Recursion - Algorithms and Data Structures

Recursion - Algorithms and Data Structures

• 1.
  Algorithms and DataStructures Recursion By- Priyanka
• 2.
  Basic Algorithms: Recursion
• 3.
  Basic Algorithms: Recursion
• 4.
  Basic Algorithms  Writea function that calculate 3! (factorial).  Write a function that calculate n!
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  Recursion helps  Avoidanceof unnecessary calling of functions.  A substitute for iteration where the iterative solution is very complex.  Extremely useful when applying the same solution.
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  Types of Recursion Linearrecursion : 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.
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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]
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  Linear Recursion A={4, 3,6, 2, 5}, n=5.
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  Student Exercise Can youthink of any drawback for recursive functions? Answer is related to computer memory
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  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])
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  Binary Recursion Recursion tracefor the execution of BinarySum(A, 0, 8) :
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  Multiple Recursion Combinatorial puzzle: pot+ pan = bib dog + cat = pig boy + girl = baby
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  Puzzle Solve(3, S,U) S is an empty sequence/string, and K=3 U = {a, b, c}
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  Example: Find asolution to cbb + ba = abc, where {a, b, c} stands for {7, 8, 9}, K=3. Soluti on
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  Thank You