From: Skullheadx <94652084+Skullheadx@users.noreply.github.com>
Date: Tue, 27 Dec 2022 04:56:50 +0000 (-0500)
Subject: brute force desc
X-Git-Url: http://git.skullheadx.com/nixos/static/gitweb.js?a=commitdiff_plain;h=48b17cb683ead47ec24e5c4e1c6611589b1bd2b3;p=The-Traveling-Salesman-Problem.git

brute force desc
---

diff --git a/.gitignore b/.gitignore
index 5159ca0..883019e 100644
--- a/.gitignore
+++ b/.gitignore
@@ -3,3 +3,4 @@
 /workspace.xml
 .idea/
 __pycache__/
+*.txt
diff --git a/README.md b/README.md
index 357d917..61b3c6b 100644
--- a/README.md
+++ b/README.md
@@ -4,8 +4,9 @@ My solutions to the Traveling Salesman Problem (TSP) inspired by video presented
 (https://youtu.be/GiDsjIBOVoA)
 
 --------------------------------------------------------------------------------------------------------------
-TSP Problem Definition
-If a salesman starts at a town and wants to travel to every other town only once, what is the shortest path he should take?
+**TSP Problem Definition**
+
+_If a salesman starts at a town and wants to travel to every other town only once, what is the shortest path he should take such that he ends up in the town he started in?_
 
 Assuming that:
 1. Each town is connected by a direct edge
@@ -13,3 +14,6 @@ Assuming that:
 3. The direct path to a town is always the shortest, i.e. going directly from town A to town C is faster than going from town A to town B and then town C
 
 --------------------------------------------------------------------------------------------------------------
+**Method 1: Brute Force**
+
+By checking every single possibility and calculating the distance of each route, the shortest path can be determined. However, this strategy does not work for a large number of towns because as **n**, the number of towns, increases, on the first turn, (starting at any town) there are n-1 towns to choose from, then on the second turn there are n-2 choices and so on until there is only one option left which is to return to the starting town. This means that there are `(n - 1)! / 2` total possibilities accounting for duplicates.