Recursion and Backtracking in DSA

Recursion and Backtracking in Data Structures and Algorithms (DSA)

Recursion:

Recursion is a programming technique where a function calls itself in order to solve a problem.
It breaks down a problem into smaller subproblems that are identical in structure to the original problem.
A base case is defined to stop the recursion and prevent infinite loops.
Examples of problems solved using recursion include calculating factorial, Fibonacci series, and traversing tree structures.

Backtracking is a method used to systematically search for a solution to a problem by trying different paths, and when a dead-end is reached, it retraces its steps back to the last valid configuration.
It is often used in problems where there are multiple possible configurations and the goal is to find one or more solutions.
Backtracking typically involves recursive algorithms.
Examples of problems solved using backtracking include the N-Queens problem, Sudoku solving, and solving mazes.

Understanding Recursion:
- What is recursion?
- How does recursion work?
- Examples of recursive functions (factorial, Fibonacci, etc.)
- Tail recursion vs. non-tail recursion.
Recursion in Data Structures:
- Recursion in trees (tree traversal, finding height, etc.)
- Recursion in graphs (depth-first search, backtracking algorithms, etc.)
Understanding Backtracking:
- What is backtracking?
- How does backtracking work?
- Difference between recursion and backtracking.
Backtracking Algorithms:
- N-Queens problem.
- Sudoku solving.
- Rat in a Maze problem.
- Subset Sum problem.
- Hamiltonian Cycle.
Optimization Techniques:
- Memoization (for optimizing recursive algorithms).
- Pruning techniques in backtracking (to reduce the search space).
- Dynamic programming approaches to problems solvable using backtracking.
Practice and Implementation:
- Writing recursive functions for various problems.
- Implementing backtracking algorithms from scratch.
- Analyzing time and space complexity of recursive and backtracking algorithms.