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Guide to Quadratic Performance Sorting Algorithms

Learn about selection sort and insertion sort, including their algorithms, performance analysis, advantages, and comparisons in different scenarios. Understand when to use each method efficiently.

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Guide to Quadratic Performance Sorting Algorithms

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  1. Quadratic performance Sorting

  2. Selection sort • elements are selected in order and placed in their final sorted positions • ith pass selects the ith largest element in the array, and places it in the (n-i)th position of the array • an “interchange sort”; i.e., based on swapping

  3. public static void selectionsort( int[] data, int first, int n) { int i, j; int temp;// used during swap int big; // index of largest value // in data[first…first + i]  }

  4. public static void selectionsort( int[] data, int first, int n) {  for (i = n-1; i>0; i--) { big = first; for (j=first+1; j<=first+i; j++) if (data[big] < data[j]) big=j; temp = data[first+i]; data[first+i] = data[big]; data[big] = temp; } }

  5. public static void selectionsort( int[] data, int first, int n) { int i, j, temp; int big; // index of largest value // in data[first…first + i] for (i = n-1; i>0; i--) { big = first; for (j=first+1; j<=first+i; j++) if (data[big] < data[j]) big=j; temp = data[first+i]; data[first+i] = data[big]; data[big] = temp; } } Trace…

  6. Analysis of selection sort • best, average, and worst case time • Θ(n2) comparisons, • Θ(n)swaps • Θ(n2)time—quadratic.

  7. Advantages of Selection sort • can be done “in-place”—no need for a second array • minimizes number of swaps

  8. Insertion sort • begin with “sorted” list of one element • sequentially insert new elements into sorted list • size of sorted list increases, size of unsorted list decreases

  9. public static void insertionsort( int[] data, int first, int n) { int i, j; int entry; for (i=1; i<n; i++) { entry = data[first + i]; for (j= first+i; test ; j--) data[j] = data[j-1]; data[j]=entry; } } // test: (j>first)&&(data[j-1]>entry)

  10. Analysis of Insertion sort • worst case: • elements initially in reverse of sorted order. • Θ(n2) comparisons, swaps • average case: • same analysis as worst case • best case: • elements initially in sorted order • no swaps • Θ(n) comparisons

  11. Analysis of Insertion sort (cont’d) Overall, insertion sort requiresO(n2)time

  12. Advantages of Insertion sort • can be done “in-place” • if data is in “nearly sorted” order, runs in Θ(n)time

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