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Analysis of Algorithm Recursive Algorithm
- 1. 1 1.1Algorithm Definition andSpecification 1.2 Space complexity 1.3Time Complexity 1.4 Asymptotic Notations 1.5 Elementary Data Structure: Stacks and Queues 1.6 Binary Tree 1.7 Binary Search Tree 1.8 Heap 1.9 Heapsort 1.10 Graph. UNIT 1- INTRODUCTION
- 2. Recursive Algorithm 2 A recursivefunction is a function that is defined in terms of itself. Similarly, an algorithm is said to be recursive if the same algorithm is invoked in the body. An algorithm that calls itself is direct recursive. Algorithm A is said to be indirect recursive if it calls another algorithm which in turn calls A. These Recursive mechanisms are extremely powerful, but even more importantly,
- 3. 3 Fact(n) { if n ==0 or 1 then Return 1; else Return (n*Fact(n-1)); } Contd… Example1 : Factorial using Recursion Implementation Fact(3) { if n == 0 or 1 then Return 1; else Return (3*Fact(2)); } Result=6 Fact(2) { if n == 0 or 1 then Return 1; else Return (2*Fact(1)); } Result=2
- 4. 4 Fact(1) { if n ==0 or 1 then Return 1; else Return (1*Fact(0)); } Result=1 Notation
- 5. 5 Contd… Example2 : Towersof Hanoi using Recursion There are three towers 64 gold disks, with decreasing sizes, placed on the first tower You need to move all of the disks from the first tower to the last tower Larger disks can not be placed on top of smaller disks The third tower can be used to temporarily hold disks
- 6. 6 The disksmust be moved within one week. Assume one disk can be moved in 1 second. Is this possible? To create an algorithm to solve this problem, it is convenient to generalize the problem to the “N-disk” problem, where in our case N = 64.
- 7. Recursive Solution Tower ATower B Tower C
- 8. Recursive Solution Tower ATower B Tower C
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- 17. Algorithm –Towers ofHanai 17