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11_sort_srch_alg

11_sort_srch_alg - Binary Search Can be performed on Sorted...

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Introduction to Computers and Programming Prof. I. K. Lundqvist Lecture 11 April 12 2004 2 Binary Search • Can be performed on – Sorted arrays – Full and balanced BSTs • Compares and cuts half the work – We cut work in ½ each time – How many times can we cut in half? Binary search is O(Log N) 3 Binary Search 11 found 3 comparisons 3 = Log (8) 55 not found 4 comparisons 4 = Log (8) +1 67 52 47 43 42 19 17 11 42 17 11 17 67 52 47 43 42 19 17 47 53 19 42 47 43 53 4 The Binary Search Algorithm Input: Array to search, element to search for Output: Index if element found, -1 otherwise set Return_Index to -1; -- c1 loop -- c2 (log n +1) set Current_Index to (UB + LB) /2 -- c3 (log n +1) if the LB > UB -- c4 (log n +1) exit ; -- c5 if Input_Array(Current_Index) = element –- c6 log n Return_Index := Current_Index -- c7 exit ; -- c8 if Input_Array(Current_Index) < element -- c9 log n LB := Current_Index +1 -- c10 log n else -- c11 log n UB := Current_Index – 1 -- c12 log n return Return_Index -- c13 T(n) = (c1+c2+c3+c4+c5+c7+c8+c13) + (c2+c3+c4+c6+c9+c10+c11+c12) log n = c’ + c’’log(n) = O(log (n)) Statement Work T(n)
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5 Merge Sort 5 96 67 12 17 42 11 47 5 96 67 12 17 42 11 47 5 96 67 12 17 42 11 47 5 96 67 12 17 42 11 47 47 11 17 42 47 17 42 11 67 12 5 96 67 12 5 96 5 11 12 47 17 42 67 96 6 Merge Sort Analysis Analysis MergeSort (A, left, right) T(n) if (left < right) O(1) mid := (left + right) / 2; O(1)
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