1. Best-fit bin packing in O(n log n) time
The search tree will contain one element for each bin which is in use and has non-zero available capacity
Notice! It is possible that for two or more bins to have the same available capacity

2. Best-fit bin packing in O(n log n) time
Example
Suppose that when object i is to be packed, there are nine bins (a through i) in use.
Available capacity of these bins are 1, 3, 12, 6, 8, 1, 20, 6 and 5, respectively.
The nine bins may be stored in a binary tree with duplicates, using as key the available capacity of a bin.

3. Best-fit bin packing in O(n log n) time
A possible binary search tree. h 6 b c 3 12 a i g d 1 5 6 20 8 e f 1

4. Best-fit bin packing in O(n log n) time
Object I that is to be packed requires s[i] = 4. h
Root h fits, proceeds to the left subtree. 6 b c 3 12 a i g d 1 5 6 20 8 e f 1

5. Best-fit bin packing in O(n log n) time
Object I that is to be packed requires s[i] = 4. h 6 b c 3 12 a i g d 1 5 6 20 8 e f 1

6. Best-fit bin packing in O(n log n) time
Object I that is to be packed requires s[i] = 4. h
b fails, proceeds to the right subtree of b. 6 b c 3 12 a i g d 1 5 6 20 8 e f 1

7. Best-fit bin packing in O(n log n) time
Object I that is to be packed requires s[i] = 4. h 6 b c 3 12 a i g d 1 5 6 20 8 e f 1

8. Best-fit bin packing in O(n log n) time
Object I that is to be packed requires s[i] = 4.
i fits, proceeds to the left subtree of i. h 6 b c 3 12 a i g d 1 5 6 20 8 e f 1
i doesn’t have any left child, it is the best candidate.

9. Best-fit bin packing in O(n log n) time
Another example, object I that is to be packed requires s[i] = 7.
h fails, proceeds to the right subtree of h. h 6 b c 3 12 a i g d 1 5 6 20 8 e f 1

10. Best-fit bin packing in O(n log n) time
Another example, object I that is to be packed requires s[i] = 7. h 6 b c 3 12 a i g d 1 5 6 20 8 e f 1

11. Best-fit bin packing in O(n log n) time
Another example, object I that is to be packed requires s[i] = 7.
c fits, proceeds to the left subtree of c. h 6 b c 3 12 a i g d 1 5 6 20 f e 1 8

12. Best-fit bin packing in O(n log n) time
Another example, object I that is to be packed requires s[i] = 7. h 6 b c 3 12 a i g d 1 5 6 20 f e 1 8

13. Best-fit bin packing in O(n log n) time
Another example, object I that is to be packed requires s[i] = 7.
d fails, proceeds to the right subtree of d. h 6 b c 3 12 a i g d 1 5 6 20 f e 1 8

14. Best-fit bin packing in O(n log n) time
Another example, object I that is to be packed requires s[i] = 7. h 6 b c 3 12 a i g d 1 5 6 20 f e 1 8

15. Best-fit bin packing in O(n log n) time
Another example, object I that is to be packed requires s[i] = 7.
e fits, proceeds to the left subtree of e. h 6 b c 3 12 a i g d 1 5 6 20 f e 1
e has no left child, so e is the best candidate. 8

16. Best-fit bin packing in O(n log n) time
When we find the best bin, we can delete it from the search tree, reduce its capacity by s[i], and reinsert it (unless its remaining capacity is zero).
If we do not find a bin with enough capacity, we can start a new bin.