Heapsort

Why study Heapsort? ,[object Object],[object Object],[object Object],[object Object],[object Object]

What is a “heap”? ,[object Object],[object Object],[object Object],[object Object],[object Object]

Balanced binary trees ,[object Object],[object Object],[object Object],[object Object],Balanced Balanced Not balanced n-2 n-1 n

Left-justified binary trees ,[object Object],[object Object],[object Object],Left-justified Not left-justified

Plan of attack ,[object Object],[object Object],[object Object]

The heap property ,[object Object],[object Object],[object Object],12 8 3 Blue node has heap property 12 8 12 Blue node has heap property 12 8 14 Blue node does not have heap property

siftUp ,[object Object],[object Object],[object Object],14 8 12 Blue node has heap property 12 8 14 Blue node does not have heap property

Constructing a heap I ,[object Object],[object Object],[object Object],[object Object],[object Object],Add a new node here Add a new node here

Constructing a heap II ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Constructing a heap III 8 1 2 3 4 8 10 10 8 10 8 5 10 8 5 12 10 12 5 8 12 10 5 8

Other children are not affected ,[object Object],[object Object],[object Object],12 10 5 8 14 12 14 5 8 10 14 12 5 8 10

A sample heap ,[object Object],[object Object],[object Object],19 14 18 22 3 21 14 11 9 15 25 17 22

Removing the root ,[object Object],[object Object],[object Object],[object Object],19 14 18 22 3 21 14 11 9 15 17 22 11

The reHeap method I ,[object Object],[object Object],[object Object],[object Object],19 14 18 22 3 21 14 9 15 17 22 11

The reHeap method II ,[object Object],[object Object],[object Object],19 14 18 22 3 21 14 9 15 17 11 22

The reHeap method III ,[object Object],[object Object],[object Object],19 14 18 11 3 21 14 9 15 17 22 22

The reHeap method IV ,[object Object],[object Object],[object Object],[object Object],19 14 18 21 3 11 14 9 15 17 22 22

Sorting ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Mapping into an array ,[object Object],[object Object],[object Object],[object Object],19 14 18 22 3 21 14 11 9 15 25 17 22 25 22 17 19 22 14 15 18 14 21 3 9 11 0 1 2 3 4 5 6 7 8 9 10 11 12

Removing and replacing the root ,[object Object],[object Object],[object Object],[object Object],25 22 17 19 22 14 15 18 14 21 3 9 11 0 1 2 3 4 5 6 7 8 9 10 11 12 11 22 17 19 22 14 15 18 14 21 3 9 25 0 1 2 3 4 5 6 7 8 9 10 11 12

Reheap and repeat ,[object Object],[object Object],[object Object],[object Object],22 22 17 19 21 14 15 18 14 11 3 9 25 0 1 2 3 4 5 6 7 8 9 10 11 12 9 22 17 19 22 14 15 18 14 21 3 22 25 0 1 2 3 4 5 6 7 8 9 10 11 12 11 22 17 19 22 14 15 18 14 21 3 9 25 0 1 2 3 4 5 6 7 8 9 10 11 12

Analysis I ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analysis II ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analysis III ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Analysis IV ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Heapsort

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Heapsort