2784 - Check if Array is Good.

Easy

You are given an integer array nums. We consider an array good if it is a permutation of an array base[n].

base[n] = [1, 2, ..., n - 1, n, n] (in other words, it is an array of length n + 1 which contains 1 to n - 1 exactly once, plus two occurrences of n). For example, base[1] = [1, 1] and base[3] = [1, 2, 3, 3].

Return true if the given array is good, otherwise return false.

Note: A permutation of integers represents an arrangement of these numbers.

Example 1:

Input: nums = 2, 1, 3

Output: false

Explanation: Since the maximum element of the array is 3, the only candidate n for which this array could be a permutation of basen, is n = 3. However, base3 has four elements but array nums has three. Therefore, it can not be a permutation of base3 = 1, 2, 3, 3. So the answer is false.

Example 2:

Input: nums = 1, 3, 3, 2

Output: true

Explanation: Since the maximum element of the array is 3, the only candidate n for which this array could be a permutation of basen, is n = 3. It can be seen that nums is a permutation of base3 = 1, 2, 3, 3 (by swapping the second and fourth elements in nums, we reach base3). Therefore, the answer is true.

Example 3:

Input: nums = 1, 1

Output: true

Explanation: Since the maximum element of the array is 1, the only candidate n for which this array could be a permutation of basen, is n = 1. It can be seen that nums is a permutation of base1 = 1, 1. Therefore, the answer is true.

Example 4:

Input: nums = 3, 4, 4, 1, 2, 1

Output: false

Explanation: Since the maximum element of the array is 4, the only candidate n for which this array could be a permutation of basen, is n = 4. However, base4 has five elements but array nums has six. Therefore, it can not be a permutation of base4 = 1, 2, 3, 4, 4. So the answer is false.

Constraints:

• 1 <= nums.length <= 100

• 1 <= num[i] <= 200