Everything in the left subtree is smaller than the current node, everything in the right subtree is larger. <span complexity="lgn"></span> lookups, but only if the tree is balanced!
Quicksort works by recursively dividing the input into two smaller arrays around a pivot item: one half has items smaller than the pivot, the other has larger items.
Heapsort is similar to selection sort—we're repeatedly choosing the largest item and moving it to the end of our array. But we use a heap to get the largest item more quickly.
Counting sort works by iterating through the input, counting the number of times each item occurs, and using those counts to compute each item's index in the final, sorted array.