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Introduction to Algorithm Complexity Bit Sum Problem
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Rol Exposition Polynomial problem of practice 1 Queues Stacks Hash tables in C++ Representing graphs Representing Trees Transverse a binary tree The role of algorithms in computing ( Cormen) Algorithms as a technology
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Evaluation Skills 10-15 minutes time exposition 5 minutes questions ( evaluate different groups) When applicable the source of a solution description of the problem Charts and draw support in presentation Presentations and code should be uploaded in claroline
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Pre-Assignment Read chapter one of the book “Introduction to algorithms” Author: Thomas Cormen.
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Definition The time complexity of a program (for a given input) is the number of elementary instructions that this program executes. This number is computed with respect to the size n of the input data. Thomas Cormen. Introduction to algorithms
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Definition The space complexity of a program (for a given input) is the number of elementary objects that this program needs to store during its execution. This number depends on n.
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Exercise ¿Why do you think is important to understand the time and the space complexity? – Write a little paragraph an examples about that.
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Importance of complexity analysis The algorithm or the programming language? C++ is faster than Java I don’t care about the programming language Note: An O(nlogn) algorithm in Java will probably be faster than a O(n 2 ) algorithm in C++
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Problem Definition Count the number of ones in an n-bit string B=b n b n-1 …b 2 b 1
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Solution c 0 for i=1 to n do if b i = 1 then c c+1 Number of steps = n Memory Space= 1
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Is possible going Faster? c 0 While B ≠ 0 do c c +1 B B ∧ (B-1) Try 11001000 Time Complexity=? Message Complexity=?
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Is possible going faster? Divide and conquer – Try 11010001 Time Complexity=? Message Complexity=?
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Is possible going faster Is possible to get an O(1) time algorithm? – What about the space complexity?
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Exercises Write formally the definition of time and space complexity Describe a real world example of a problem in which is important to get an optimal algorithm approach to get the solution Implement one of the optimal in time solutions to the bit sum problem.
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