Average selection sort always involves nn 12 12

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Unformatted text preview: al 3)+ n(n Notice that we haven't said anything about Notice average performance. average Selection sort always involves n(n-1)/2 1)/2 comparisons. comparisons. This occurs even if the array was sorted already. Not very good. Maybe we should try to speed this up. Applied Programming Applied Before we do, why is this not as good? Before why Applied Programming Bubble Sort This involves the same number of passes but This more moves (selection sort involved less than n). more Sounds worse. We'll see. for (i=0;i<n-1;i++) { for (j=i+1;j<n;j++) { if (X[i] > X[j]) { temp = X[i]; X[i] = X[j]; X[j] = temp; } } } On each outer loop pass, consecutive values in On the array are compared and swapped if in the wrong order. wrong Because we have to swap too often – adds to the Because adds number of operations we have to perform.Programming number Applied After each pass one extra value is guaranteed to be in its correct one position (at the upper end of the array) position So only n-1 passes will be needed Big values 'bubble up' the array. Applied Programming for (i=n-1;i>0;i--) { for (j=0;j<i;j++) if (X[j] > X[j+1]) swap values j and j+1 } Same number of comparisons as selection sort Same but a whole lot more swaps. but There are our guarantees. Note that the variable i iindicates the highest ndicates Note position in the array which is yet to be sorted. position We can rewrite code to reflect. Let's look at the code. Applied Programming Applied Programming for (i=n-1;i>0;i--) { for (j=0;j<i;j++) if (X[j] > X[j+1]) swap values j and j+1 } LastUnsorted = n-1; while (LastUnsorted > 0) { for (j=0;j<LastUnsorted;j++) if (X[j] > X[j+1]) swap values j and j+1 LastUnsorted--; } If there was a point in the inner loop after which If no swapping was performed, then those remaining entries in the array must be sorted. remaining Call that value LastSwapIndex. Call LastSwapIndex LastUnsorted = n-1; while (LastUnsorted > 0) { for (j=0;j<LastUnsorted;j++) if (X[j] > X[j+1]) swap values j and j+1 LastUnsorted--; } Applied Programming Applied LastUnsorted = n-1; while (LastUnsorted > 0) { LastSwapIndex = 0; for (j=0;j<LastUnsorted;j++) { if (X[j] > X[j+1])...
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This document was uploaded on 04/07/2014.

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