I've recently become interested in algorithms and have begun exploring them by writing a naive implementation and then optimizing it in various ways.
I'm already familiar with the standard Python module for profiling runtime (for most things I've found the timeit magic function in IPython to be sufficient), but I'm also interested in memory usage so I can explore those tradeoffs as well (e.g. the cost of caching a table of previously computed values versus recomputing them as needed). Is there a module that will profile the memory usage of a given function for me?
This one has been answered already here: Python memory profiler
Basically you do something like that (cited from Guppy-PE):
>>> from guppy import hpy; h=hpy()
>>> h.heap()
Partition of a set of 48477 objects. Total size = 3265516 bytes.
Index Count % Size % Cumulative % Kind (class / dict of class)
0 25773 53 1612820 49 1612820 49 str
1 11699 24 483960 15 2096780 64 tuple
2 174 0 241584 7 2338364 72 dict of module
3 3478 7 222592 7 2560956 78 types.CodeType
4 3296 7 184576 6 2745532 84 function
5 401 1 175112 5 2920644 89 dict of class
6 108 0 81888 3 3002532 92 dict (no owner)
7 114 0 79632 2 3082164 94 dict of type
8 117 0 51336 2 3133500 96 type
9 667 1 24012 1 3157512 97 __builtin__.wrapper_descriptor
<76 more rows. Type e.g. '_.more' to view.>
>>> h.iso(1,[],{})
Partition of a set of 3 objects. Total size = 176 bytes.
Index Count % Size % Cumulative % Kind (class / dict of class)
0 1 33 136 77 136 77 dict (no owner)
1 1 33 28 16 164 93 list
2 1 33 12 7 176 100 int
>>> x=[]
>>> h.iso(x).sp
0: h.Root.i0_modules['__main__'].__dict__['x']
>>>