The core challenge of this problem is to efficiently manipulate arrays and strings while considering the time complexity of various operations. This is significant in many real-world applications such as data processing, text analysis, and more. Potential pitfalls include not accounting for edge cases like empty arrays or strings, and misunderstanding the time complexity of certain operations.

To solve this problem, we need to consider different methods for manipulating arrays and strings, and analyze their time complexities. We will start with a naive approach and then move to more optimized solutions.

A naive solution might involve using nested loops for operations like finding duplicates in an array or concatenating strings. While this approach is straightforward, it is not optimal due to its high time complexity.

We will explore multiple optimized solutions:

- Using hash sets to find duplicates in an array.
- Using StringBuilder for efficient string concatenation.

We can use a hash set to keep track of elements we have seen so far. This allows us to check for duplicates in O(1) time.

```
import java.util.HashSet;
public class FindDuplicates {
public static boolean hasDuplicates(int[] array) {
HashSet<Integer> seen = new HashSet<>();
for (int num : array) {
if (seen.contains(num)) {
return true; // Duplicate found
}
seen.add(num);
}
return false; // No duplicates
}
}
```

Using StringBuilder allows us to concatenate strings in O(n) time, where n is the total length of all strings.

```
public class StringConcatenation {
public static String concatenateStrings(String[] strings) {
StringBuilder sb = new StringBuilder();
for (String str : strings) {
sb.append(str);
}
return sb.toString();
}
}
```

For the hash set approach to finding duplicates, the time complexity is O(n) and the space complexity is O(n), where n is the number of elements in the array. For the StringBuilder approach, the time complexity is O(n) and the space complexity is also O(n), where n is the total length of all strings.

Potential edge cases include:

- Empty arrays or strings.
- Arrays with all unique elements.
- Strings with special characters.

Each algorithm handles these edge cases effectively by design.

To test the solutions comprehensively, consider the following test cases:

- Empty array or string array.
- Array with all unique elements.
- Array with multiple duplicates.
- String array with varying lengths of strings.

When approaching such problems, consider the following tips:

- Break down the problem into smaller parts.
- Think about the time complexity of each operation.
- Use data structures that provide efficient lookups and insertions.

Understanding the time complexity of array and string methods is crucial for writing efficient code. By using optimized solutions like hash sets and StringBuilder, we can significantly improve performance. Practice and familiarity with different data structures and algorithms will help in solving such problems more effectively.

For further reading and practice, consider the following resources:

- LeetCode - Practice coding problems.
- GeeksforGeeks - Tutorials and explanations.
- Java Documentation - Official Java documentation.