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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 dont 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 dont merely measure how long a piece of code takes to determine its time complexity Why not? That approach would have results strongly skewed by: size/kind of input speed of the computers 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 Well 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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 Spring '08
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