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The choice between **Sliding Window** and **Prefix Sum + HashMap** techniques depends on the problem's requirements and how the conditions for the solution are defined. Here’s a detailed comparison:

 **Sliding Window**
When to Use:
Sliding Window is ideal for problems where:
1. **Window size or range is explicitly defined:**
   - Fixed-size window: When the subarray length is predetermined.
   - Dynamic-size window: When the window size changes based on constraints.

2. **The condition to satisfy can be checked incrementally:**
   - Adding or removing elements from the window should make it easy to update the condition (e.g., sum, max, min, frequency count).

3. **Local properties of the array are considered:**
   - Problems where the solution depends only on the current window, without needing to store or compare results globally.

 Common Examples:
- **Fixed-size window problems:** Maximum/Minimum sum of subarrays of size \( k \).
- **Dynamic-size window problems:** Smallest or largest subarray satisfying a condition (e.g., \( \text{sum} \geq x \)).
- **Range-based sliding window:** Problems involving substrings with specific properties (e.g., "longest substring with at most \( k \) distinct characters").


 **Prefix Sum + HashMap**
 When to Use:
Prefix Sum + HashMap is ideal for problems where:
1. **Global properties of the array need to be checked:**
   - Conditions like sums or products involving subarrays that are not local to a moving window.

2. **Comparison between different segments is required:**
   - E.g., comparing sums of subarrays or checking if a subarray satisfies a modulo condition.

3. **The problem involves cumulative values or differences:**
   - Use prefix sums to represent cumulative sums and a HashMap to efficiently check for conditions between two points in the array.

4. **Subarray of any size (not fixed):**
   - When subarrays of arbitrary length need to be considered efficiently.

 Common Examples:
- **Sum-related problems:** Check if a subarray has a sum equal to \( x \), or sum modulo \( k \) is \( 0 \).
- **Count distinct subarrays:** Efficiently find the count of subarrays with a given sum or difference.
- **Finding repeating patterns:** Use prefix sums to detect cycles or repeating states.

 **Key Decision Points**
- **Sliding Window:** Use when the problem focuses on contiguous elements with easily adjustable sizes or when optimizing over a local condition.
- **Prefix Sum + HashMap:** Use when the problem requires comparing cumulative results or checking for global properties across multiple segments of the array. 

If you’re ever in doubt, focus on:
- The type of condition (local vs global).
- Subarray size constraints (fixed/dynamic vs arbitrary).