Algorithms and data structures are essential to computer science, and Leetcode offers a plethora of challenges to hone these skills. One such interesting problem is “Design an Ordered Stream.” In this extensive guide, we’ll delve into Pythonic approaches to tackle this problem, understand the underpinning logic, and gauge their performance in terms of time and space complexity.

### 1. Problem Statement

There is a stream of `n(id, value)`

pairs arriving in an arbitrary order, where `id`

is an integer between 1 and `n`

and `value`

is a string. No two pairs have the same id.

Design a stream that returns the values in increasing order of their IDs by returning a chunk (list) of values after each insertion. The concatenation of these chunks should result in a list of the sorted values.

Implement the `OrderedStream`

class:

`OrderedStream(int n)`

: Constructs the stream to take`n`

values.`insert(int id, String value)`

: Inserts the`(id, value)`

pair into the stream, then returns a list of the largest possible chunk of currently inserted values that appear next in the order.

**Constraints**:

`1 <= n <= 1000`

`1 <= id <= n`

`value.length == 5`

- At most
`n`

calls will be made to`insert`

.

### 2. Understanding the Problem

The problem asks us to design a class called `OrderedStream`

that can insert `(id, value)`

pairs and return a list of sorted values by their IDs whenever possible.

### 3. Class Design Approach

#### 3.1 Brute-Force Approach

One of the simplest methods is to insert each `(id, value)`

pair into a list and sort it every time, extracting and returning values that are contiguous.

Python Code:

```
class OrderedStream:
def __init__(self, n: int):
self.stream = [None] * n
self.ptr = 0
def insert(self, id: int, value: str):
self.stream[id - 1] = value
chunk = []
while self.ptr < len(self.stream) and self.stream[self.ptr]:
chunk.append(self.stream[self.ptr])
self.ptr += 1
return chunk
```

#### 3.2 Optimized Approach

The optimized approach avoids sorting and re-traversing the entire list by keeping track of a pointer.

Python Code:

```
class OrderedStream:
def __init__(self, n: int):
self.stream = [None] * (n + 1)
self.ptr = 1
def insert(self, id: int, value: str):
self.stream[id] = value
chunk = []
while self.ptr < len(self.stream) and self.stream[self.ptr]:
chunk.append(self.stream[self.ptr])
self.ptr += 1
return chunk
```

### 4. Time Complexity Analysis

The time complexity of the optimized approach is O(1) for each `insert`

operation, assuming appending to a list is constant time.

### 5. Space Complexity Analysis

The space complexity for both approaches is O(n), where n is the size specified during the class instantiation.

### 6. Conclusion

The “Design an Ordered Stream” problem serves as an excellent introductory problem for data stream design and object-oriented programming. It not only allows us to ponder over data structure choice but also encourages us to think about optimization.