fixed info box & added to Bronze Rectangle Geo

content/3_Bronze/Rect_Geo.md

@@ -1,7 +1,7 @@
 ---
 id: rect-geo
 title: "Rectangle Geometry"
-author: Darren Yao
+author: Darren Yao, Michael Cao
 ---
 
 "Geometry" problems on USACO Bronze are usually quite simple and limited to intersections and unions of squares or rectangles. 
@@ -11,8 +11,79 @@ author: Darren Yao
  - Some only include two or three squares or rectangles, in which case you can simply draw out cases on paper. This should logically lead to a solution. 
  - Also, the coordinates typically only go up to $1000$, so a program that performs $\approx 1000^2$ operations (ex. with a nested loop) should pass.
 
-## Problems
+## Rectangle Class (Java)
+A useful class in `Java` for dealing with rectangle geometry problems is the built-in `Rectangle` class. To create a new rectangle, use the following constructor:
 
+```java
+//creates a rectangle with upper-left corner at (x,y) with a specified width and height
+Rectangle newRect = new Rectangle(x, y, width, height); 
+```
+
+The `Rectangle` class supports numerous useful methods. 
+    - `firstRect.intersects(secondRect)` checks if two rectangles intersect.
+    - `firstRect.union(secondRect)` returns a rectangle representing the union of two rectangles.
+    - `firstRect.contains(x, y)` checks whether the integer point (x,y) exists in firstRect.
+    - `firstRect.intersect(secondRect)` returns a rectangle representing the intersection of two rectangles.
+
+This class can often lessen the implementation needed in a lot of bronze problems and codeforces problems.
+
+For example, here is a nice implementation of the problem Blocked Billboard (see below). See the editorial [here](http://www.usaco.org/current/data/sol_billboard_bronze_dec17.html) for more information on the solution.
+
+```java
+import java.awt.Rectangle; //needed to use Rectangle class
+
+public class BlockedBillboard{
+    public static void main(String[] args) throws IOException{
+        Scanner sc = new Scanner(new File("billboard.in"));
+        PrintWriter pw = new PrintWriter(new FileWriter("billboard.out"));
+        Rectangle firstRect = new Rectangle(sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt());
+        Rectangle secondRect = new Rectangle(sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt());
+        Rectangle truck = new Rectangle(sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt());
+        pw.println(getArea(firstRect) + getArea(secondRect) 
+                - getArea(firstRect.intersect(truck)) - getArea(secondRect.intersect(truck)));
+        pw.close();
+    }
+
+    public static long getArea(Rectangle r){
+        return r.getHeight() * r.getWidth()
+    }
+}
+```
+(someone test code pls)
+
+## Rectangle Class (C++)
+
+Unfortunately, C++ doesn't have a built in rectangle class, so you need to write the functions yourself. Here is the solution to Blocked Billboard written in C++ (thanks, Brian Dean!).
+
+```cpp
+struct Rect{
+    int x1, y1, x2, y2;
+    int area(Rect r){
+        return (y2 - y1) * (x2 - x1);
+    }
+};
+
+int intersect(Rect p, Rect q){
+  int xOverlap = max(0, min(p.x2, q.x2) - max(p.x1, q.x1));
+  int yOverlap = max(0, min(p.y2, q.y2) - max(p.y1, q.y1));
+  return xOverlap * yOverlap;
+}
+
+int main(){
+  ifstream cin ("billboard.in");
+  ofstream cout ("billboard.out");
+
+  Rect a, b, t;  // billboards a, b, and the truck
+ 
+  cin >> a.x1 >> a.y1 >> a.x2 >> a.y2;
+  cin >> b.x1 >> b.y1 >> b.x2 >> b.y2;
+  cin >> t.x1 >> t.y1 >> t.x2 >> t.y2;
+
+  cout << area(a) + area(b) - intersect(a, t) - intersect(b, t);
+}
+```
+
+## Problems
  - USACO Bronze
    - [Fence Painting](http://usaco.org/index.php?page=viewproblem2&cpid=567)
      - 1D geometry!!
@@ -22,4 +93,6 @@ author: Darren Yao
    - [Blocked Billboard II](http://usaco.org/index.php?page=viewproblem2&cpid=783)
      - Also rectangles
  - Other
-   - [CF 587 (Div. 3) C: White Sheet](https://codeforces.com/contest/1216/problem/C)
+   - [CF 587 (Div. 3) C: White Sheet](https://codeforces.com/contest/1216/problem/C)
+        - See this code (TODO; codeforces is down) for a nice implementation using the Java Rectangle class.
+

content/5_Gold/DP_Trees.md

@@ -18,8 +18,8 @@ prerequisites:
 
 ## Problems
 
-  [[info | Pro Tip]]
-  | Don't just dive into trying to figure out a DP state and transitions -- make some observations if you don't see any obvious DP solution! 
+[[info | Pro Tip]]
+| Don't just dive into trying to figure out a DP state and transitions -- make some observations if you don't see any obvious DP solution! 
 
   * [Subtree](https://atcoder.jp/contests/dp/tasks/dp_v)
   * [Independent Set](https://atcoder.jp/contests/dp/tasks/dp_p)