adventofcode2023/day23/sol.py

import sys
input = sys.stdin
map = []
for line in input:
    map.append(list(line.strip()))

# find points where the path forks

def neighbors(x,y):
    n = []
    c = map[y][x]
    for i,j in [(y-1,x),(y+1,x),(y,x-1),(y,x+1)]:
        if c == '<' and not j < x: continue
        if c == '>' and not j > x: continue
        if c == '^' and not i < y: continue
        if c == 'v' and not i > y: continue
        if 0 <= i < len(map) and 0 <= j < len(map[i]):
            if map[i][j] != '#':
                n.append((j,i))
    return n

spots = []
for i in range(len(map)):
    for j in range(len(map[i])):
        if map[i][j] == '.':
            n = neighbors(j,i)
            if len(n) not in (0,2):
                spots.append((j,i))

# construct a graph of paths between fork points

def find_paths(start,spots):
    q = [(0,start)]
    dist = {}
    r = []
    while q:
        q.sort()
        n,(x,y) = q.pop(0)
        if (x,y) in dist:
            continue
        dist[x,y] = n
        #print(x,y,neighbors(x,y))
        if (x,y) in spots and (x,y) != start:
                r.append((n,(x,y)))
        else:
            for j,i in neighbors(x,y):
                if (j,i) not in dist:
                    q.append((n+1,(j,i)))

    return r

G = {}
for p in spots:
    G[p] = find_paths(p,spots)

print(G)


# find start position

for i,c in enumerate(map[0]):
    if c == '.':
        start = (i,0)
        break

# algorithm for finding the shortest path between points in a
# a weighted directed acyclic graph
#
# from wikipedia:
# https://en.wikipedia.org/w/index.php?title=Topological_sorting&oldid=1188428695#Application_to_shortest_path_finding
#
# this is a variant of the bellman-ford and shortest path faster algorithms
# except we can take some shortcuts because the graph is acyclic
#
# we implicitly invert the weights of the graph so that, in effect,
# it finds the longest path instead

def topo(G, start):
    t = []
    seen = set()
    tmp = set()
    def visit(n):
        if n in seen:
            return
        if n in tmp:
            raise Exception("cycle with %s %s"  % (n,tmp))
        tmp.add(n)
        for _, p in G[n]:
            visit(p)
        tmp.remove(n)
        seen.add(n)
        t.append(n)
    visit(start)
    t.reverse()
    return t

print("topo=",topo(G,start))


dist = {n: float('-inf') for n in G}
dist[start] = 0
T = topo(G, start)
for u in T:
    for n,v in G[u]:
        if dist[v] < dist[u] + n:
            dist[v] = dist[u] + n

print(dist)
print(max(dist.values()))