Recently, I encountered an interesting issue while solving a problem on Codeforces. Initially, I submitted a solution using Arrays.sort() to sort my array. Unfortunately, it resulted in a Time Limit Exceeded (TLE) error. After some experimentation, I replaced Arrays.sort() with Collections.sort() for the same logic, and to my surprise, the solution was accepted. Curious about this behavior? Let’s dive into the details!

Understanding the Sorting Mechanisms

Both Arrays.sort() and Collections.sort() are Java utilities designed to sort data, but they differ in terms of implementation and behavior:

1. Arrays.sort()

Algorithm Used:

For primitive types (int[], long[], etc.), Arrays.sort() uses Dual-Pivot QuickSort, which has an average time complexity of O(n log n) but can degrade to O(n²) in the worst case.

For objects (Integer[], String[], etc.), Arrays.sort() uses TimSort, which has a guaranteed time complexity of O(n log n) in all cases.

Edge Cases:

Dual-Pivot QuickSort, used for primitive arrays, may perform poorly if the data is highly repetitive or adversarial (e.g., sorted or reverse-sorted input).

1. Collections.sort()

Algorithm Used:

Collections.sort() always uses TimSort, a stable and adaptive sorting algorithm, which is efficient for both partially sorted and random data.

Behavior:

Collections.sort() works on List objects like ArrayList and guarantees O(n log n) complexity for all inputs.

Why TLE with Arrays.sort()?

In competitive programming, test cases are often designed to stress algorithms to their limits. If you are sorting a large array of primitive types using Arrays.sort(), and the input is crafted to hit the worst-case performance of QuickSort, it can degrade to O(n²). This happens because Dual-Pivot QuickSort does not handle certain patterns (e.g., many duplicates or nearly sorted data) efficiently.

On the other hand, Collections.sort() uses TimSort for all data types, which has a worst-case complexity of O(n log n) regardless of the input characteristics. This makes it more robust for competitive programming.

Recent 998 Div 3 C :Collections.sort():https://codeforces.net/contest/2060/submission/302922077 :Arrays.sort():https://codeforces.net/contest/2060/submission/302922359