day 9 cleanup

day09/sol.py

@@ -1,31 +1,54 @@
 from math import dist
+
 def solve(input):
     points = []
     for line in open(input):
         x,y = map(int, line.strip().split(","))
         points.append((x,y))
 
+    # Part 1:
+    # find the largest rectangle created by two points
+
     def areas():
         for p in points:
             for q in points:
                 if p != q:
                     yield area(p,q)
 
+    # answer 1
     print(max(areas()))
 
+    # Part 2:
+    # find the largest rectangle formed by a pair of points
+    # which is contained within the polygon defined by the list of points.
+
     lines = list(zip(points, points[1:]+[points[0]]))
-    # keep only vertical lines, and sort so the uppermost point (lowest x coord) is the first of the pair
+    # keep only vertical lines, and sort so the uppermost point (lowest y coord) is the first of the pair
     lines = [(min(p,q),max(p,q)) for p,q in lines if p[1] != q[1]]
-    # sort by y coord
+    # sort lines by y coord
     lines.sort(key=lambda l: (l[0][1],l[1][1],l[0][0],l[1][0]))
-    print(lines)
+
+    #print(lines)
 
     # we want to know if the rectangle formed by a pair of points
-    # is completely contained within the axis-aligned polygon defined
-    # by the list of points.
-    # we can do that with a scanline algorithm:
-    # for each x position in the list of points,
+    # is completely contained within an axis-aligned polygon.
     #
+    # we can do that with a pseudo-scanline algorithm.
+    #
+    # we make a couple simplifying assumptions:
+    # 1. first, that the polygon is not self-intersecting
+    # 2. second, that the polygon is not "U shaped" --
+    #    that is, it has a definite, single width in every horizontal slice
+    #    and it doesn't curve around at all -- so we don't have to worry
+    #    about voids
+    #
+    # for each y position, we first calculate the horizontal bounds of the
+    # polygon at that line.
+    #
+    # then, to test if a rectangle is contained within the polygon,
+    # we just need to iterate through the y positions which fall inside the rectangle
+    # and check whether the rectangle would exceed the previously computed bounds
+    # of the polygon at any of those points.
 
     bounds = {}
     ys = sorted(set(p[1] for l in lines for p in l))
@@ -34,11 +57,14 @@ def solve(input):
         mylines = []
         for p,q in lines:
             if p[1] <= y <= q[1]:
-                mylines.append(p[0])
+                mylines.append(p[0]) # only keep the x coord
+        # since we are assuming no self-intersection and no voids,
+        # the bounds on this line are just the leftmost and rightmost
+        # x coordinate of the intersecting lines
         bounds[y] = (min(mylines),max(mylines))
 
-    print(ys)
-    print(bounds)
+    #print(ys)
+    #print(bounds)
 
     def inbounds(p,q):
         y0 = min(p[1],q[1])
@@ -46,21 +72,23 @@ def solve(input):
         x0 = min(p[0],q[0])
         x1 = max(p[0],q[0])
         #print(y0, y1, ys)
-        i = ys.index(y0)
-        j = ys.index(y1) + 1
-        for y in ys[i:j]:
+        start = ys.index(y0)
+        for i in range(start,len(ys)):
+            y = ys[i]
+            if y > y1:
+                break
             if not bounds[y][0] <= x0 <= x1 <= bounds[y][1]:
                 return False
         return True
 
-    def areas2():
+    def inbound_areas():
         for p in points:
             for q in points:
                 if p != q and inbounds(p,q):
                     yield area(p,q)
 
-    print(max(areas2()))
-
+    # answer 2
+    print(max(inbound_areas()))
 
 def area(p,q):
     dx = abs(p[0] - q[0]) + 1