LeetCode 3640 | Trionic Array II | Java | Hard | Dynamic Programming Kadane Algorithm | CodeByTushu
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In today’s video, we solve LeetCode 3640 - Trionic Array II using Dynamic Programming and Two Pointers in Java.
A trionic subarray requires finding four indices l, p, q, and r in strictly increasing index order, such that the elements strictly increase from l to p, strictly decrease from p to q, and strictly increase from q to r. The key structural insight is that any interior element in a strictly decreasing sequence cannot serve as either the peak p or the valley q without violating adjacent strict monotonicity. Therefore, every valid decreasing segment must span an entire maximal strictly decreasing run from a local peak down to a local valley.
To maximize the total subarray sum, we precompute the maximum suffix sum of strictly increasing elements leading into each peak and the maximum prefix sum of strictly increasing elements descending out of each valley using Kadane-style dynamic programming arrays. By combining these optimal left and right extensions with the exact sum of each candidate decreasing segment, we identify the global maximum trionic subarray sum in linear O(n) time and O(n) auxiliary space.
🔥 Problem Highlights
✅ Discovered the strict peak-and-valley boundary invariant for every decreasing sequence
✅ Evaluated maximal strictly decreasing segments without redundant nested scans
✅ Precomputed maximum strictly increasing suffix sums with forward Kadane DP
✅ Precomputed maximum strictly increasing prefix sums with backward Kadane DP
✅ Handled negative values safely by using 64-bit signed integers and negative infinity initializations
✅ Achieved optimal O(n) time and O(n) space complexity
⏱️ TIMESTAMPS
00:00 Intro
00:54 Problem Understanding and Constraints
01:55 Key Mathematical Observations
03:04 Prefix-Suffix DP and Peak-Valley Scan Strategy
04:19 Java Code Walkthrough
05:28 Execution and Test Cases
06:43 Time Complexity Analysis - O(n)
07:28 Space Complexity Analysis - O(n)
07:59 Outro and Wrap-up
📂 Problem Folder and Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/February/4-February/3640-Trionic-Array-II
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/4-February/3640-Trionic-Array-II/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/4-February/3640-Trionic-Array-II/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/4-February/3640-Trionic-Array-II/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/4-February/3640-Trionic-Array-II/solution.js
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💬 Question of the Day
Why must the middle decreasing segment from peak p to valley q be an entire maximal strictly decreasing run rather than an arbitrary sub-segment of it?
1️⃣ Because any interior element k has a preceding value greater than nums[k] and a following value smaller than nums[k], violating the required peak or valley conditions
2️⃣ Because decreasing sequences can never have length greater than 2
3️⃣ Because the greedy choice always prefers the longest possible subarray length
4️⃣ Because the problem requires indices to be spaced by powers of 2
#LeetCode3640 #LeetCode #TrionicArrayII #Java #JavaDSA #DynamicProgramming #KadaneAlgorithm #TwoPointers #Array #DSA #CodingInterview #ProblemSolving #LeetCodeHard #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description
In today’s video, we solve LeetCode 3640 - Trionic Array II using Dynamic Programming and Two Pointers in Java.
A trionic subarray requires finding four indices l, p, q, and r in strictly increasing index order, such that the elements strictly increase from l to p, strictly decrease from p to q, and strictly increase from q to r. The key structural insight is that any interior element in a strictly decreasing sequence cannot serve as either the peak p or the valley q without violating adjacent strict monotonicity. Therefore, every valid decreasing segment must span an entire maximal strictly decreasing run from a local peak down to a local valley.
To maximize the total subarray sum, we precompute the maximum suffix sum of strictly increasing elements leading into each peak and the maximum prefix sum of strictly increasing elements descending out of each valley using Kadane-style dynamic programming arrays. By combining these optimal left and right extensions with the exact sum of each candidate decreasing segment, we identify the global maximum trionic subarray sum in linear O(n) time and O(n) auxiliary space.
🔥 Problem Highlights
✅ Discovered the strict peak-and-valley boundary invariant for every decreasing sequence
✅ Evaluated maximal strictly decreasing segments without redundant nested scans
✅ Precomputed maximum strictly increasing suffix sums with forward Kadane DP
✅ Precomputed maximum strictly increasing prefix sums with backward Kadane DP
✅ Handled negative values safely by using 64-bit signed integers and negative infinity initializations
✅ Achieved optimal O(n) time and O(n) space complexity
⏱️ TIMESTAMPS
00:00 Intro
00:54 Problem Understanding and Constraints
01:55 Key Mathematical Observations
03:04 Prefix-Suffix DP and Peak-Valley Scan Strategy
04:19 Java Code Walkthrough
05:28 Execution and Test Cases
06:43 Time Complexity Analysis - O(n)
07:28 Space Complexity Analysis - O(n)
07:59 Outro and Wrap-up
📂 Problem Folder and Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/February/4-February/3640-Trionic-Array-II
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/4-February/3640-Trionic-Array-II/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/4-February/3640-Trionic-Array-II/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/4-February/3640-Trionic-Array-II/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/February/4-February/3640-Trionic-Array-II/solution.js
🔗 LeetCode Source Code
📌 Admin type the link
🌐 All LeetCode Solutions
📌 https://codebytushu.com/Leetcode/
📱 Join CodeByTushu on WhatsApp
Get coding updates, LeetCode solutions, daily questions and more.
https://whatsapp.com/channel/0029Vb8k5mCDeON2Xwlkxe40
❤️ Donate
📌 https://codebytushu.com/Leetcode/donate.php
🔥 Perfect For
LeetCode Hard Problems
Java DSA Preparation
Dynamic Programming Patterns
Kadane Algorithm Variations
Two Pointers Technique
Time Complexity Optimization
Coding Interview Preparation
Problem Solving
🌐 Follow CodeByTushu
▶️ YouTube: https://www.youtube.com/@codebytushu
📸 Instagram: https://instagram.com/codebytushu/
💼 LinkedIn: https://www.linkedin.com/company/codebytushu/
🌍 Website: https://codebytushu.com
🐙 GitHub: https://github.com/CodeByTushu
❤️ Don’t Forget To
👍 Like | 💬 Comment | 🔔 Subscribe
💬 Question of the Day
Why must the middle decreasing segment from peak p to valley q be an entire maximal strictly decreasing run rather than an arbitrary sub-segment of it?
1️⃣ Because any interior element k has a preceding value greater than nums[k] and a following value smaller than nums[k], violating the required peak or valley conditions
2️⃣ Because decreasing sequences can never have length greater than 2
3️⃣ Because the greedy choice always prefers the longest possible subarray length
4️⃣ Because the problem requires indices to be spaced by powers of 2
#LeetCode3640 #LeetCode #TrionicArrayII #Java #JavaDSA #DynamicProgramming #KadaneAlgorithm #TwoPointers #Array #DSA #CodingInterview #ProblemSolving #LeetCodeHard #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description