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

…kunion, optimized

Graphs/UnionFind/DisjointSet/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(10)
+
+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)
+print(uu.root)
+print([i for i in range(10)])

Graphs/UnionFind/DisjointSet/02_path_compression.py

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+
+class UnionFind: 
+    def __init__(self,size): 
+        self.root = [i for i in range(size)]
+
+    def find(self, n): 
+        if self.root[n] == n: 
+            return n
+
+        self.root[n] = self.find(self.root[n])
+        return self.root[n]
+    # quick union 
+    def union(self, a, b): 
+        fa = self.find(a)
+        fb = self.find(b)
+        if fa != fb: 
+            self.root[fa] = fb 
+
+    def connected(self, x, y): 
+        return self.find(x) == self.find(y)
+# Test Case
+uf = UnionFind(10)
+# 1-2-5-6-7 3-8-9 4
+uf.union(1, 2)
+uf.union(2, 5)
+uf.union(5, 6)
+uf.union(6, 7)
+uf.union(3, 8)
+uf.union(8, 9)
+print(uf.connected(1, 5))  # true
+print(uf.connected(5, 7))  # true
+print(uf.connected(4, 9))  # false
+# 1-2-5-6-7 3-8-9-4
+uf.union(9, 4)
+print(uf.connected(4, 9))  # true

Graphs/UnionFind/DisjointSet/03_quickfind_disjoint.py

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+class UnionFind: 
+    def __init__(self, size): 
+        self.root = [i for i in range(size)]
+    # changing quickfind to have the parent node be stored in the array 
+    # effectively making it an O(1) operation to find the root of a given node 
+    # however, union will take a hit in performance 
+
+    def find(self, n):  
+        return self.root[n]
+
+    def union(self, a, b):
+        fa = self.find(a)
+        fb = self.find(b)
+        if fa != fb:
+            for i, v in enumerate(self.root): 
+                if fa == v: 
+                    self.root[i] = fb
+
+    def connected(self, x, y):
+        return self.find(x) == self.find(y)
+
+
+# Test Case
+uf = UnionFind(10)
+# 1-2-5-6-7 3-8-9 4
+uf.union(1, 2)
+uf.union(2, 5)
+uf.union(5, 6)
+uf.union(6, 7)
+uf.union(3, 8)
+uf.union(8, 9)
+print(uf.connected(1, 5))  # true
+print(uf.connected(5, 7))  # true
+print(uf.connected(4, 9))  # false
+# 1-2-5-6-7 3-8-9-4
+uf.union(9, 4)
+print(uf.connected(4, 9))  # true

Graphs/UnionFind/DisjointSet/04_quickunion_disjoint.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,a,b): 
+        # Basically we want to take the parent node of the given thing
+        fa = self.find(a)
+        fb = self.find(b)
+        if fa != fb: 
+            self.root[fa] = fb
+
+    # 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(10)
+
+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)
+print(uu.root)
+print([i for i in range(10)])

Graphs/UnionFind/DisjointSet/05_optimized_disjoint.py

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+# Optimized union find program that implements union by rank 
+
+class UnionFind: 
+    def __init__(self, size):
+        self.root = [i for i in range(size)]
+        self.rank = [1] * size
+
+    # Recurrsively update root 
+    def find(self, n): 
+        if self.root[n] != n: 
+          self.root[n] = self.find(self.root[n])
+        return self.root[n]
+
+    def union(self, a, b): 
+        fa = self.find(a)
+        fb = self.find(b)
+
+        if fa != fb: 
+            if self.rank[fa] > self.rank[fb]: 
+                self.root[fb] = fa
+            elif self.rank[fa] < self.rank[fb]: 
+                self.root[fa] = fb 
+            else: 
+                self.root[fa] = fb 
+                self.rank[fb] += 1 
+
+    def connected(self, x, y): 
+        return self.find(x) == self.find(y)
+
+# Test Case
+uf = UnionFind(10)
+# 1-2-5-6-7 3-8-9 4
+uf.union(1, 2)
+uf.union(2, 5)
+uf.union(5, 6)
+uf.union(6, 7)
+uf.union(3, 8)
+uf.union(8, 9)
+print(uf.connected(1, 5))  # true
+print(uf.connected(5, 7))  # true
+print(uf.connected(4, 9))  # false
+# 1-2-5-6-7 3-8-9-4
+uf.union(9, 4)
+print(uf.connected(4, 9))  # true