P p Two slow but simple algorithms are Selectionsort and Insertionsort. p p This presentation demonstrates how the two algorithms work. Quadratic Sorting.

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Presentation transcript:

p p Two slow but simple algorithms are Selectionsort and Insertionsort. p p This presentation demonstrates how the two algorithms work. Quadratic Sorting Data Structures and Other Objects Using Java

Sorting an Array of Integers p p The picture shows an array of six integers that we want to sort from smallest to largest [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p Start by finding the smallest entry. [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p Start by finding the smallest entry. p p Swap the smallest entry with the first entry. [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p Start by finding the smallest entry. p p Swap the smallest entry with the first entry. [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p Part of the array is now sorted. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p Find the smallest element in the unsorted side. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p Find the smallest element in the unsorted side. p p Swap with the front of the unsorted side. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p We have increased the size of the sorted side by one element. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p The process continues... Sorted side Unsorted side Smallest from unsorted Smallest from unsorted [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p The process continues... Sorted side Unsorted side [0] [1] [2] [3] [4] [5] Swap with front Swap with front

The Selectionsort Algorithm p p The process continues... Sorted side Unsorted side Sorted side is bigger Sorted side is bigger [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p The process keeps adding one more number to the sorted side. p p The sorted side has the smallest numbers, arranged from small to large. Sorted side Unsorted side [0] [1] [2] [3] [4] [5]

The Selectionsort Algorithm p p We can stop when the unsorted side has just one number, since that number must be the largest number. [0] [1] [2] [3] [4] [5] Sorted side Unsorted side

The Selectionsort Algorithm p p The array is now sorted. p p We repeatedly selected the smallest element, and moved this element to the front of the unsorted side. [0] [1] [2] [3] [4] [5]

The Insertionsort Algorithm p p The Insertionsort algorithm also views the array as having a sorted side and an unsorted side. [0] [1] [2] [3] [4] [5]

The Insertionsort Algorithm p p The sorted side starts with just the first element, which is not necessarily the smallest element. [0] [1] [2] [3] [4] [5] Sorted side Unsorted side

The Insertionsort Algorithm p p The sorted side grows by taking the front element from the unsorted side... [0] [1] [2] [3] [4] [5] Sorted side Unsorted side

The Insertionsort Algorithm p p...and inserting it in the place that keeps the sorted side arranged from small to large. [0] [1] [2] [3] [4] [5] Sorted side Unsorted side

The Insertionsort Algorithm p p In this example, the new element goes in front of the element that was already in the sorted side. [0] [1] [2] [3] [4] [5] Sorted side Unsorted side

The Insertionsort Algorithm p p Sometimes we are lucky and the new inserted item doesn't need to move at all. [0] [1] [2] [3] [4] [5] Sorted side Unsorted side

The Insertionsort Algorithm p p Sometimes we are lucky twice in a row. [0] [1] [2] [3] [4] [5] Sorted side Unsorted side

How to Insert One Element ¶ ¶ Copy the new element to a separate location. [0] [1] [2] [3] [4] [5] Sorted side Unsorted side

How to Insert One Element · · Shift elements in the sorted side, creating an open space for the new element. [0] [1] [2] [3] [4] [5]

How to Insert One Element · · Shift elements in the sorted side, creating an open space for the new element. [0] [1] [2] [3] [4] [5]

How to Insert One Element · · Continue shifting elements... [0] [1] [2] [3] [4] [5]

How to Insert One Element · · Continue shifting elements... [0] [1] [2] [3] [4] [5]

How to Insert One Element · ·...until you reach the location for the new element. [0] [1] [2] [3] [4] [5]

How to Insert One Element ¸ ¸ Copy the new element back into the array, at the correct location. [0] [1] [2] [3] [4] [5] Sorted side Unsorted side

How to Insert One Element p The last element must also be inserted. Start by copying it... [0] [1] [2] [3] [4] [5] Sorted side Unsorted side

Merge Sort

A Quiz How many shifts will occur before we copy this element back into the array? [0] [1] [2] [3] [4] [5]

A Quiz p Four items are shifted. [0] [1] [2] [3] [4] [5]

A Quiz p Four items are shifted. p And then the element is copied back into the array. [0] [1] [2] [3] [4] [5]

p p Both Selectionsort and Insertionsort have a worst- case time of O(n 2 ), making them impractical for large arrays. p p But they are easy to program, easy to debug. p p Insertionsort also has good performance when the array is nearly sorted to begin with. p p But more sophisticated sorting algorithms are needed when good performance is needed in all cases for large arrays. Timing and Other Issues