Lectures12-part-09-algorithms-1

# linearsearchvsbinarysearch

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Unformatted text preview: 5 M(13)= 48 M(14)= 50 M(15)= 55 M(16)= 57 Running Times Running Times Binary Search At each iteration, range is cut in half Total number of iterations to find an item among N elements is y such that “cut N in half y times to get down to 1” Yes, this is just (base 2) log N Searching among 2300 elements takes only 300 steps (this exceeds the number of particles in the universe!!) Linear search vs. Binary search Linear search vs. Binary search Sorting Algorithms Sorting Algorithms Different methods to put things in order Which are fastest methods? Bubble Sort Bubble Sort Put left, right fingers on M(0), M(1) IF M(left) > M(right) THEN swap them Move left, right fingers to right IF right finger = n THEN done with this pass, start again BUT next time only go up to n­1 Etc., for passes ending at n­2, n­3, etc. Aside: FOR loops Aside: FOR loops new kind of iteration command (similar to WHILE) Example FOR i = 1 to 10 Outputs 3,6,9,…,30 print 3*i Example FOR count = 100 downto 1 print count Outputs 100,99,98,…,1 Bubble Sort Bubble Sort FOR max = n­1 downto 1 make a pass up to position max FOR left = 1 upto max right = left + 1 IF M(left) > M(right) THEN swap them LET’S UNROLL THIS CODE TO MAKE SURE WE UNDERSTAND Bubble Sort Bubble Sort FOR max = n­1 downto 1 FOR left = 1 upto max right = left + 1 IF M(left) > M(right) THEN swap them Let max = n­1 blah blah blah Let max = n­2 blah blah blah … etc Let max = 2 blah blah blah Let max = 1 blah blah blah make a pass up to p...
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