Merge pull request #4892 from freakin23/fix

py sol for Modern Art

solutions/silver/usaco-744.mdx

@@ -208,4 +208,73 @@ public class Art {
 ```
 
 </JavaSection>
+<PySection>
+
+```py
+class Bound:
+	def __init__(self, min_r: int, max_r: int, min_c: int, max_c: int):
+		self.min_r = min_r
+		self.max_r = max_r
+		self.min_c = min_c
+		self.max_c = max_c
+
+
+with open("art.in") as read:
+	width = int(read.readline().strip())
+	canvas = [list(map(int, read.readline().split())) for _ in range(width)]
+
+visible = {}
+for r in range(width):
+	for c in range(width):
+		color = canvas[r][c]
+		if color not in visible:
+			visible[color] = Bound(r, r, c, c)
+
+		bounds = visible[color]
+		bounds.min_r = min(r, bounds.min_r)
+		bounds.max_r = max(r, bounds.max_r)
+		bounds.min_c = min(c, bounds.min_c)
+		bounds.max_c = max(c, bounds.max_c)
+
+
+visible.pop(0, None)  # 0 isn't a color
+
+# all the non-visible colors could've been painted first
+poss_first = width * width - len(visible)
+
+# handle the edge case where there's only 1 color
+if len(visible) > 1:
+	# rect_num[r][c] is *going* to contain the # of rectangles
+	# that must contain the point (r, c)
+	rect_num = [[0] * (width + 1) for _ in range(width + 1)]
+	valid_colors = set(visible.keys())
+
+	for color, bounds in visible.items():
+		# initialize it as a difference array
+		rect_num[bounds.min_r][bounds.min_c] += 1
+		rect_num[bounds.min_r][bounds.max_c + 1] -= 1
+		rect_num[bounds.max_r + 1][bounds.min_c] -= 1
+		rect_num[bounds.max_r + 1][bounds.max_c + 1] += 1
+
+	# Apply the difference array to get the actual count
+	for r in range(width):
+		for c in range(width):
+			if r > 0:
+				rect_num[r][c] += rect_num[r - 1][c]
+			if c > 0:
+				rect_num[r][c] += rect_num[r][c - 1]
+			if r > 0 and c > 0:
+				rect_num[r][c] -= rect_num[r - 1][c - 1]
+
+			# if 2 rectangles overlap, the one at the top
+			# (aka the shown one) can't have been painted first
+			if rect_num[r][c] > 1:
+				valid_colors.discard(canvas[r][c])
+
+	poss_first += len(valid_colors)
+
+print(poss_first, file=open("art.out", "w"))
+```
+
+</PySection>
 </LanguageSection>