day 8 optimization

day08/sol.py

@@ -1,43 +1,55 @@
-import math
-from math import floor, sqrt
+from math import floor, sqrt, dist
 
-def dist(p,q):
-    return sqrt(sum((x-y)**2 for x,y in zip(p,q)))
-
-def solve(input, limit):
+def solve(input, limit, D=4000.0):
+    # Parse
     points = []
     for line in open(input):
         x,y,z = map(int,line.split(','))
         points.append((x,y,z))
 
-    def nearest(p):
-        mindist = float('inf')
-        minpoint = p
-        for q in points:
-            if q != p:
-                d = dist(p,q)
-                if d < mindist:
-                    mindist = d
-                    minpoint = q
-        return minpoint
 
-    #for p in points:
-    #    q = shrink(p)
-    #    print(p, nearest(p), list(chain(*[m.get(x,[]) for x in near(q)])))
+    # Optimization: Instead of computing the distance between
+    # every pair of points (which is slow - it grows as n^2.
+    # for n=1000 that's 1 million pairs), only compute the distance
+    # between pairs of "nearby" points, as controlled by the parameter D.
+    # We map each point to a cube in a DxDxD grid and only look at points
+    # in adjacent cubes. This is the core idea in Rabin and Lipton's algorithm
+    # for finding the closest pair of points. It works here because our points
+    # are roughly evenly distributed and none of the pairs we care about
+    # are more than about D units apart. (We end up only having to
+    # look at ~22,000 pairs, which is much quicker.)
+
+    def shrink(p):
+        x,y,z = p
+        return floor(x/D), floor(y/D), floor(z/D)
+
+    def neighbors(p):
+        x,y,z = shrink(p)
+        for dx in (0,-1,+1):
+            for dy in (0,-1,+1):
+                for dz in (0,-1,+1):
+                    i = (x+dx,y+dy,z+dz)
+                    if i in m:
+                        yield from m[i]
+
+    m = {}
+    for p in points:
+        m.setdefault(shrink(p),[]).append(p)
 
     pairs = []
     for p in points:
-        for q in points:
-        #q = nearest(p)
+        for q in neighbors(p):
             if p != q:
                 d = dist(p,q)
                 pairs.append((d,p,q))
 
     pairs.sort()
-    print(len(pairs))
+    print("#pairs =", len(pairs))
     print(*pairs[:10], sep='\n')
 
-    circuit = []
+    # Use a union-find (aka disjoint set) data structure to
+    # keep track of which circuit each point belongs to
+    #
     direct = set()
     parent = {p:p for p in points}
     size = {p:1 for p in points}
@@ -69,7 +81,7 @@ def solve(input, limit):
         if (p,q) in direct or (q,p) in direct:
             # already directly connected
             continue
-        print("connecting", p, q)
+        #print("connecting", p, q)
         n += 1
         union(p,q)
         direct.add((p,q))
@@ -81,7 +93,7 @@ def solve(input, limit):
         if r in seen:
             continue
         seen.add(r)
-        print(r, size[r])
+        #print(r, size[r])
         sizes.append(size[r])
 
     sizes.sort(reverse=True)
@@ -97,7 +109,7 @@ def solve(input, limit):
         if (p,q) in direct or (q,p) in direct:
             # already directly connected
             continue
-        print("connecting", p, q)
+        #print("connecting", p, q)
         n += 1
         union(p,q)
         direct.add((p,q))
@@ -106,8 +118,9 @@ def solve(input, limit):
             print(p,q)
             print(p[0]*q[0])
             break
+    else:
+        print("fail")
 
 
-solve("sample", 10)
-solve("input", 1000)
-
+solve("sample", 10, D=400.0)
+solve("input", 1000, D=10000.0)