For Friday

1
For Friday

• Read Weiss, chapter 7, sections 8-10
• Homework
• Chapter 7, exercises 4, 11, and 12

2
Exam 1

• Will be one week from Friday
• Will cover material through quicksort

3
Programming Assignment 2
4
Shellsort

• Whats the concept?
• h-sorting
• increment sequence
• Shells sequence 1, 2, 4, 8,
• Hibbards sequence 1, 3, 7, 15,
• best sequence known 1, 5, 19, 41, 109,

5
Performance of Shellsort
6
Heapsort

• Whats the concept?

7
Heapsort

• Use max heaps instead of min heaps
• Use BuildHeap to turn the array into a heap
• Use deleteMax to remove items from the beginning
  of the array, continually moving them to the end
  of the tree

8
Performance of Heapsort
9
Mergesort

• Whats the concept?

10
Mergesort

• void MergeSort(int arr, int temp, int left,
• int right)
• if (left lt right)
• int center (left right)/ 2
• // sort left half
• MergeSort(arr, temp, left, center)
• // sort right half
• MergeSort(arr, temp, center1, right)
• // merge left and right halves
• Merge(arr, temp, left, center1, right)

11

• void Merge(int arr, int temp, int curLeft,
• int curRight, int endRight)
• int endLeft curRight 1
• int curTemp curLeft
• int numElems endRight startLeft 1
• // Main loop
• while (curLeft lt endLeft curRight lt
  endRight)
• if ( arrcurLeft lt arrcurRight)
• tempcurTemp arrcurLeft
• else
• tempcurTemp arrcurRight
• while (curLeft lt endLeft) // finish left
• tempcurTemp arrcurLeft
• while (curRight lt endRight) // finish right
• tempcurTemp arrcurRight
• // copy back to arr
• for (int i 0 i lt numElems i,
  endRight--)
• aendRight tempArrayendRight

12
Performance of Mergesort
13
Bottom-up Mergesort
14
Quicksort

• Basic concept
• Were going to select a pivot
• Were going to swap items into either smaller or
  large than the pivot, giving us two portions
  (partitions) of the array
• Were going to sort each resulting partition
  using quicksort

15
void quicksort(int a, int left, int right)
int i, j, v, temp   if (right - left gt 0) //
at least two items in the partition v
aright //v is the pivot i left - 1 //
1 to the left of the beginning j right
// 1 to the right of where search starts while
(true) // infinite loop while (ai lt v)
// pre-increment i until ai is gt the pivot
while (a--j gt v) // pre-decrement j until
aj is lt the pivot   if (i gt j) break
//if i and j have crossed -- get out of the loop
temp ai // otherwise, swap ai and
aj ai aj aj temp   //
i and j have crossed, so swap ai and the pivot
aright ai ai v // the pivot
is now in place at i   // now call quicksort on
the two partitions quicksort(a, left, i-1) //
left partition quicksort(a, i1, right) //
right partition
16
Performance of Quicksort
17
Improving Quicksort

• Median of 3
• Cutoffs