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Sorting Algorithms Sorting Algorithms n 2 Sorts ◦ Selection Sort ◦ Insertion Sort ◦ Bubble Sort Better Sorts ◦ Merge Sort ◦ Quick Sort ◦ Radix Sort
Sorting AlgorithmsSorting Algorithms
n2 Sorts◦Selection Sort◦Insertion Sort◦Bubble Sort
Better Sorts◦Merge Sort◦Quick Sort◦Radix Sort
Radix SortRadix Sort
Sorts all values as StringsLoop thru the Strings backwards,
arranging Stings in sets based on the character being compared.
Reload the array from the sets.
weiner, bankemper, caldwell, goldston, rechtin, rhein, rust, walters, whelan
{ weiner, caldwell, goldston, rechtin, rhein, rust, walters, whelan }{ bankemper }weiner, caldwell, goldston, rechtin, rhein, rust, walters, whelan, bankemper
{ weiner, rechtin, rhein, rust, walters, whelan }{ bankemper }{ caldwell }{ goldston }weiner, rechtin, rhein, rust, walters, whelan, bankemper, caldwell, goldston
{ weiner, rhein, rust, whelan }{ caldwell }{ rechtin }{ goldston }{ bankemper }{ walters }weiner, rhein, rust, whelan, caldwell, rechtin, goldston, bankemper, walters
weiner, rhein, rust, whelan, caldwell, rechtin, goldston, bankemper, walters
{ rhein, rust }{ caldwell }{ rechtin }{ bankemper }{ whelan }{ weiner, walters }{ goldston }rhein, rust, caldwell, rechtin, bankemper, whelan, weiner, walters, goldston
{ rust }{ whelan}{ bankemper, weiner, walters }{ rhein }{ goldston }{ rechtin }{ caldwell }rust, whelan, bankemper, weiner, walters, rhein, goldston, rechtin, caldwell
rust, whelan, bankemper, weiner, walters, rhein, goldston, rechtin, caldwell
{ goldston, caldwell }{ rechtin }{ rhein }{ bankemper }{ whelan }{ weiner }{ rust, walters }goldston, caldwell, rechtin, rhein, bankemper, whelan, weiner, rust, walters
{ rechtin }{ rhein, whelan }{ weiner }{ goldston, caldwell, walters }{ bankemper }{ rust }rechtin, rhein, whelan, weiner, goldston, caldwell, walters, bankemper, rust
rechtin, rhein, whelan, weiner, goldston, caldwell, walters, bankemper, rust
{ caldwell, walters, bankemper }{ rechtin, weiner }{ rhein, whelan }{ goldston }{ rust }caldwell, walters, bankemper, rechtin, weiner, rhein, whelan, goldston, rust
{ bankemper }{ caldwell }{ goldston }{ rechtin, rhein, rust }{ walters, weiner, whelan }
bankemper, caldwell, goldston, rechtin, rhein, rust, walters, weiner, whelan
Merge SortMerge Sort
One of the Divide-And-Conquer algorithmsSplit the array in half, sort each half, then
merge the two halves together.The trick is to call it recursively, splitting
the array in half each time, until you get one element in each half, then merge them into proper sequence.
69, 68, 19, 84, 60, 1, 23, 35, 10, 37, 16
69, 68, 19, 84, 60, 1 23, 35, 10, 37, 16
69, 68, 19 84, 60, 1
69, 68 19
23, 35, 10 37, 16
84, 60 1 23, 35 10 37 16
69 68 84 60 23 35
68, 69 19 60, 84 1 23, 35 10 37 16
19, 68, 69 1, 60, 84 10, 23, 35 16, 37
1, 19, 60, 68, 69, 84 10, 16, 23, 35, 37
1, 10, 16, 19, 23, 35, 37, 60, 68, 69, 84
Merge Sort AlgorithmMerge Sort Algorithm
Find the mid-point of the array I'm responsible for.
Mergesort the low half of the array.Mergesort the high half of the array.Merge the two halves back together.
Merge AlgorithmMerge Algorithm
Starting from the first element of each array section, find the lowest of the two values, and move it to the final position.
Incrementing the pointer in the array section that just lost a value, find the new lowest of the two, and move it.
When all of the values in one array section have been moved, move all the remaining values in the other section.
QuicksortQuicksort
Another Divide-And-Conquer algorithm.Generally considered to be the fastest
sorting algorithm available, but...Average cases are O(n log n)Two cases move it towards O(n2)
◦Small n◦When list is already close to sorted.
Quicksort AlgorithmQuicksort Algorithm
1. Partition the portion of the array I'm responsible for.
2. Quicksort the low part of the array.
3. Quicksort the high part of the array.
Partition AlgorithmPartition Algorithm
Select a Pivot value.Move up the array, stopping at the first value
greater than the Pivot value.Move down the array, stopping at the first value less than the Pivot value.
Swap the two values.Repeat until the counter moving up the array
crosses the counter moving down the array.Finally, swap the pivot value with the value at the
down counter.By the time you're done, all the values < than
Pivot are in the left part of the array and all the values > than Pivot are in the right part of the array.
A Partition VisualizationA Partition Visualization
6968 19 84 60 1 23 35 1037 16
A Partition VisualizationA Partition Visualization
6968 19 84 60 1 23 35 1037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
6968 19 84 60 1 23 35 1037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 84 60 1 23 35 1037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 84 60 1 23 35 1037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 84 60 1 23 35 1037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 84 60 1 23 35 1037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 84 60 1 23 35 1037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 8460 1 23 351037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 8460 1 23 351037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 8460 1 23 351037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 84601 23351037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 84601 23351037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 84601 23351037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 84601 23351037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 84601 23351037 16
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 8460123 3510 3716
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 8460123 3510 3716
Pivot Value = 37
A Partition VisualizationA Partition Visualization
69 6819 8460123 3510 3716
Pivot Value = 37
Comparison of Sorting Comparison of Sorting AlgorithmsAlgorithms
