PPT-Algorithm Analysis: Efficiency and Complexity

bit twiddling 1 pejorative An exercise in tuning see tune in which incredible amounts of time and effort go to produce little noticeable improvement often with the result that the code becomes incomprehensible. Shantanu. . Dutt. ECE Dept.. UIC. Time Complexity. An algorithm time complexity is a function T(n) of problem size n that represents how much time the algorithm will take to complete its task.. Note that there could be more than one problem size parameter n, in which case we can denote the time complexity function as T(S), where S is the set of size parameters. E.g., for the shortest path problem on a graph G, we have 2 size parameters, n the # of vertices and e the # of edges (thus T(S) = T(. Shantanu. . Dutt. ECE Dept.. UIC. Time Complexity. An . algorithm’s . time complexity is a function T(n) of problem size n that represents how much time the algorithm will take to complete its task.. CS . 1037a . – Topic . 13. Overview. Time complexity. - exact count of operations . T(n). as a function of input size . n. - complexity analysis using . O(...). bounds . - constant time, linear, logarithmic, exponential,… complexities. Prof. Andy Mirzaian. Machine Model. &. Time Complexity. STUDY MATERIAL:. . [CLRS]. chapters 1, 2, 3. Lecture Note. 2. 2. Example. Time Complexity. Execution time. n. 1 sec.. n log n. and Sorting. a. cademy.zariba.com. 1. Lecture Content. Algorithms Overview. Complexity. Sorting . Algorithms. Homework. 2. 3. Algorithms Overview. An . Algorithm. is a step-by-step procedure to perform calculations.. Algorithm. Input. Output. 1. Analysis of Algorithms. How long does this take to open 1) know 2) don’t know. . Analysis of Algorithms. 2. If know combination O(n) . where n is number of rings. . If the alphabet is size m, O(nm). Instructor: Arun Sen. Office: BYENG . 530. Tel: 480-965-6153. E-mail: asen@asu.edu. Office Hours: . MW 3:30-4:30 or by appointment. TA: . TBA. Office. : TBA. Tel: . TBA. E-mail: . TBA. Office Hours. : . Dr. Jeyakesavan Veerasamy. jeyv@utdallas.edu. The University of Texas at Dallas, USA. Program running time. When is the running time (waiting time for user) noticeable/important?. Program running time – Why? . Fall . 2011. Sukumar Ghosh. What is an algorithm. . A finite set (or sequence) of . precise instructions . for performing a computation. . . . Example: Maxima finding. . . procedure . max. (. What is the best way to measure the time complexity of an algorithm?. - Best-case run time?. - Worst-case run time?. - Average run time?. Which should we try to optimize?. Best-Case Measures. How can we modify almost any algorithm to have a good best-case running time?. Reading: Chapter 2. 2. Complexity Analysis. Measures efficiency (time and memory) of algorithms and programs. Can be used for the following. Compare different algorithms. See how time varies with size of the input. Overview. Time complexity. - exact count of operations . T(n). as a function of input size . n. - complexity analysis using . O(...). bounds . - constant time, linear, logarithmic, exponential,… complexities. Readings: [SG] Ch. 3. Chapter Outline:. Attributes of Algorithms. Measuring Efficiency of Algorithms. Simple Analysis of Algorithms. Polynomial vs Exponential Time Algorithms. Efficiency of Algorithms . the execution time required or. the space used in memory or in disk by an algorithm . Big O notation is used describe the rough estimate of the number of “steps” to complete the algorithm. Definition.