p16.py

#!/usr/bin/env python3
# -*- coding: utf8 -*-

import numpy as np 

f = open('16.in').read().strip()

l = np.array([int(s) for s in f], dtype=int)

def get_matrix(llen):
    r = np.zeros((llen, llen), dtype=int)
    base_pattern = np.array([0,1,0,-1],dtype=int)
    nrep = 1
    for i in range(llen):
        
        b = np.transpose(np.tile(base_pattern, (nrep,1))).flatten()    
        c = len(l)//len(b) + 1
        b = np.tile(b, c)
        r[i] = b[1:(llen+1)]
        nrep = nrep + 1

    return r

m = get_matrix(len(l))
for i in range(100):
    l = np.abs(np.dot(m, l)) % 10

print("Pt 1:",''.join(l[:8].astype(str)))

l = np.array([int(s) for s in f]*10000, dtype=int)
offset = int(f[:7])

# print(offset / len(l), len(l), offset)
# 7 digits -> ~1 M. Input length 6.5 M. At least for my case I'm at 5971269. 
# At this point the tail end of the list is all multiplied by 1's.
# The nth element from the back is the cumulative sum of elements from the end back to that point.
# This seems to hold for all the examples as well, probably not a coincidence.

l2 = l[offset:][::-1]
for i in range(100):
    l2 = l2.cumsum() % 10

print("Pt 2:",''.join((l2[-8:][::-1]).astype(str)))