day 9 cleanup

day09/input

@@ -0,0 +1,496 @@
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day09/sample

@@ -0,0 +1,8 @@
+7,1
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+7,3

day09/sol.py

@@ -0,0 +1,99 @@
+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 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 lines 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 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))
+    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]) # 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)
+
+    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)
+        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 inbound_areas():
+        for p in points:
+            for q in points:
+                if p != q and inbounds(p,q):
+                    yield area(p,q)
+
+    # answer 2
+    print(max(inbound_areas()))
+
+def area(p,q):
+    dx = abs(p[0] - q[0]) + 1
+    dy = abs(p[1] - q[1]) + 1
+    return dx*dy
+
+solve("sample")
+solve("input")