I will be happy to get some help.
I have the following problem:
I'm given a list of numbers seq
and a target number and I need to write 2 things:
A recursive solution that returns True
if there is a sum of a subsequence that equals the target number and False
otherwise.
example:
subset_sum([-1,1,5,4],0) # True
subset_sum([-1,1,5,4],-3) # False
Secondly, I need to write a solution using what I wrote in the previous solution
but now with memoization that uses a dictionary in which the keys are tuples:
(len(seq),target)
For number 1 this is what I got to so far:
def subset_sum(seq, target):
if target == 0:
return True
if seq[0] == target:
return True
if len(seq) > 1:
return subset_sum(seq[1:],target-seq[0]) or subset_sum(seq[1:],target)
return False
Not sure I got it right so if I could get some input I will be grateful.
For number 2:
def subset_sum_mem(seq, target, mem=None ):
if not mem:
mem = {}
key=(len(seq),target)
if key not in mem:
if target == 0 or seq[0]==target:
mem[key] = True
if len(seq)>1:
mem[key] = subset_sum_mem(seq[1:],target-seq[0],mem) or subset_sum_mem(seq[1:],target,mem)
mem[key] = False
return mem[key]
I can't get the memoization to give me the correct answer so I'd be glad for some guidance here.
Thanks for anyone willing to help!
Just for reference, here's a solution using dynamic programming:
def positive_negative_sums(seq):
P, N = 0, 0
for e in seq:
if e >= 0:
P += e
else:
N += e
return P, N
def subset_sum(seq, s=0):
P, N = positive_negative_sums(seq)
if not seq or s < N or s > P:
return False
n, m = len(seq), P - N + 1
table = [[False] * m for x in xrange(n)]
table[0][seq[0]] = True
for i in xrange(1, n):
for j in xrange(N, P+1):
table[i][j] = seq[i] == j or table[i-1][j] or table[i-1][j-seq[i]]
return table[n-1][s]