Implementing memoization in recursive code break functionality

Question

I can't seem to figure out what broke my code.

I wrote a code that takes a pyramid:

[[1],
 [2,3],
 [4,5,6],
 [7,8,9,10]]

Starting from the head (pyramid[0][0]) calculates the maximum sum possible to achieve by moving to either the item below, or to the item below and to the right recursively

In this example the output should be 20.

This is the code without memoization, which works fine:

def max_trail(pyramid,row=0,col=0):
    if row == (len(pyramid)-1):
        return pyramid[row][col]
    else:
        return pyramid[row][col] + max(max_trail(pyramid ,row+1 ,col),
                                       max_trail(pyramid ,row+1, col+1))

But when I try to apply memoization, something along the way breaks. What am I missing?

This is the broken code:

def max_trail_mem(pyramid,row=0,col=0,mem=None):
    if mem==None:
        mem={}
    key = ((row),(col))
    if row == (len(pyramid)-1):
        if key not in mem:
            value = pyramid[row][col]
            mem[key]=value
            return mem[key]
        return mem[key]
    else:
        key = (row+1),(col)
        if key not in mem:
            mem[(row+1),(col)] = max_trail_mem(pyramid ,row+1 ,col,mem)
        key = (row+1),(col+1)
        if key not in mem:
            mem[(row+1),(col+1)]=max_trail_mem(pyramid ,row+1, col+1,mem)
    return max(mem[(row+1),(col)],mem[(row+1),(col+1)])

This has taken hours off my poor studential life. Any help will be greatly appreciated!

Welcome to StackOverflow! please take the time to take the [tour](http://stackoverflow.com/tour) and see [what can I ask here?](http://stackoverflow.com/help/on-topic). As it is written your question is asking for debugging help "why is this code not working?" which is specifically outlined in [what can I ask here?](http://stackoverflow.com/help/on-topic) as offtopic for stackoverflow. — Tadhg McDonald-Jensen, Dec 17 '16 at 19:09
Have you tried testing where it fails? You can add print statements for quick testing or use [pdb](https://docs.python.org/3.6/library/pdb.html). — Nister, Dec 17 '16 at 19:14

score 1 · Accepted Answer · answered Dec 17 '16 at 19:13

1

You forgot pyramid[row][col] + before max(... at your last return. Adding it gives 20 for your example (see last line of code):

def max_trail_mem(pyramid,row=0,col=0,mem=None):
    if mem==None:
        mem={}
    key = ((row),(col))
    if row == (len(pyramid)-1):
        if key not in mem:
            value = pyramid[row][col]
            mem[key]=value
            return mem[key]
        return mem[key]
    else:
        key = (row+1),(col)
        if key not in mem:
            mem[(row+1),(col)] = max_trail_mem(pyramid ,row+1 ,col,mem)
        key = (row+1),(col+1)
        if key not in mem:
            mem[(row+1),(col+1)] = max_trail_mem(pyramid ,row+1, col+1,mem)
    return pyramid[row][col] + max(mem[(row+1),(col)],mem[(row+1),(col+1)])

answered Dec 17 '16 at 19:13

Mike Müller

82,630
20
166
161

Thank you! That works! but... seems like the memoization here really isn't improving the running time... Does it contribute anything at all? I tried a size 10 pyramid and it returned the same running time in my version without the memoization, and with.. Any advice here? – Guy Seltenreich Dec 17 '16 at 19:18
I get 41.2 µs for the memoized and 201 µs for the pure recursive version. So it is about 5 times faster for a pyramid of size 10. For a pyramid of size 15 the difference is 101 µs and 6.15 ms, i.e. a factor of over 60. For size 20 this factor is over 1000. – Mike Müller Dec 17 '16 at 19:39
Thank you mike, I tried a bigger pyramid and it does work! – Guy Seltenreich Dec 17 '16 at 19:43

Ivan Chaer · Answer 2 · 2016-12-21T11:18:43.043

from timeit import timeit
import math

from repoze.lru import CacheMaker
cache_maker=CacheMaker()


def max_trail(pyramid,row=0,col=0):
    if row == (len(pyramid)-1):
        return pyramid[row][col]
    else:

        mt1 = max_trail(pyramid ,row+1 ,col)
        mt2 = max_trail(pyramid ,row+1, col+1)
        return pyramid[row][col] + max(mt1, mt2)

@cache_maker.lrucache(maxsize='1000', name='pyramid')
def max_trail_with_memoization(pyramid,row=0,col=0):
    if row == (len(pyramid)-1):
        return pyramid[row][col]
    else:

        mt1 = max_trail(pyramid ,row+1 ,col)
        mt2 = max_trail(pyramid ,row+1, col+1)
        return pyramid[row][col] + max(mt1, mt2)

# Build pyramid
pyramid = ()
c = 0
for i in range(20):
    row = ()
    for j in range(i):
        c += 1
        row += (c,)
    if row:
        pyramid += (tuple(row),)

# Repetitions to time
number = 20

# Time it
print('without memoization:  ', timeit('f(t)', 'from __main__ import max_trail as f, pyramid as t', number=number))
print('with memoization      ', timeit('f(t)', 'from __main__ import max_trail_with_memoization as f, pyramid as t', number=number))




print max_trail(pyramid)

Returns:

without memoization:   3.9645819664001465
with memoization:      0.18628692626953125

Implementing memoization in recursive code break functionality

2 Answers2