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CSE 310-Lecture3

# CSE 310-Lecture3 - CSE 310 A lgor ithms and D ata Click to...

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C M L Click to edit Master subtitle style 10/22/10 CSE 310 Algorithms and Data Aviral Shrivastava Assistant Professor Computer Science and Engineering Arizona State University

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C M L 10/22/10 Announcements Class schedule Monday, Wednesday, 7:00 pm – 10:00 pm Assignment 1 is online Due Monday, June 14, 2010 Assignment 2 will be online today Due by Monday, June 21, 2010 Cheating policy on homeworks Can discuss with your friends, but write independently Learn from web, but write your own programs
C M L 10/22/10 CSE 310 Roadmap Induction Recursion Running Time Analysis

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C M L 10/22/10 Algorithm An ' algorithm' is a method for solving a problem expressed as a finite sequence of instructions. Proof of correctness: always give the right answer and never give a wrong answer Proof of termination: always be completed in a finite number of steps, rather than in an infinite number
C M L 10/22/10 55 Insertion Sort Algorithm --It sorts a list of values by repetitively inserting a particular value into a subset of the list that has already been sorted. Example: 3 9 6 1 2 9 should be inserted after 3 – no change 3 9 6 1 2 6 should be inserted between 3 and 9 3 6 9 1 2 1 should be inserted before 3 1 3 6 9 2 2 should be inserted between 1 and 3 1 2 3 6 9 Running Time Analysis

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C M L 10/22/10 66 /*Pseudocode of Insertion Sort*/ INSERTION-SORT(A) for j = 2 to length(A) do n key = A[j] /* insert A[j] into sorted sequence A[1 … j-1] */ i = j – 1 while (i > 0 and A[i] > key) do A[i+1] = A[i] i = i – 1 A[i+1] = key tj= the number of times the while loop test is executed for a value of j. tj -1= # of elements in A[1…j-1] that are > A[j] I nsertion Sort
C M L 10/22/10 77 INSERTION-SORT(A) for j = 2 to length(A) do n key = A[j] /* insert A[j] into sorted sequence A[1 … j-1]*/ i = j – 1 while i > 0 and A[i] > key do A[i+1] = A[i] i = i – 1 A[i+1] = key times cost n c1 n-1 c2 0 c3=0 n-1 c4 y nj=2 tj c5 W nj= 2 (tj-1) c6 y nj=2(tj-1) c7 n-1 c8 tj= the number of times the while loop test is executed for that value of j.

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