added Union Find progression basic, path_compression, quickfind, quic…

Graphs/UnionFind/01_basic_disjointset.py

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+# The vey basics of union find and disjoint sets 
+# Basically an array and within that array lies a disjoint set 
+
+
+# There are two functions when discussing disjoint sets 
+
+# find(a) which takes in a single argument and returns the root of 
+# that particular node 
+
+# union(a,b) which takes in two arguments and combines them together 
+# let's watch a quick video on how this works and then implement from there 
+
+# First lets implement UnionFind as an object and instantiate it with an array 
+
+class UnionFind: 
+    def __init__(self, size):
+        self.root = [i for i in range(size)]
+
+    # union connects two nodes with a left bias meaning that b will always 
+    # connect to a 
+    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
+
+    # takes in a node a and returns the root node of such
+    def find(self, a): 
+        while a != self.root[a]: 
+            a = self.root[a]
+        return a 
+
+uu = UnionFind(6)
+
+print(uu.root)
+uu.union(0,1)
+uu.union(4,5)
+uu.union(1,4)
+
+print(uu.root)
+#print([i for i in range(6)])

Graphs/UnionFind/README.md

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+## 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">  
+