Lecture topic-BruteForce

# Exercise a can you design a faster algorithm than the

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Unformatted text preview: k ∑ ( xi − yi ) 2 i =1 • Efficiency: Θ (n2) Design and Analysis of Algorithms – Chapter 3 34 In-class exercise a Can you design a faster algorithm than the one based on Can the brute-force strategy to solve the closest-pair problem for n points x1, x2, … , xn on the real line? for a What is the time efficiency of your algorithm? What Design and Analysis of Algorithms – Chapter 3 35 In-class exercise a Can you design a faster algorithm than the one based on Can the brute-force strategy to solve the closest-pair problem for n points x1, x2, … , xn on the real line? for a Algorithm: Algorithm: • Step1: Sort the numbers in ascending order, O(nlogn) • Step 2: Compute the differences between adjacent numbers in Step the sorted list, Θ (n) • Step 3: Find the smallest such difference, Θ (n) Step Running time of the entire algorithm: Running O(nlogn) + Θ (n) + Θ (n) = O(nlogn) (n) Design and Analysis of Algorithms – Chapter 3 36 Convex hull problem Convex a Convex hull • Problem: Problem: Find sm...
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