Recursion

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Proving that a Recursive Method is Correct • Proof by induction • Prove the theorem is true for the base case • Show that if the theorem is assumed true for n, then it must be true for n+1 • Recursive proof is similar to induction • Verify the base case is recognized and solved correctly • Verify that each recursive case makes progress towards the base case • Verify that if all smaller problems are solved correctly, then the original problem is also solved correctly
Tracing a Recursive Method
Page 1 and 2: Recursion Chapter 7
Page 3 and 4: Chapter Objectives (continued) •
Page 5 and 6: Recursive Thinking
Page 7: String Length Algorithm
Page 11 and 12: Recursive Factorial Method
Page 13 and 14: Recursion Versus Iteration • Ther
Page 15 and 16: Efficiency of Recursion • Recursi
Page 17 and 18: An O(n) Recursive Fibonacci Method
Page 19 and 20: Efficiency of Recursion: O(n) Fibon
Page 21 and 22: Algorithm for Recursive Linear Arra
Page 23 and 24: Design of a Binary Search Algorithm
Page 25 and 26: Design of a Binary Search Algorithm
Page 27 and 28: Implementation of a Binary Search A
Page 29 and 30: Method Arrays.binarySearch • Java
Page 31 and 32: Recursive Definition of a Linked Li
Page 33 and 34: Recursive toString Method
Page 35 and 36: Recursive Add Method
Page 37 and 38: Recursive Remove Method (continued)
Page 39 and 40: Towers of Hanoi
Page 41 and 42: Algorithm for Towers of Hanoi
Page 43 and 44: Algorithm for Towers of Hanoi (cont
Page 45 and 46: Implementation of Recursive Towers
Page 47 and 48: Counting Cells in a Blob (continued
Page 49 and 50: Implementation
Page 51 and 52: Counting Cells in a Blob (continued
Page 53 and 54: Backtracking (continued) • Never
Page 55 and 56: Recursive Algorithm for Finding Maz
Page 57 and 58: Implementation (continued)
Page 59 and 60:
Chapter Review • A recursive meth
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Recursion

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