2784. Check if Array is Good
Description
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 base[n], is n = 3. However, base[3] has four elements but array nums has three. Therefore, it can not be a permutation of base[3] = [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 base[n], is n = 3. It can be seen that nums is a permutation of base[3] = [1, 2, 3, 3] (by swapping the second and fourth elements in nums, we reach base[3]). 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 base[n], is n = 1. It can be seen that nums is a permutation of base[1] = [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 base[n], is n = 4. However, base[4] has five elements but array nums has six. Therefore, it can not be a permutation of base[4] = [1, 2, 3, 4, 4]. So the answer is false.
Constraints:
1 <= nums.length <= 100
1 <= num[i] <= 200
Solutions
Solution 1: Counting
We can use a hash table or array $cnt$ to record the number of occurrences of each element in the array $nums$. Then we determine whether the following conditions are met:
- $cnt[n] = 2$, i.e., the largest element in the array appears twice;
- For $1 \leq i \leq n-1$, it holds that $cnt[i] = 1$, i.e., except for the largest element, all other elements appear only once.
If the above two conditions are met, then the array $nums$ is a good array, otherwise it is not.
The time complexity is $O(n)$, and the space complexity is $O(n)$. Where $n$ is the length of the array $nums$.
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