Added Basic UnionFind

Graphs/UnionFind/DisjointSet/01_basic_disjointset.py → Graphs/UnionFind/01_basic_disjointset.py

@@ -32,14 +32,12 @@ def find(self, a):
  a = self.root[a]
  return a 
 
-uu = UnionFind(10)
+uu = UnionFind(6)
 
 print(uu.root)
 uu.union(0,1)
-uu.union(0,2)
-uu.union(1,3)
-uu.union(4,8)
-uu.union(5,6)
-uu.union(5,7)
+uu.union(4,5)
+uu.union(1,4)
+
 print(uu.root)
-print([i for i in range(10)])
+#print([i for i in range(6)])

Graphs/UnionFind/README.md

@@ -0,0 +1,86 @@
+## Overview:
+A way that we can easily check membership in an undirected graph is through the use of UnionFind aka. Disjoint Set. 
+The word Union Find and Disjoint Set are relatively interchangable within the coding world with Disjoint Set reffering to 
+the data structure and Union Find referring to the actual algorithm. This data structure plays an especially important role in Kruskal's algorithm for finding a minimum spanning tree as it can 
+help determine if an undirected graph contains any cycles.
+
+## What is a Disjoint Set (Union Find)?
+A Disjoint set is essentially an undirected graph. It's a datastructure that stores a collection of disjoint (non-overlapping) sets. 
+It stores a subsection of a set into disjoint subsets. 
+The basic operations are as follows:
+
+### Find()
+Find the root of a given disjoint subset 
+
+```python
+ def find(self, a): 
+ while a != self.root[a]: 
+ a = self.root[a]
+ return a 
+```
+
+### Union()
+Combine subsets into a larger subset 
+```python 
+ def union(self, x, y):
+ rootX = self.find(x)
+ rootY = self.find(y)
+ if rootX != rootY:
+ for i in range(len(self.root)):
+ if self.root[i] == rootY:
+ self.root[i] = rootX
+```
+
+At the initialization of a disjoint set each element represents a separate subset with its parent being the element itself. 
+
+This is what's called the root array. 
+
+
+## Algorithm of UnionFind in Python
+Every time we reach a new node, we will take the following steps:
+1. Call find(x), and find(y) to find the root of each of the subsets, with x and y representing the elements to combine. 
+2. Loop through entire root array and update the root of y with the root of x
+
+## Time & Space Complexity
+* **Time Complexity:**
+Time complexity of the basic UnionFind algorithm is `O(N)`, for find and `O(N)` for union, where N is the number of elements
+
+However, depending on the uitilization of this algorithm it often can scale to `O(N^2)` as you often times find yourself doing 
+N operations of Union.
+
+
+* **Space Complexity:**
+Since the initialization array is of length N. 
+
+The space complexity of the UnionFind algorithm is `O(N)`, where N is the number of elements
+
+## Input & Output:
+
+At the start each element is the root of itself. 
+```python
+uf = UnionFind(6)
+ ```
+<img width=50% src="../UnionFind/Images/basic_union/basic_union.png"> 
+
+```python
+uf.union(0,1)
+ ```
+When we call the union function we update the root of one element to the root of the other.
+
+<img width=50% src="../UnionFind/Images/basic_union/basic_union_1.png"> 
+
+```python
+uf.union(4,5)
+ ```
+
+
+<img width=50% src="../UnionFind/Images/basic_union/basic_union_2.png">
+
+```python
+uf.union(1,4)
+ ```
+
+ This also applies to all subsequent elements with the same root
+
+<img width=50% src="../UnionFind/Images/basic_union/basic_union_3.png"> 
+