Agree, buy a good book (for example Cormen), learn the algorithms and implement them to get a good understanding.
Try to use the table to answer a following question: what is a time complexity for finding a next item (according to a key) to a given one in a hash table? Memorizing such stuff does not make much sense, but if you understand basic concepts, you will figure it out quickly.
There are basic errors in the table:
BFS, DFS are for graphs, not just trees, and their complexity is not b^d (what is b and d anyway?).
Quick sort expected complexity is nlogn and this is different than average complexity. You can also make quicksort worst-case complexity to be nlogn.
You can't sort anything with space smaller than number of items you are sorting.
You can use buble and insertion sort not only for arrays but also for lists and time complexity does not suffer.
If one takes the time to select optimal pivots it becomes O(nlogn). The selection is free from a big-O perspective, because it's O(n) immediately before the O(n) list division step.
Of course, nobody does this, because the selection is not really free. The constant factor cost of choosing the optimal pivot hurts the average case, making the modified quicksort tend to do worse than heapsort or introsort.
Say, the smallest item in a hash table for which item.key is larger than given_item.key.
Well, keys in a hash table are hashed. This implies that unless you're searching for a specific key (e.g. "42") rather than a condition (e.g. "smallest key greater than 42") then the time complexity is necessarily O(N).