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lect13

# lect13 - Recall from last lecture Bubble Sort Algorithm 1...

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Recall from last lecture: Bubble Sort Algorithm 1 Input the numbers x (1) ,...,x ( n ) (as a vector). 2 Input (or compute) n . 3 for k = 1 ,...,n - 1 for j = 1 ,...n - k if ( x ( j ) > x ( j + 1)) swop x ( j ) and x ( j + 1) end if end for j end for k 4 Output the sorted list 1

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Programs: bubble.m , complexity2.m Time for execution grows with O ( n 2 ). We showed this by counting the number of comparisons and swops: n ( n - 1) / 2. Can we do better? 2
Selection Sort Algorithm Items 1, 2 and 4 are as for bubble sort, but item 3 is replaced by the following 3 for k = 1 ,...,n - 1 assign l = k for j = k + 1 ,...,n if ( x ( j ) < x ( l )) assign l = j end if end for j if ( l 6 = k ) swop x ( k ) and x ( l ) end if end for k Whole thing coded as selection.m 3

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input vector x with the smallest element, then the second with the second smallest, and so on. The j -loop ﬁnds the position l of a smallest entry of the sub-vector [ x ( k ) ,...,x ( n )], after the sub-vector [ x (1) ,...,x ( k - 1)] has already been sorted. 4
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lect13 - Recall from last lecture Bubble Sort Algorithm 1...

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