Post on 15-Dec-2015
What else can we do with heaps?
Use the heap for sorting.
Heapsort!
Basic Idea
• Given an unsorted array we use BuildHeap to convert it into a heap
• While(heap is not empty)– removeMin– The heap is one smaller but the array hasn't changed– Put the item just removed in the element just after the end of
the heap
• At conclusion the array is sorted
HeapSortafter BuildHeap
1
5 2
5 6 3 9
11 19 7 12 23 22 68 14
87 43 27 35 99 42 77 71 33 67 89
size = 26
HeapSort
1
5 2
5 6 3 9
11 19 7 12 23 22 68 14
87 43 27 35 99 42 77 71 33 67 89
size = 26removeMin
HeapSort
2
5 3
5 6 22 9
11 19 7 12 23 89 68 14
87 43 27 35 99 42 77 71 33 67
size = 25removeMin = 1
Not in heap now
HeapSort
2
5 3
5 6 22 9
11 19 7 12 23 89 68 14
87 43 27 35 99 42 77 71 33 67 1
size = 25
heap is 1 element smaller, smallest element is at end of array
HeapSort
2
5 3
5 6 22 9
11 19 7 12 23 89 68 14
87 43 27 35 99 42 77 71 33 67 1
size = 25
Now do it again!
HeapSort
3
5 9
5 6 22 14
11 19 7 12 23 89 68 67
87 43 27 35 99 42 77 71 33 2 1
size = 24
HeapSort
5
5 9
11 6 22 14
33 19 7 12 23 89 68 67
87 43 27 35 99 42 77 71 3 2 1
size = 23
HeapSort
5
6 9
11 7 22 14
33 19 42 12 23 89 68 67
87 43 27 35 99 71 77 5 3 2 1
size = 22
HeapSort
6
7 9
11 7 22 14
33 19 42 12 23 89 68 67
87 43 27 35 99 71 5 5 3 2 1
size = 21
HeapSort
7
7 9
11 12 22 14
33 19 42 71 23 89 68 67
87 43 27 35 99 6 5 5 3 2 1
size = 20
HeapSort
7
11 9
19 12 22 14
33 27 42 71 23 89 68 67
87 43 99 35 7 6 5 5 3 2 1
size = 19
HeapSort
9
11 14
19 12 22 35
33 27 42 71 23 89 68 67
87 43 99 7 7 6 5 5 3 2 1
size = 18
HeapSort
11
12 14
19 42 22 35
33 27 99 71 23 89 68 67
87 43 9 7 7 6 5 5 3 2 1
size = 17
HeapSort
12
19 14
27 42 22 35
33 43 99 71 23 89 68 67
87 11 9 7 7 6 5 5 3 2 1
size = 16
HeapSort
14
19 22
27 42 23 35
33 43 99 71 87 89 68 67
12 11 9 7 7 6 5 5 3 2 1
size = 15
HeapSort
19
27 22
33 42 23 35
67 43 99 71 87 89 68 14
12 11 9 7 7 6 5 5 3 2 1
size = 14
HeapSort
22
27 23
33 42 68 35
67 43 99 71 87 89 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 13
HeapSort
23
27 35
33 42 68 89
67 43 99 71 87 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 12
HeapSort
27
33 35
43 42 68 89
67 87 99 71 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 11
HeapSort
33
42 35
43 71 68 89
67 87 99 27 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 10
HeapSort
35
42 68
43 71 99 89
67 87 33 27 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 9
HeapSort
42
43 68
67 71 99 89
87 35 33 27 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 8
HeapSort
43
67 68
87 71 99 89
42 35 33 27 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 7
HeapSort
67
71 68
87 89 99 43
42 35 33 27 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 6
HeapSort
68
71 99
87 89 67 43
42 35 33 27 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 5
HeapSort
71
87 99
89 68 67 43
42 35 33 27 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 4
HeapSort
87
89 99
71 68 67 43
42 35 33 27 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 3
HeapSort
89
99 87
71 68 67 43
42 35 33 27 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 2
HeapSort
99
89 87
71 68 67 43
42 35 33 27 23 22 19 14
12 11 9 7 7 6 5 5 3 2 1
size = 1