From 31559401cb694b49396fd20708583249ee0db09e Mon Sep 17 00:00:00 2001
From: projectPythonator <ard902@mail.usask.ca>
Date: Thu, 30 Jul 2020 06:53:54 -0600
Subject: [PATCH 1/2] consistency

Agis Daniels
for consistency reasons i removed sub and re added vec
ccw already used it in a difference file so i just used it from the points line .py as well < had a more elegant version from that file too so i used it here too
retested and still holds ac on kattis
---
 ch7/polygon.py | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/ch7/polygon.py b/ch7/polygon.py
index 54cf62f..cf31122 100644
--- a/ch7/polygon.py
+++ b/ch7/polygon.py
@@ -16,10 +16,8 @@ def __init__(self, x, y):                       # constructor
     self.x = x
     self.y = y
   
-  def __sub__(self, b): #tovec(a,b)==b-a
-    return point(self.x-b.x, self.y-b.y)
   def __lt__(self, b):  #self<b mod for floats :)
-    return (self.x<b.x) if self.x!=b.x else (self.y<b.y)
+    return (self.x, self.y) < (b.x, b.y)
   
   def __str__(self): return "{} {}".format(self.x, self.y)
   def __hash__(self):return hash((self.x,self.y))
@@ -28,6 +26,13 @@ def __hash__(self):return hash((self.x,self.y))
 #   bool operator <(const point &p) const {
 #    return x < p.x || (abs(x-p.x) < EPS && y < p.y); } };
 
+class vec:
+  def __init__(self, x=0, y=0):
+    self.x = x
+    self.y = y
+
+def toVec(a, b):
+  return vec(b.x-a.x, b.y-a.y)
 # struct vec { double x, y;  // name: `vec' is different from STL vector
 #   vec(double _x, double _y) : x(_x), y(_y) {} };
 
@@ -73,7 +78,7 @@ def cross(a, b): return a.x*b.y-a.y*b.x
 #   return fabs(ans)/2.0;
 # }
 
-def ccw(p, q, r): return (cross(q-p, r-p) > 0)
+def ccw(p, q, r): return (cross(toVec(p,q),toVec(p,r)) > 0)
 # note python i used class opperators for tovec (Agis Daniels)
 # // note: to accept collinear points, we have to change the `> 0'
 # // returns true if point r is on the left side of line pq

From fc12bae0c9e42fcd862f128ddc28f8996de86329 Mon Sep 17 00:00:00 2001
From: projectPythonator <ard902@mail.usask.ca>
Date: Thu, 30 Jul 2020 07:17:34 -0600
Subject: [PATCH 2/2] added in the area

Agis Daniels
nice one liner for area
i called cross product function to avoid the need to retype the code again
should help avoid typos when implementing it from paper
the less than for point seems to work nicely with floats :)
also added a oneliner version of the perimeter function above the code as well
---
 ch7/polygon.py | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/ch7/polygon.py b/ch7/polygon.py
index cf31122..2db6ddd 100644
--- a/ch7/polygon.py
+++ b/ch7/polygon.py
@@ -16,8 +16,7 @@ def __init__(self, x, y):                       # constructor
     self.x = x
     self.y = y
   
-  def __lt__(self, b):  #self<b mod for floats :)
-    return (self.x, self.y) < (b.x, b.y)
+  def __lt__(self, b): return (self.x, self.y) < (b.x, b.y)
   
   def __str__(self): return "{} {}".format(self.x, self.y)
   def __hash__(self):return hash((self.x,self.y))
@@ -44,12 +43,15 @@ def dist(p1, p2):                                 # Euclidean distance
 
 # returns the perimeter of polygon P, which is the sum of
 # Euclidian distances of consecutive line segments (polygon edges)
+# def perimeter(P) return math.fsum(dist(P[i], P[i+1]) for i in range(len(P)-1)) 
 def perimeter(P):
   ans = 0.0
   for i in range(len(P)-1):                       # note: P[n-1] = P[0]
     ans += dist(P[i], P[i+1])                     # as we duplicate P[0]
   return ans
 
+def area(P):
+  return math.fsum(cross(P[i], P[i+1]) for i in range(len(P)-1))/2
 # // returns the area of polygon P
 # double area(const vector<point> &P) {
 #   double ans = 0.0;
@@ -186,8 +188,8 @@ def CH_Andrew(ps):
   def f(B): #f is a mapping of the two loops since its dup code
     for p in P:
       while len(H)>B and not ccw(H[-2], H[-1], p): H.pop()
-        H.append(p)
-      H.pop()
+      H.append(p)
+    H.pop()
   f(1); P=P[::-1]; f(len(H)+1); return H #4 line low, rev, up, ret
 #c++ implementation below 
 # vector<point> CH_Andrew(vector<point> &Pts) {    // overall O(n log n)