### [2020-10-21] Challenge #386 [Intermediate] Partition counts

Python solution with no recursion. Finds p(666) in ~0.017s, p(66666) in ~30s.

``````def third_seq_first():
val = 0
while True:
val += 1
yield val

def third_seq_second():
val = 1
while True:
val += 2
yield val

def third_seq():
first = third_seq_first()
second = third_seq_second()
for i, j in zip(first, second):
yield i
yield j

def second_seq():
val = 1
n = 0
third = third_seq()
for i in third:
yield val
val += i

def generate_p_list(p_in_progress):
if tuple(p_in_progress) in gen_p_list_memos:
return gen_p_list_memos[tuple(p_in_progress)].copy()
lst = []
seq = second_seq()
if p_in_progress[0] <= 0:
return [[0, p_in_progress[1]]]
for i in seq:
curr = p_in_progress[0] - i
if curr < 0:
break
else:
lst.append(curr)
for i in range(len(lst)):
if (i % 4) <= 1:
lst[i] = [lst[i], 1]
else:
lst[i] = [lst[i], -1]
if p_in_progress[1] == -1:
for i in lst:
i[1] = -i[1]
lst.reverse()
gen_p_list_memos[tuple(p_in_progress)] = lst.copy()
return lst
gen_p_list_memos = {}

memos = {0:1}

def p(n):
sum = 0
lst = generate_p_list([n, 1])
while lst != []:
i = lst.pop()
if i[0] in memos:
sum += memos[i[0]] * i[1]
else:
flag = False
temp = generate_p_list(i)
for j in temp:
if j[0] not in memos:
flag = True
break
if not flag:
acc = 0
for j in temp:
acc += memos[j[0]] * j[1]
memos[i[0]] = abs(acc)
sum += acc
else:
lst += temp
return sum

import time
def timed(num):
st = time.time()
p(num)
print("%s seconds" % (time.time() - st))
``````