorting

Print true if the array is a non-decreasing sorted array that was rotated some number of places (zero places also counts). Otherwise print false. Duplicates are allowed.

Constraints

1 <= n <= 10^5

Examples

Input

5
3 4 5 1 2

Output

true

rotation
arrays

Solutions

Best approachTime O(n)Space O(1)

A sorted array has no fall around the circle. A rotation creates exactly one fall: the place where the biggest number meets the smallest. Two or more falls cannot come from a rotation.

Same code works in Java810172125Basic features only, so nothing changes between versions.

/*
 * Problem : Sorted and rotated?
 * Input   : n, then n integers.
 * Output  : true or false.
 * Approach: Count the falls.
 * Time    : O(n)
 * Space   : O(1)
 * Java    : 8 or newer.
 */
import java.util.Scanner;

public class Main {
    // This method solves the task. It receives the input and returns the answer.
    static boolean solve(int[] a) {
        // Step 1: In a sorted and rotated array, going around the circle the numbers fall at most once.
        int falls = 0;
        for (int i = 0; i < a.length; i++) {
            // Step 2: Compare each number with the next one. The last number is compared with the first.
            if (a[i] > a[(i + 1) % a.length]) {
                falls++;
            }
        }
        return falls <= 1;
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int size = scanner.nextInt();
        int[] a = new int[size];
        for (int i = 0; i < size; i++) {
            a[i] = scanner.nextInt();
        }
        System.out.println(solve(a));
    }
}

Hints (2)

Why is the last number compared with the first?
How many falls does [1, 2, 3] have around the circle?