Looks like the number of states for memoization is $$$n \cdot 2 \cdot 2 \cdot 2$$$, where $$$n$$$ is up to $$$10^5$$$. Well, that's $$$800\,000$$$ states, which are not fast to put into a map, even with a compiled language, as you can see.

Note: the hash you use in the C++ submission is bad. It literally gives the same result for quadruples of inputs:

• $$$(x, 0, 0, 0)$$$, $$$(x, 0, 1, 1)$$$, $$$(x, 1, 0, 1)$$$, $$$(x, 1, 1, 0)$$$ have the same hash,
• $$$(x, 0, 0, 1)$$$, $$$(x, 0, 1, 0)$$$, $$$(x, 1, 0, 0)$$$, $$$(x, 1, 1, 1)$$$ have the same hash.

Consider using some other hash, or an ordered map.

I tested running your code with @bootstrap in GYM. It takes 2.6 s / 2.0 s. So your solution is just slightly too slow.

Btw there is a simple trick here to get around recursion (and bootstrap) in its entirety. By switching

print(dp(0,False,False,False))

to

for i in range(days)[::-1]:
    dp(i,False,False,False)
print(dp(0,False,False,False))

you have essentially a bottom-up DP solution. Note that any recursive call done will be stored in the cache. Using this trick, your code gets AC in 1.2 s / 2.0 s 247814957.