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J 1 subarray 1 but in sorted order but correctness of

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Unformatted text preview: data – E.g. At the start of each iteration of the “outer” for loop of line 1-8, E.g. 8, the subarray A[1..j-1] consists of the elements originally in A[1..j-1] subarray 1] but in sorted order. but • Correctness of algorithm: – Using loop invariant – Similar to the math induction • Initialization, maintenance, termination maintenance termination NCKU IIM NCKU 資料結構 Chapter 2 資料結構 6 2.2 Analyzing algorithms 2.2 Analyzing an algorithm: Analyzing predicting the resources that the algorithm requires. • Resources: memory, communication, bandwidth, logic memory, gate, time. time • Assumptions: one processor, random-access machine one access RAM (how real computers are designed) (how – Instructions are executed one after another (NO concurrent Instructions operations) operations) – Use common instructions (assume each one takes a constant Us amount of time): Arithmetic (+,-,*,/,mod,floor,ceiling,shift right/left), amount ,*,/,mod,floor,ceiling,shift data movement (load,store,copy), control (if..else,case) data – Uses integer and floating-point types – Never mind precisions – Limit on the word size: inputs of size n, assume integers are Li assume represented by clg n bits (lg n means log2 n) clg NCKU IIM NCKU 資料結構 Chapter 2 資料結構 7 Analyzing Running Time How to analyze an algorithm’s running time? • Time taken by an algorithm depends on the input Time input • The input size...
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