From d3d175a038c66cedc11316ea7c7d62504d392ce7 Mon Sep 17 00:00:00 2001
From: Andrew Ekstedt <andrew.ekstedt@gmail.com>
Date: Sat, 23 Dec 2023 08:35:10 +0000
Subject: [PATCH] day 23 cleanup part 1

---
 day23/sol.py | 68 ++++++++++++++++++++++++----------------------------
 1 file changed, 31 insertions(+), 37 deletions(-)

diff --git a/day23/sol.py b/day23/sol.py
index d830d2d..babca62 100644
--- a/day23/sol.py
+++ b/day23/sol.py
@@ -4,11 +4,7 @@ map = []
 for line in input:
     map.append(list(line.strip()))
 
-# construct a graph
-for i,c in enumerate(map[0]):
-    if c == '.':
-        start = (i,0)
-        break
+# find points where the path forks
 
 def neighbors(x,y):
     n = []
@@ -31,7 +27,9 @@ for i in range(len(map)):
             if len(n) not in (0,2):
                 spots.append((j,i))
 
-def reachable(start,spots):
+# construct a graph of paths between fork points
+
+def find_paths(start,spots):
     q = [(0,start)]
     dist = {}
     r = []
@@ -53,11 +51,30 @@ def reachable(start,spots):
 
 G = {}
 for p in spots:
-    G[p] = reachable(p,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()
@@ -66,7 +83,7 @@ def topo(G, start):
         if n in seen:
             return
         if n in tmp:
-            raise Exception("cycle with %s %s"  % (repr(n),tmp))
+            raise Exception("cycle with %s %s"  % (n,tmp))
         tmp.add(n)
         for _, p in G[n]:
             visit(p)
@@ -80,36 +97,13 @@ def topo(G, start):
 print("topo=",topo(G,start))
 
 
-dist = {n:float('inf') for n in G}
-pred = {}
+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]:
-        w = -n
-        if dist[v] > dist[u] + w:
-            dist[v] = dist[u] + w
-        pred[v] = u
-    
-print(dist)
-print(-min(dist.values()))
+        if dist[v] < dist[u] + n:
+            dist[v] = dist[u] + n
 
-#import astar
-#def goal(state):
-#    x,y = state
-#    return y == len(map)-1
-#
-#M = max(n for p in G for n,_ in G[p])
-#
-#def nb(state):
-#    p = state
-#    for n,q in G[p]:
-#        yield 1+M-n, q
-#
-#n, g, path = astar.search(start, goal, nb)
-#print(g,path)
-#t = 0
-#for p, q in zip(path, path[1:]):
-#    t += sum(n for n,r in G[p] if r == q)
-#
-#print(t)
+print(dist)
+print(max(dist.values()))