Python

import sys

fh = open(sys.argv[1])
rows = [map(int, line.split()) for line in fh.readlines()]

cache = {}

def max_sum(level=0, index=0):
    try:
        return cache[(level,index)]
    except:
        pass
    try:
        assert index >= 0
        n = rows[level][index]
    except:
        result = 0
    else:
        next_level = level+1
        result = n + max(max_sum(next_level, index),
                         max_sum(next_level, index+1),
                         )
    cache[(level,index)] = result
    return result

print max_sum()
print 'cache size', len(cache)

def _reduce(level=len(rows)-1):
    #print
    #print 'level', rows[level]
    if len(rows) <= 1:
        return rows[0][0]
    level_above = level-1
    for index, _ in enumerate(rows[level_above]):
        #print 'index', index
        l = max(0, index)
        r = min(index+2, len(rows[level]))
        #print 'range', l, '-', r
        sub_max = max(rows[level][l:r])
        #print 'sub_max', sub_max
        rows[level_above][index] += sub_max
        #print 'level above', rows[level_above]
    del rows[level]
    return _reduce(level_above)

print _reduce()