From 276bf447e808737a001106e534d0c13d8db429cb Mon Sep 17 00:00:00 2001
From: freakin23 <rameezparwez@gmail.com>
Date: Sun, 27 Oct 2024 12:43:00 +0530
Subject: [PATCH 1/5] py sol for Polygon Lattice Points

---
 content/5_Plat/Geo_Pri.mdx | 40 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 40 insertions(+)

diff --git a/content/5_Plat/Geo_Pri.mdx b/content/5_Plat/Geo_Pri.mdx
index a5e1404c0f..6e19cfbdaf 100644
--- a/content/5_Plat/Geo_Pri.mdx
+++ b/content/5_Plat/Geo_Pri.mdx
@@ -466,6 +466,46 @@ int main() {
 ```
 
 </CPPSection>
+<PySection>
+
+```py
+from math import gcd
+
+class Point:
+    def __init__(self, x: int = 0, y: int = 0):
+        self.x = x
+        self.y = y
+
+    def __sub__(self, other):
+        return Point(self.x - other.x, self.y - other.y)
+    
+n = int(input())
+points = []
+
+for _ in range(n):
+    x, y = map(int, input().split())
+    points.append(Point(x, y))
+
+points.append(points[0])
+
+area = 0
+for i in range(n):
+    area += points[i].x * points[i + 1].y - points[i].y * points[i + 1].x
+
+area = abs(area)
+boundary_points = 0
+
+for i in range(n):
+    diff = points[i + 1] - points[i]
+    g = gcd(abs(diff.x), abs(diff.y))
+    boundary_points += g
+
+interior_points = (area - boundary_points) // 2 + 1
+
+print(interior_points, boundary_points)
+```
+
+</PySection>
 </LanguageSection>
 
 <Problems problems="standard" />

From 866e3f216d79d0404c3b069ab8a72035794332cb Mon Sep 17 00:00:00 2001
From: freakin23 <rameezparwez@gmail.com>
Date: Sun, 27 Oct 2024 12:44:19 +0530
Subject: [PATCH 2/5] add TC

---
 content/5_Plat/Geo_Pri.mdx | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/content/5_Plat/Geo_Pri.mdx b/content/5_Plat/Geo_Pri.mdx
index 6e19cfbdaf..5413ab2b5c 100644
--- a/content/5_Plat/Geo_Pri.mdx
+++ b/content/5_Plat/Geo_Pri.mdx
@@ -421,6 +421,8 @@ $A$ can be computed using cross-product.
 
 ## Implementation
 
+**Time Complexity:** $\mathcal{O}(N)$
+
 <LanguageSection>
 <CPPSection>
 

From 8a975b28a3ace183ec3caf89028927159e7aa31f Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 27 Oct 2024 07:17:27 +0000
Subject: [PATCH 3/5] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 content/5_Plat/Geo_Pri.mdx | 26 ++++++++++++++------------
 1 file changed, 14 insertions(+), 12 deletions(-)

diff --git a/content/5_Plat/Geo_Pri.mdx b/content/5_Plat/Geo_Pri.mdx
index 5413ab2b5c..b7f5b3836c 100644
--- a/content/5_Plat/Geo_Pri.mdx
+++ b/content/5_Plat/Geo_Pri.mdx
@@ -473,34 +473,36 @@ int main() {
 ```py
 from math import gcd
 
+
 class Point:
-    def __init__(self, x: int = 0, y: int = 0):
-        self.x = x
-        self.y = y
+	def __init__(self, x: int = 0, y: int = 0):
+		self.x = x
+		self.y = y
+
+	def __sub__(self, other):
+		return Point(self.x - other.x, self.y - other.y)
+
 
-    def __sub__(self, other):
-        return Point(self.x - other.x, self.y - other.y)
-    
 n = int(input())
 points = []
 
 for _ in range(n):
-    x, y = map(int, input().split())
-    points.append(Point(x, y))
+	x, y = map(int, input().split())
+	points.append(Point(x, y))
 
 points.append(points[0])
 
 area = 0
 for i in range(n):
-    area += points[i].x * points[i + 1].y - points[i].y * points[i + 1].x
+	area += points[i].x * points[i + 1].y - points[i].y * points[i + 1].x
 
 area = abs(area)
 boundary_points = 0
 
 for i in range(n):
-    diff = points[i + 1] - points[i]
-    g = gcd(abs(diff.x), abs(diff.y))
-    boundary_points += g
+	diff = points[i + 1] - points[i]
+	g = gcd(abs(diff.x), abs(diff.y))
+	boundary_points += g
 
 interior_points = (area - boundary_points) // 2 + 1
 

From 9a886483f3ef21a4390b6974fb452598e2441bd6 Mon Sep 17 00:00:00 2001
From: Rameez Parwez <79394137+freakin23@users.noreply.github.com>
Date: Sun, 27 Oct 2024 20:26:29 +0530
Subject: [PATCH 4/5] Update TC

---
 content/5_Plat/Geo_Pri.mdx | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/content/5_Plat/Geo_Pri.mdx b/content/5_Plat/Geo_Pri.mdx
index b7f5b3836c..6d8e3c58ee 100644
--- a/content/5_Plat/Geo_Pri.mdx
+++ b/content/5_Plat/Geo_Pri.mdx
@@ -421,7 +421,7 @@ $A$ can be computed using cross-product.
 
 ## Implementation
 
-**Time Complexity:** $\mathcal{O}(N)$
+**Time Complexity:** $\mathcal{O}(N \log P)$, where `P` is the maximum difference between coordinates of points.
 
 <LanguageSection>
 <CPPSection>

From 17b167463544822e7b346c0598c048799ce02a27 Mon Sep 17 00:00:00 2001
From: Rameez Parwez <79394137+freakin23@users.noreply.github.com>
Date: Sun, 27 Oct 2024 20:28:40 +0530
Subject: [PATCH 5/5] Update Geo_Pri.mdx

---
 content/5_Plat/Geo_Pri.mdx | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/content/5_Plat/Geo_Pri.mdx b/content/5_Plat/Geo_Pri.mdx
index 6d8e3c58ee..6924fe01e5 100644
--- a/content/5_Plat/Geo_Pri.mdx
+++ b/content/5_Plat/Geo_Pri.mdx
@@ -421,7 +421,7 @@ $A$ can be computed using cross-product.
 
 ## Implementation
 
-**Time Complexity:** $\mathcal{O}(N \log P)$, where `P` is the maximum difference between coordinates of points.
+**Time Complexity:** $\mathcal{O}(N \log P)$, where $P$ is the maximum difference between coordinates of points.
 
 <LanguageSection>
 <CPPSection>