A dynamic problem in data structure refers to a problem where the input data is changing over time or with each operation. Unlike static problems, which have a fixed set of data that doesn’t change, dynamic problems require a more flexible approach to handle the changing data.

**Dynamic Data Structures**

Dynamic problems often involve the use of dynamic data structures. These are data structures that can grow or shrink in size as needed during program execution. Dynamic data structures are essential for efficiently solving dynamic problems, as they provide the flexibility required to handle changing data.

__Lists__

One common type of dynamic data structure is a list. A list allows us to store and manipulate a collection of elements.

In HTML, we can represent a list using the

- (unordered list) and
- (list item) tags. Let’s consider an example:
- Create an empty list
- Add elements to the list
- Remove elements from the list
- Access elements in the list
- Modify elements in the list

**Dynamic Problem Example: Stack**

A classic example of a dynamic problem is implementing a stack data structure. A stack follows the Last-In-First-Out (LIFO) principle, where elements are added and removed from only one end called the top.## The Stack Operations:

**Push:**Inserts an element onto the top of the stack.**Pop:**Removes and returns the top element from the stack.**Peek:**Returns the value of the top element without removing it.**isEmpty:**Checks if the stack is empty.

**Implementation of Stack using Lists**

Let’s see how we can implement a stack using a list in Python:“`python

class Stack:

def __init__(self):

self.items = []def push(self, item):

self.items.append(item)def pop(self):

if not self.is_empty():

return self.pop()def peek(self):

if not self.items[-1]def is_empty(self):

return len(self.items) == 0

“`### Dynamic Problem Solving

Solving dynamic problems requires careful consideration of the changing data and how it affects the algorithm or data structure being used. It often involves iterating over the changing data and performing operations accordingly.

**Advantages of Dynamic Data Structures**

The use of dynamic data structures offers several advantages:- Flexibility: Dynamic data structures can adapt to changing data, making them suitable for dynamic problems.
- Efficiency: Dynamic data structures allow for efficient operations on changing data without wasting memory.
- Scalability: Dynamic data structures can handle large amounts of changing data without sacrificing performance.

In conclusion, dynamic problems in data structure are those that involve changing input data. To solve these problems efficiently, dynamic data structures like lists are used. By understanding and implementing dynamic data structures, you can tackle a wide range of real-world problems that involve changing or evolving datasets.