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| # Magic constants derived from the ALU code | |
| As = [12,10,10,-6,11,-12,11,12,12,-2,-5,-4,-4,-12] | |
| Bs = [ 6, 2,13, 8,13, 8, 3,11,10, 8,14, 6, 8, 2] | |
| Cs = [ 1, 1, 1,26, 1, 26, 1, 1, 1,26,26,26,26, 26] | |
| # to get these, I split the input by "inp w" lines | |
| # and diffed the blocks: the A is the varying x addend, | |
| # the B the varying y addend and the C the varying z divisor | |
| # (apparently always 1 or 26 depending on the sign of A) | |
| import itertools as it | |
| # testing tools (not needed for the actual solution) | |
| def forward(A, B, C, z, w): | |
| "this is what a single block does" | |
| z1 = z//C | |
| if w == z % 26 + A: | |
| return z1 | |
| else: | |
| return 26 * z1 + w + B | |
| def forward_all(ws,As=As,Bs=Bs,Cs=Cs,z=0): | |
| "the whole program" | |
| for A,B,C,w in zip(As,Bs,Cs,ws): | |
| z = forward(A,B,C,z,w) | |
| return z | |
| # solution starts here | |
| def backward(A, B, C, z2, w): | |
| """The possible values of z before a single block | |
| if the final value of z is z2 and w is w""" | |
| zs = [] | |
| x = z2 - w - B | |
| if x % 26 == 0: | |
| zs.append(x//26 * C) | |
| if 0 <= w-A < 26: | |
| z0 = z2 * C | |
| zs.append(w-A+z0) | |
| return zs | |
| def solve(part,As=As,Bs=Bs,Cs=Cs): | |
| zs = {0} | |
| result = {} | |
| if part == 1: | |
| ws = range(1,10) | |
| else: | |
| ws = range(9,0,-1) | |
| for A,B,C in zip(As[::-1],Bs[::-1],Cs[::-1]): | |
| #print(len(zs)) | |
| newzs = set() | |
| for w,z in it.product(ws,zs): | |
| z0s = backward(A,B,C,z,w) | |
| for z0 in z0s: | |
| newzs.add(z0) | |
| result[z0] = (w,) + result.get(z, ()) | |
| zs = newzs | |
| return ''.join(str(digit) for digit in result[0]) | |
| print(solve(1)) | |
| print(solve(2)) |
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