day 9 part 2

day09/sol.py

@@ -13,6 +13,55 @@ def solve(input):
 
     print(max(areas()))
 
+    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
+    lines = [(min(p,q),max(p,q)) for p,q in lines if p[1] != q[1]]
+    # sort by y coord
+    lines.sort(key=lambda l: (l[0][1],l[1][1],l[0][0],l[1][0]))
+    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,
+    #
+
+    bounds = {}
+    ys = sorted(set(p[1] for l in lines for p in l))
+    for y in ys:
+        # select lines which intersect with the scanline at y
+        mylines = []
+        for p,q in lines:
+            if p[1] <= y <= q[1]:
+                mylines.append(p[0])
+        bounds[y] = (min(mylines),max(mylines))
+
+    print(ys)
+    print(bounds)
+
+    def inbounds(p,q):
+        y0 = min(p[1],q[1])
+        y1 = max(p[1],q[1])
+        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]:
+            if not bounds[y][0] <= x0 <= x1 <= bounds[y][1]:
+                return False
+        return True
+
+    def areas2():
+        for p in points:
+            for q in points:
+                if p != q and inbounds(p,q):
+                    yield area(p,q)
+
+    print(max(areas2()))
+
+
 def area(p,q):
     dx = abs(p[0] - q[0]) + 1
     dy = abs(p[1] - q[1]) + 1