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Algorithm Correctness & Analysis

Summary ,[object Object],[object Object],[object Object]

Correctness ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Correctness of Recursive algorithms ,[object Object],[object Object],[object Object],[object Object],[object Object]

Recursive Fibonacci Numbers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Recursive Fibonacci Numbers Claim: For all n ≥ 0 , fib( n ) return F n Base: For n =0 , fib( n ) returns 0 as claimed. For n = 1 , fib( n ) returns 1 as claimed. Induction: Suppose that n ≥ 2 and for all 0 ≤ m < n, fib ( m ) returns F m . Required to prove fib( n ) returns F n What does fib( n ) returns? fib( n-1 ) + fib( n-2 ) = F n-1 + F n-2 (by Ind. Hyp.) = F n

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Constant Multiples

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Example

Note that we need Second example

But we have lost the tree structure To Delete the Minimum

But we have violated the structure condition Contd…

Analysis of Priority Queue Operation

[object Object],[object Object],[object Object],[object Object],[object Object],Algorithms Course Notes Algorithm Analysis 3

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