Example
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.)
1. Build the heap
| Heap | newly added element | swap elements |
|---|---|---|
| nul | 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 |
Read more about this topic: Heapsort
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)