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Unformatted text preview: CSE 143 Lecture 8 Complexity slides created by Ethan Apter http://www.cs.washington.edu/143/ 2 Intuition • Are the following operations “fast” or “slow”? behavior fast/slow add at front add at back get at index resizing binary search behavior fast/slow add at front add at back get at index resizing binary search array linked list behavior fast/slow add at front slow add at back fast get at index fast resizing slow binary search (pretty) fast behavior fast/slow add at front fast add at back slow get at index slow resizing N/A (fast!) binary search (really) slow 3 Complexity • “Complexity” is a word that has a special meaning in computer science • complexity : the amount of computational resources a block of code requires in order to run • main computational resources: – time : how long the code takes to execute – space : how much computer memory the code consumes • Often, one of these resources can be traded for the other: – e.g.: we can make some code use less memory if we don’t mind that it will need more time to finish (and viceversa) 4 Time Complexity • We usually care more about time complexity – we want to make our code run fast! • But we don’t merely measure how long a piece of code takes to determine it’s time complexity – Why not? • That approach would have results strongly skewed by: – size/kind of input – speed of the computer’s hardware – other programs running at the same time – operating system – etc 5 Time Complexity • Instead, we care about the growth rate as the input size increase • First, we have to be able to measure the input size – the number of names to sort – the number of nodes in a linked list – the number of students in the IPL queue • We usually call the input size “n” • What happens if we double the input size (n 2n)? – Will the running time double? quadruple? take forever? 6 Time Complexity • We can learn about this growth rate in two ways: – by examining code – by running the same code over different input sizes • Measuring the growth rate by is one of the few places where computer science is like the other sciences – here, we actually collect data • But this data can be misleading – modern computers are very complex – some features (code optimizations) interfere with our data 7 Time Complexity • We’ll count most “simple” statements as 1 time unit – this includes i = i + 1 , int x = elementData[i] , etc – but not loops! (or methods that contain loops!) 8 Time Complexity • Examples: int x = 4 * 10 / 3 + 2  10 * 42; for (int i = 0; i < 100; i++) { x += i; } for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { x += i + j; } } 1 100 9...
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