What is the difference between “sliding window or sliding range minimum/maximum query” 

Give me a concrete example 
Certainly! Here's the formatted version:

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### Sliding Window vs. Sliding Range Minimum/Maximum Query

#### Sliding Window

**Definition**:  
A sliding window is a technique used to maintain and process a subset (window) of a larger data set or sequence. As new elements enter the window, old elements exit, effectively “sliding” the window across the data.

**Purpose**:  
- Used to perform computations on all possible contiguous subarrays of a fixed or variable size.  
- Applied in various scenarios like calculating moving averages, finding patterns, etc.

**Common Operations**:  
- Summing elements within the window.  
- Tracking all elements or specific properties within the window.

---

#### Sliding Range Minimum/Maximum Query

**Definition**:  
A sliding range minimum (or maximum) query is a specific application of the sliding window technique. The goal is to efficiently find the minimum (or maximum) element within the current window as it slides over the data set.

**Purpose**:  
- Allows quick retrieval of the minimum or maximum within each window without re-computing from scratch as the window moves.  
- Optimized for performance-critical scenarios where such queries are frequent.

**Common Implementations**:  
- Use of data structures like deque (double-ended queues) to achieve O(n) time complexity for processing all windows.  
- Use of segment trees or binary indexed trees for more dynamic scenarios.

---

### Concrete Example

**Problem Statement**:  
Given an array of integers and a window size `k`, compute the maximum value within each sliding window as it moves from left to right across the array.

**Array**:  
`[1, 3, -1, -3, 5, 3, 6, 7]`  
**Window Size (k)**: 3

---

#### 1. Sliding Window Approach (General)

**Objective**:  
Compute some property (e.g., sum) for each window.

**Example Operation**:  
Calculate the sum of elements in each window.

**Process**:
- Window 1: `[1, 3, -1]` → Sum = `1 + 3 + (-1) = 3`  
- Window 2: `[3, -1, -3]` → Sum = `3 + (-1) + (-3) = -1`  
- Window 3: `[-1, -3, 5]` → Sum = `(-1) + (-3) + 5 = 1`  
- Window 4: `[-3, 5, 3]` → Sum = `(-3) + 5 + 3 = 5`  
- Window 5: `[5, 3, 6]` → Sum = `5 + 3 + 6 = 14`  
- Window 6: `[3, 6, 7]` → Sum = `3 + 6 + 7 = 16`  

**Output**:  
`[3, -1, 1, 5, 14, 16]`

**Time Complexity**: O(n), where n is the number of elements in the array.

---

#### 2. Sliding Range Maximum Query

**Objective**:  
Find the maximum element in each window efficiently using a deque.

**Process Using Deque**:
1. **Initialize**: Use a deque to store indices of useful elements for each window.
2. **Iterate through the array**:
   - Remove indices from the front if they are out of the current window.
   - Remove indices from the back if the current element is greater than elements at those indices.
   - Add the current index to the deque.
   - The front of the deque always holds the index of the maximum element for the current window.

**Step-by-Step**:
- Window 1: `[1, 3, -1]` → Max = `3`  
- Window 2: `[3, -1, -3]` → Max = `3`  
- Window 3: `[-1, -3, 5]` → Max = `5`  
- Window 4: `[-3, 5, 3]` → Max = `5`  
- Window 5: `[5, 3, 6]` → Max = `6`  
- Window 6: `[3, 6, 7]` → Max = `7`  

**Output**:  
`[3, 3, 5, 5, 6, 7]`

**Time Complexity**: O(n), achieved by ensuring each element is processed at most twice (once added and once removed from the deque).

---

### Key Differences Highlighted by the Example

**Purpose**:
- **Sliding Window**: General technique for computing any property (e.g., sum, average) over each window.
- **Sliding Range Min/Max Query**: Specialized for finding the minimum or maximum within each window.

**Implementation**:
- **Sliding Window**: May use simple iteration with cumulative computations.
- **Sliding Range Min/Max Query**: Often employs optimized data structures like deques to maintain and retrieve min/max efficiently.

**Output**:
- **Sliding Window (Sum Example)**: `[3, -1, 1, 5, 14, 16]`
- **Sliding Range Maximum**: `[3, 3, 5, 5, 6, 7]`

**Efficiency**:  
Both can achieve O(n) time complexity, but sliding range queries use specific strategies to maintain the required information (min or max) without reprocessing the entire window.

---

### When to Use Each

- **Sliding Window**: When you need to perform a variety of operations on each window, such as sum, average, or more complex statistical measures.
- **Sliding Range Min/Max Query**: When the primary requirement is to frequently query the minimum or maximum value within the moving window, especially where performance is crucial.

---

I hope this clarifies the distinction between the general sliding window technique and the more specialized sliding range minimum/maximum queries, along with how they are applied in practice!


Q- for each one give list of sorted problem 

From absolute beginner , to beginner , to medium , to minimal hard to hard 
In each category 5 problems with order oky 

Certainly! Here’s a formatted version of your curated list of programming problems for Sliding Window techniques and Sliding Range Minimum/Maximum Queries, organized by difficulty levels:

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### 🧩 **Sliding Window Problems**

**1. Absolute Beginner**  
Introductory problems for learning the fundamentals of sliding window techniques.
- **Maximum Average Subarray I**
- **Subarray Product Less Than K**
- **Permutations in String**
- **Longest Substring with At Most Two Distinct Characters**
- **Minimum Window Substring**

**2. Beginner**  
Problems requiring a solid understanding of sliding window concepts with slightly increased complexity.
- **Longest Substring Without Repeating Characters**
- **Sliding Window Maximum**
- **Fruit Into Baskets**
- **Longest Repeating Character Replacement**
- **Longest Well-Performing Interval**

**3. Medium**  
Challenges that combine sliding window techniques with other algorithmic strategies.
- **Find All Anagrams in a String**
- **Longest Substring with At Least K Repeating Characters**
- **Sliding Window Median**
- **Longest Continuous Subarray With Absolute Diff Less Than or Equal to Limit**
- **Minimum Size Subarray Sum**

**4. Minimal Hard**  
These problems are slightly more challenging and may require optimized solutions.
- **Window Size Sliding**
- **Number of Subarrays with Bounded Maximum**
- **At Most K Distinct Characters**
- **Number of Subarrays with Sum Exactly K**
- **Sliding Window Unique Characters**

**5. Hard**  
Advanced problems often requiring innovative applications of sliding window techniques.
- **Maximum Sum of 3 Non-Overlapping Subarrays**
- **Substring with Concatenation of All Words**
- **Data Stream as Disjoint Intervals**
- **Longest Substring with Exactly K Distinct Characters**
- **Maximum Number of Vowels in a Substring of Given Length**

---

### 📉 **Sliding Range Minimum/Maximum Query Problems**

**1. Absolute Beginner**  
Introductory problems focused on finding the minimum or maximum in fixed-size windows.
- **Sliding Window Maximum**
- **Sliding Window Median**
- **Daily Temperatures**
- **Next Greater Element I**
- **Next Greater Element II**

**2. Beginner**  
More nuanced applications of sliding range queries.
- **Trapping Rain Water**
- **Largest Rectangle in Histogram**
- **Maximal Rectangle**
- **Sum of Subarray Minimums**
- **Shortest Subarray with Sum at Least K**

**3. Medium**  
Challenges that involve sliding range queries combined with advanced data structures.
- **Minimum Window Substring**
- **Sliding Window Maximum**
- **Sliding Window Median**
- **Largest Rectangle in Histogram**
- **Sum of Subarray Minimums**

**4. Minimal Hard**  
Problems requiring optimized approaches and efficient data handling.
- **Shortest Subarray with Sum at Least K**
- **Sum of Subarray Minimums**
- **Minimum Number of Refueling Stops**
- **Longest Well-Performing Interval**
- **Sliding Window Maximum**

**5. Hard**  
Advanced problems that often involve complex optimizations and deep algorithmic insights.
- **Maximum Sum of 3 Non-Overlapping Subarrays**
- **Data Stream as Disjoint Intervals**
- **Find the Maximum Number of Marked Indices**
- **Longest Subarray with Maximum Sum**
- **Sliding Window Maximum II**

---

### 📚 **Additional Resources**
Enhance your understanding of these techniques with the following resources:
- **Sliding Window Technique** - [GeeksforGeeks](https://www.geeksforgeeks.org/sliding-window-algorithm/)
- **Monotonic Queue** - [LeetCode Discuss](https://leetcode.com/problems/sliding-window-maximum/discuss/)
- **Dynamic Sliding Window Algorithms**

**Books:**
- *Introduction to Algorithms* by Cormen et al.
- *Competitive Programming* by Halim and Halim.

By systematically solving these problems, you'll build a strong foundation in sliding window techniques and sliding range queries, preparing you for a variety of algorithmic challenges.

**Happy Coding! 🚀**

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This structure ensures clarity and easy navigation for learners as they work through the problems.

Q- give me the problem descripion 

Using Codeforces story telling style then make it formal oky like leetCode for this probem 
Maximum Average Subarray I
“Maximum Average Subarray I”