Discuss different types of recursion with examples. Linear/Binary/Multiple recursion (Download is recommended to make the animations work)

1. Algorithms and Data Structures
Recursion
By- Priyanka

2. Basic Algorithms: Recursion

3. Basic Algorithms: Recursion

4. Basic Algorithms
 Write a function that calculate 3!
(factorial).
 Write a function that calculate n!

5. Recursion helps
 Avoidance of unnecessary calling of functions.
 A substitute for iteration where the iterative
solution is very complex.
 Extremely useful when applying the same solution.

6. Types of Recursion
Linear recursion : makes at most one recursive call each
time it is invoked.
Binary recursion : algorithm makes two recursive calls.
Multiple recursion : method may make (potentially more
than two) recursive calls.

7. Linear Recursion
Algorithm LinearSum(A, n)
if n = 1 then
return A[0]
else
return LinearSum(A, n-1) + A[n-1]

8. Linear Recursion
A={4, 3, 6, 2, 5}, n=5.

9. Student Exercise
Can you think of any drawback for recursive
functions?
Answer is related to computer memory

10. Binary Recursion
Algorithm BinarySum(A, i, n)
if n = 1 then
return A[i]
else
return BinarySum(A, i, [n/2])+
BinarySum (A, i+[n/2], [n/2])

11. Binary Recursion
Recursion trace for the execution of BinarySum(A, 0, 8) :

12. Multiple Recursion
Combinatorial puzzle:
pot + pan = bib
dog + cat = pig
boy + girl = baby

13. Puzzle Solve(3, S, U)
S is an empty sequence/string, and K=3
U = {a, b, c}

14. Example: Find a solution to cbb + ba = abc, where {a, b, c}
stands for {7, 8, 9}, K=3.
Soluti
on

15. Thank You