Data Structures, Algorithms, & Applications in C++
Chapter 2, Exercise 35

No, a program can exhibit its worst-case time behavior on one input and its worst-case space behavior on another. For example, we may have two ways to solve the same problem. One may be fast but uses a lot of space, and the other may be slow and space efficient. We can combine these two methods into a single program in which the solution method actually used is selected on the basis of some input property. Inputs that satisfy this property run fast using worst-case space; inputs that do not satisfy this property run in worst-case time but use minimal space.