Recursion - Algorithms and Data Structures
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The document discusses basic algorithms, particularly focusing on recursion as a method for solving problems like calculating factorials and summing elements in an array. It describes different types of recursion: linear, binary, and multiple, providing algorithms for each type and examples of their execution. Additionally, it introduces a combinatorial puzzle related to multiple recursion and encourages students to think about the drawbacks of recursive functions.
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![Linear Recursion
Algorithm LinearSum(A, n)
if n = 1 then
return A[0]
else
return LinearSum(A, n-1) + A[n-1]](https://image.slidesharecdn.com/recursion-170415030718/85/Recursion-Algorithms-and-Data-Structures-7-320.jpg)
![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])](https://image.slidesharecdn.com/recursion-170415030718/85/Recursion-Algorithms-and-Data-Structures-10-320.jpg)
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- 1. Algorithms and Data Structures Recursion By- Priyanka
- 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