堆排序 （Heapsort）

原文：http://en.wikipedia.org/wiki/Heap_sort

Let { 6, 5, 3, 1, 8, 7, 2, 4 } be the list that we want to sort from the smallest to the largest. (NOTE, for 'Building the Heap' step: Larger nodes don't stay below smaller node parents. They are swapped with parents, and then recursively checked if another swap is needed, to keep larger numbers above smaller numbers on the heap binary tree.)

An example on heapsort.

1. Build the heap

Heap	newly added element	swap elements
nil	6
6	5
6, 5	3
6, 5, 3	1
6, 5, 3, 1	8
6, 5, 3, 1, 8		5, 8
6, 8, 3, 1, 5		6, 8
8, 6, 3, 1, 5	7
8, 6, 3, 1, 5, 7		3, 7
8, 6, 7, 1, 5, 3	2
8, 6, 7, 1, 5, 3, 2	4
8, 6, 7, 1, 5, 3, 2, 4		1, 4
8, 6, 7, 4, 5, 3, 2, 1

2. Sorting.

Heap	swap elements	delete element	sorted array	details
8, 6, 7, 4, 5, 3, 2, 1	8, 1			swap 8 and 1 in order to delete 8 from heap
1, 6, 7, 4, 5, 3, 2, 8		8		delete 8 from heap and add to sorted array
1, 6, 7, 4, 5, 3, 2	1, 7		8	swap 1 and 7 as they are not in order in the heap
7, 6, 1, 4, 5, 3, 2	1, 3		8	swap 1 and 3 as they are not in order in the heap
7, 6, 3, 4, 5, 1, 2	7, 2		8	swap 7 and 2 in order to delete 7 from heap
2, 6, 3, 4, 5, 1, 7		7	8	delete 7 from heap and add to sorted array
2, 6, 3, 4, 5, 1	2, 6		7, 8	swap 2 and 6 as they are not in order in the heap
6, 2, 3, 4, 5, 1	2, 5		7, 8	swap 2 and 5 as they are not in order in the heap
6, 5, 3, 4, 2, 1	6, 1		7, 8	swap 6 and 1 in order to delete 6 from heap
1, 5, 3, 4, 2, 6		6	7, 8	delete 6 from heap and add to sorted array
1, 5, 3, 4, 2	1, 5		6, 7, 8	swap 1 and 5 as they are not in order in the heap
5, 1, 3, 4, 2	1, 4		6, 7, 8	swap 1 and 4 as they are not in order in the heap
5, 4, 3, 1, 2	5, 2		6, 7, 8	swap 5 and 2 in order to delete 5 from heap
2, 4, 3, 1, 5		5	6, 7, 8	delete 5 from heap and add to sorted array
2, 4, 3, 1	2, 4		5, 6, 7, 8	swap 2 and 4 as they are not in order in the heap
4, 2, 3, 1	4, 1		5, 6, 7, 8	swap 4 and 1 in order to delete 4 from heap
1, 2, 3, 4		4	5, 6, 7, 8	delete 4 from heap and add to sorted array
1, 2, 3	1, 3		4, 5, 6, 7, 8	swap 1 and 3 as they are not in order in the heap
3, 2, 1	3, 1		4, 5, 6, 7, 8	swap 3 and 1 in order to delete 3 from heap
1, 2, 3		3	4, 5, 6, 7, 8	delete 3 from heap and add to sorted array
1, 2	1, 2		3, 4, 5, 6, 7, 8	swap 1 and 2 as they are not in order in the heap
2, 1	2, 1		3, 4, 5, 6, 7, 8	swap 2 and 1 in order to delete 2 from heap
1, 2		2	3, 4, 5, 6, 7, 8	delete 2 from heap and add to sorted array
1		1	2, 3, 4, 5, 6, 7, 8	delete 1 from heap and add to sorted array
			1, 2, 3, 4, 5, 6, 7, 8	completed

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