Trionic Array I

Difficulty: Easy | Acceptance: 49.50% | Paid: No Topics: Array

You are given a 0-indexed integer array nums. An array is called trionic if it consists of exactly three distinct elements and the sum of the first two elements equals the third element.

Return true if nums is a trionic array, otherwise return false.

• Examples
• Constraints
• Direct Conditional Check
• Set-based Validation

Examples

Example 1

Input:

nums = [1,3,5,4,2,6]

Output:

true

Explanation: Pick p = 2, q = 4:

nums[0…2] = [1, 3, 5] is strictly increasing (1 < 3 < 5).

nums[2…4] = [5, 4, 2] is strictly decreasing (5 > 4 > 2).

nums[4…5] = [2, 6] is strictly increasing (2 < 6).

Example 2

Input:

nums = [2,1,3]

Output:

false

Explanation: There is no way to pick p and q to form the required three segments.

Constraints

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

Direct Conditional Check

Intuition We can verify the definition of a trionic array by explicitly checking the three required conditions: the array length must be 3, all elements must be distinct, and the sum of the first two must equal the third.

Steps

• Check if the length of nums is exactly 3. If not, return false.
• Check if nums[0], nums[1], and nums[2] are all distinct from each other.
• Check if nums[0] + nums[1] == nums[2].
• Return true only if all checks pass.

from typing import List

class Solution:
    def isTrionicArray(self, nums: List[int]) -> bool:
        if len(nums) != 3:
            return False
        if nums[0] == nums[1] or nums[1] == nums[2] or nums[0] == nums[2]:
            return False
        return nums[0] + nums[1] == nums[2]

Complexity

• Time: O(1)
• Space: O(1)
• Notes: This is the most efficient approach as it avoids any overhead from data structures.

Set-based Validation

Intuition We can utilize a Set data structure to efficiently check for distinctness. By inserting all elements into a Set, we can verify if the count of unique elements is exactly 3.

Steps

• Check if the length of nums is exactly 3.
• Insert all elements of nums into a Set.
• Check if the size of the Set is 3 (ensuring all elements are distinct).
• Check if nums[0] + nums[1] == nums[2].
• Return true if all conditions are met.

from typing import List

class Solution:
    def isTrionicArray(self, nums: List[int]) -> bool:
        if len(nums) != 3:
            return False
        distinct_elements = set(nums)
        if len(distinct_elements) != 3:
            return False
        return nums[0] + nums[1] == nums[2]

Complexity

• Time: O(1) - Since the array size is fixed at 3, operations are constant.
• Space: O(1) - The Set stores at most 3 integers.
• Notes: While functionally correct, this approach has slightly higher constant overhead than direct comparison.