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Trionic Array I
Determine if an integer array contains indices forming a trionic sequence for efficient pattern detection in interviews.
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Easy · Trionic Array I core interview pattern
Answer-first summary
Determine if an integer array contains indices forming a trionic sequence for efficient pattern detection in interviews.
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This problem requires quickly identifying whether an array can be split into three parts that satisfy the trionic property. The simplest approach is brute force, iterating through potential index pairs to verify the conditions. Understanding how the indices interact is key to avoiding unnecessary computations and common pitfalls in this pattern.
Problem Statement
Given an integer array nums of length n, determine if it is trionic. An array is considered trionic if there exist indices 0 < p < q < n - 1 that satisfy the required sequence properties.
Return true if such indices exist and the array meets the trionic condition, otherwise return false. You must handle arrays with n between 3 and 100 and values between -1000 and 1000.
Examples
Example 1
Input: nums = [1,3,5,4,2,6]
Output: true
Pick p = 2 , q = 4 :
Example 2
Input: nums = [2,1,3]
Output: false
There is no way to pick p and q to form the required three segments.
Constraints
- 3 <= n <= 100
- -1000 <= nums[i] <= 1000
Solution Approach
Brute Force Check
Iterate through all valid pairs of indices (p, q) and verify whether they form a trionic sequence. This ensures correctness but may have higher time complexity for larger arrays.
Prefix and Suffix Tracking
Maintain prefix maxima and suffix minima to quickly check potential trionic splits. This reduces redundant checks and speeds up the core pattern verification.
Early Termination Optimization
Stop iterating once a valid trionic sequence is found. Recognizing this pattern early avoids full array traversal and improves runtime efficiency in common interview test cases.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity depends on the method: brute force can reach O(n^2), prefix/suffix optimization can reduce it to O(n). Space complexity is O(n) if storing auxiliary arrays for prefix and suffix tracking.
What Interviewers Usually Probe
- Looking for correct detection of trionic index patterns in array splits.
- Expect candidates to avoid unnecessary nested loops when possible.
- Interest in whether early termination and index reasoning are applied.
Common Pitfalls or Variants
Common pitfalls
- Failing to respect the strict index constraints 0 < p < q < n-1.
- Checking all pairs without optimization, leading to timeouts for larger n.
- Misidentifying sequences when array values are equal or negative.
Follow-up variants
- Trionic Array II with reversed conditions or modified comparison rules.
- Arrays with additional constraints, such as strictly increasing or decreasing segments.
- Counting the total number of trionic sequences instead of just existence.
FAQ
What is a trionic array in Trionic Array I?
A trionic array contains indices 0 < p < q < n-1 such that the array can be split into three segments meeting the problem's sequence conditions.
Can I use brute force for this problem?
Yes, brute force works for small arrays and helps illustrate the core pattern, but optimizations are preferred for larger inputs.
What are typical constraints to remember?
The array length n ranges from 3 to 100, and each value is between -1000 and 1000, which affects iteration limits.
How can I avoid common mistakes in checking sequences?
Ensure index constraints are strictly followed and consider prefix/suffix tracking to reduce redundant checks.
Does GhostInterview provide step-by-step verification for Trionic Array I?
Yes, it shows which indices form a valid trionic split and explains early termination opportunities in the array.
Solution
Solution 1: Single Pass
We first define a pointer $p$, initially $p = 0$, pointing to the first element of the array. We move $p$ to the right until we find the first element that doesn't satisfy strict increasing order, i.e., $nums[p] \geq nums[p + 1]$. If $p = 0$ at this point, it means the first part of the array doesn't have a strictly increasing section, so we return $\text{false}$ directly.
class Solution:
def isTrionic(self, nums: List[int]) -> bool:
n = len(nums)
p = 0
while p < n - 2 and nums[p] < nums[p + 1]:
p += 1
if p == 0:
return False
q = p
while q < n - 1 and nums[q] > nums[q + 1]:
q += 1
if q == p or q == n - 1:
return False
while q < n - 1 and nums[q] < nums[q + 1]:
q += 1
return q == n - 1