the solution I got runs more than 1 second, which is terrible. Please help if you have better algorithm
"""
Project Euler Problem #14
==========================
The following iterative sequence is defined for the set of positive
integers:
n->n/2 (n is even)
n->3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following
sequence:
13->40->20->10->5->16->8->4->2->1
It can be seen that this sequence (starting at 13 and finishing at 1)
contains 10 terms. Although it has not been proved yet (Collatz Problem),
it is thought that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
NOTE: Once the chain starts the terms are allowed to go above one million.
"""
limit=1000000
uplimit = limit * 3
answer = 1
maxval = 0
data = [0] * uplimit
data[1] = 1
for ind in xrange(1,limit):
cval = ind
stack = []
while True:
if cval < uplimit and data[cval] > 0:
break
stack.append(cval)
if cval % 2 == 0:
cval = cval / 2
else:
cval = cval * 3 + 1
val = data[cval]
while stack:
val += 1
ind = stack.pop()
if ind < uplimit:
data[ind] = val
if val > maxval:
maxval = val
answer = ind
print answer
==========================
$ time python 014.py
837799
real 0m1.744s
user 0m1.734s
sys 0m0.011s
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