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CSC211 Data Structures CSC211 Data Structures
Lecture 21Lecture 21
Quadratic SortingQuadratic Sorting
Instructor: Prof. Xiaoyan LiInstructor: Prof. Xiaoyan LiDepartment of Computer Science Department of Computer Science
Mount Holyoke CollegeMount Holyoke College
Template classes in visual studioTemplate classes in visual studio
Building C++ Applications with Template Building C++ Applications with Template Classes in Visual StudioClasses in Visual Studio
http://www.ecs.fullerton.edu/~sowell/cs331/TemplateClasses.htmlhttp://www.ecs.fullerton.edu/~sowell/cs331/TemplateClasses.html
Review: hashing/hash tableReview: hashing/hash table
Chapter 13 presents several common algorithms for sorting an array of integers.
Two slow but simple algorithms are Selectionsort and Insertionsort.
This presentation demonstrates how the two algorithms work.
Quadratic SortingQuadratic Sorting
Data StructuresData Structuresand Other Objectsand Other ObjectsUsing C++Using C++
How to sort an array of integers?How to sort an array of integers?
Data: {40, 20, 50 ,60, 10 ,15}Data: {40, 20, 50 ,60, 10 ,15}
Sorting an Array of IntegersSorting an Array of Integers
The picture shows an array of six integers that we want to sort from smallest to largest
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The Selectionsort AlgorithmThe Selectionsort Algorithm
Start by finding the smallest entry.
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The Selectionsort AlgorithmThe Selectionsort Algorithm
Start by finding the smallest entry.
Swap the smallest entry with the first entry.
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The Selectionsort AlgorithmThe Selectionsort Algorithm
Start by finding the smallest entry.
Swap the smallest entry with the first entry.
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The Selectionsort AlgorithmThe Selectionsort Algorithm
Part of the array is now sorted.
Sorted side Unsorted side
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The Selectionsort AlgorithmThe Selectionsort Algorithm
Find the smallest element in the unsorted side.
Sorted side Unsorted side
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The Selectionsort AlgorithmThe Selectionsort Algorithm
Find the smallest element in the unsorted side.
Swap with the front of the unsorted side.
Sorted side Unsorted side
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The Selectionsort AlgorithmThe Selectionsort Algorithm
We have increased the size of the sorted side by one element.
Sorted side Unsorted side
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The Selectionsort AlgorithmThe Selectionsort Algorithm
The process continues...
Sorted side Unsorted side
Smallestfrom
unsorted
Smallestfrom
unsorted
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The Selectionsort AlgorithmThe Selectionsort Algorithm
The process continues...
Sorted side Unsorted side
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Swap
with
front
Swap
with
front
The Selectionsort AlgorithmThe Selectionsort Algorithm
The process continues...
Sorted side Unsorted sideSorted side
is bigger
Sorted sideis bigger
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The Selectionsort AlgorithmThe Selectionsort Algorithm
The process keeps adding one more number to the sorted side.
The sorted side has the smallest numbers, arranged from small to large.
Sorted side Unsorted side
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The Selectionsort AlgorithmThe Selectionsort Algorithm
We can stop when the unsorted side has just one number, since that number must be the largest number.
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Sorted side Unsorted side
The Selectionsort AlgorithmThe Selectionsort Algorithm
The array is now sorted.
We repeatedly selected the smallest element, and moved this element to the front of the unsorted side. [0] [1] [2] [3] [4] [5]
The Selectionsort AlgorithmThe Selectionsort Algorithm
Question 1: Can you write out the code?
Question 2: What is the Big-O of the selectionsort algorithm?
Question 3: Best case, worst case and average case
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The Insertionsort AlgorithmThe Insertionsort Algorithm
The Insertionsort algorithm also views the array as having a sorted side and an unsorted side. [0] [1] [2] [3] [4] [5]
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The Insertionsort AlgorithmThe Insertionsort Algorithm
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
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The Insertionsort AlgorithmThe Insertionsort Algorithm
The sorted side grows by taking the front element from the unsorted side...
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The Insertionsort AlgorithmThe Insertionsort Algorithm
...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
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The Insertionsort AlgorithmThe Insertionsort Algorithm
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
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The Insertionsort AlgorithmThe Insertionsort Algorithm
Sometimes we are lucky and the new inserted item doesn't need to move at all.
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Sorted side Unsorted side
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The Insertionsort AlgorithmThe Insertionsort Algorithm
Sometimes we are lucky twice in a row.
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How to Insert One ElementHow to Insert One Element
Copy the new element to a separate location.
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How to Insert One ElementHow to Insert One Element
Shift elements in the sorted side, creating an open space for the new element.
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How to Insert One ElementHow to Insert One Element
Shift elements in the sorted side, creating an open space for the new element.
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How to Insert One ElementHow to Insert One Element
Continue shifting elements...
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How to Insert One ElementHow to Insert One Element
Continue shifting elements...
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How to Insert One ElementHow to Insert One Element
...until you reach the location for the new element.
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How to Insert One ElementHow to Insert One Element
Copy the new element back into the array, at the correct location.
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How to Insert One ElementHow to Insert One Element
The last The last element element must also be must also be inserted. inserted. Start by Start by copying it...copying it...
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Sorted side Unsorted side
Question:Question:
How many shifts will occur before we copy this element back into the array?
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Question:Question:
Four items Four items are shifted.are shifted.
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Question:Question:
Four items Four items are shifted.are shifted.And then the And then the element is element is copied back copied back into the array.into the array.
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The Insertionsort AlgorithmThe Insertionsort Algorithm
Question 1: Can you write out the code easily?
Question 2: What is the Big-O of the insertsort algorithm?
Question 3: Best case, worst case and average case
Both Selectionsort and Insertionsort have a worst-case time of O(n2), making them impractical for large arrays.
But they are easy to program, easy to debug. Insertionsort also has good performance when the
array is nearly sorted to begin with. But more sophisticated sorting algorithms are
needed when good performance is needed in all cases for large arrays.
Timing and Other Issues Timing and Other Issues
Quiz: (turn in your code) Quiz: (turn in your code)
Implement one of the sorting methods: Implement one of the sorting methods: Selectionsort, Insertionsort or BubblesortSelectionsort, Insertionsort or Bubblesort
Assignment 7: (optional for extra credits)Assignment 7: (optional for extra credits)
Assignment:Assignment: Implement and Test the Priority Queue using a Implement and Test the Priority Queue using a
HeapHeap
Purposes:Purposes: Ensure that you understand and can use heap which Ensure that you understand and can use heap which
is implemented in an array.is implemented in an array. Due date: Due date:
Dec. 19Dec. 19thth (the last day of the exam period) (the last day of the exam period)
It is online now!It is online now!
THE ENDTHE END
Presentation copyright 1997 Addison Wesley Longman,For use with Data Structures and Other Objects Using C++by Michael Main and Walter Savitch.
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