CSE20 Lecture 12

# CSE20 Lecture 12 - 1 CSE 20 Lecture 12 2 3 Analysis • 3.1...

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Unformatted text preview: 1 CSE 20 Lecture 12 2/25/10 2 3. Analysis • 3.1 Introduction • 3.2 Homogeneous Linear Recursion • 3.3 Pigeonhole Principle • 3.4 Inclusion-Exclusion Principle 3 3.1 Introduction • Derive the bound of functions or recursions • Estimate CPU time and memory allocation • Example on Fibonacci Sequence: We estimate Fn. – 0 1 2 3 4 5 6 7 8 9 – 0 1 1 2 3 4 5 8 13 21 34 – Fn = 1/r5(((1+rr5)/2)^n-((1-rr5)/2)^n) • F0 = 1/rr5(1-1) = 0 • F1 = 1/rr5(((1+rr5)/2)-((1-rr5)/2)) = 1 4 Example: Fibonacci Sequence 0 1 2 3 4 5 6 7 8 9 0 1 1 2 3 5 8 13 21 34 • • • • 5 3.2 Homogeneous Linear Recursion • (1) Arithmetic Recursion – a, a+d, a+2d, …, a+kd • (2) Geometric Recursion – A, ar, ar 2 , …, ar k • (3) Linear Recursion – a n = e 1 a n-1 +e 2 a n-2 +…+e k a n-k + f(n) 6 Linear Recursion and Homogeneous Linear Recursion • Linear Recursion: There are no powers or products of • Homogenous Linear Recursion: A linear recursion with f(n)=0. 7 Solving Linear Recursion Input: ° ,...
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CSE20 Lecture 12 - 1 CSE 20 Lecture 12 2 3 Analysis • 3.1...

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