🎯 Aim

To study and understand the concept of recursion in C++, and explore how problems can be solved by functions calling themselves until a base condition is reached.

---

📚 Theory

Recursion is a programming technique in which a function calls itself directly or indirectly to solve a problem.
The problem is broken into smaller subproblems of the same type, and the process continues until a base case is satisfied.

---

🔑 Key Points

• Recursive Function: A function that calls itself.
• Base Case: The terminating condition that stops recursion.
• Recursive Case: The part of the function where it calls itself with a smaller/simpler input.
• Call Stack: Each recursive call is stored in memory; when the base case is reached, the stack unwinds and results are returned.

---

🏗️ Types of Recursion

1. Direct Recursion – Function calls itself directly.
2. Indirect Recursion – Function A calls B, and B calls A.
3. Tail Recursion – Recursive call is the last operation.
4. Non‑Tail Recursion – Recursive call is followed by extra work.
5. Linear Recursion – Only one recursive call per step.
6. Tree Recursion – Multiple recursive calls per step.

---

📋 Algorithms

🧾 Factorial using Recursion

1. Start
2. Input an integer n.
3. Define recursive function fact(n):
   • If n == 0, return 1 (base case).
   • Else, return n * fact(n-1) (recursive case).
4. Call fact(n) from main().
5. Display the result.
6. End

---

🧾 Sum of Natural Numbers using Recursion

1. Start
2. Input an integer n.
3. Define recursive function sum(n):
   • If n <= 1, return n (base case).
   • Else, return n + sum(n-1) (recursive case).
4. Call sum(n) from main().
5. Display the result.
6. End

---

🧾 String Reversal using Recursion

1. Start
2. Input a string str.
3. Find the length of the string n.
4. Define recursive function reverse(str, i, n):
   • If i == n, stop (base case).
   • Else, call reverse(str, i+1, n) (recursive case).
   • After returning, print str[i].
5. Call reverse(str, 0, n) from main().
6. Display the reversed string.
7. End

---

🚀 Applications of Recursion

Recursion is widely used in mathematics, algorithms, and data structures. Some key applications include:

• Mathematical Computations

  • Factorial, Fibonacci series, power functions, GCD.

• Searching and Sorting

  • Binary Search, Merge Sort, Quick Sort.

• Data Structures

  • Traversal of trees (preorder, inorder, postorder).
  • Graph traversal (DFS).
  • Linked list operations.

• Backtracking Problems

  • N‑Queens problem.
  • Sudoku solver.
  • Maze pathfinding.

• String and Array Operations

  • Reversing strings.
  • Palindrome checking.
  • Generating permutations and combinations.

---

🧠 Conclusion

This study of recursion in C++ demonstrates:

• 🔄 Self‑Referential Nature – Functions can call themselves to solve problems.
• 🛑 Base Case Importance – Prevents infinite recursion and stack overflow.
• ♻️ Code Simplification – Complex problems become easier to express.
• ⚡ Applications – Factorial, sum of numbers, string reversal, sorting, searching, and tree/graph traversal.

👉 Recursion is elegant and powerful, but must be used carefully due to memory and performance considerations.# Recursion.cpp