Implement Kruskal's Minimum Spanning Tree Algorithm

dsu.py

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+class DSU:
+    def __init__(self, n):
+        self.parent = list(range(n))
+        self.rank = [0] * n
+
+    def find(self, x):
+        if self.parent[x] != x:
+            self.parent[x] = self.find(self.parent[x])
+        return self.parent[x]
+
+    def union(self, x, y):
+        root_x, root_y = self.find(x), self.find(y)
+        if root_x == root_y:
+            return
+        if self.rank[root_x] > self.rank[root_y]:
+            self.parent[root_y] = root_x
+        elif self.rank[root_x] < self.rank[root_y]:
+            self.parent[root_x] = root_y
+        else:
+            self.parent[root_y] = root_x
+            self.rank[root_x] += 1
+
+def kruskal_mst(graph):
+    edge_list = sorted((weight, u, v) for u, v, weight in graph.edges(data='weight'))
+    dsu = DSU(graph.number_of_nodes())
+    mst_weight = 0
+
+    for weight, u, v in edge_list:
+        if dsu.find(u) != dsu.find(v):
+            dsu.union(u, v)
+            mst_weight += weight
+
+    return mst_weight

graph.py

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+import heapq
+
+class Graph:
+    def __init__(self, vertices):
+        self.V = vertices
+        self.graph = []
+
+    def add_edge(self, u, v, w):
+        self.graph.append([u, v, w])
+
+    # find set of an element i
+    def find(self, parent, i):
+        if parent[i] == i:
+            return i
+        return self.find(parent, parent[i])
+
+    # union of two sets of x and y
+    def union(self, parent, rank, x, y):
+        xroot = self.find(parent, x)
+        yroot = self.find(parent, y)
+
+        # attach smaller rank tree under root of high rank tree
+        if rank[xroot] < rank[yroot]:
+            parent[xroot] = yroot
+        elif rank[xroot] > rank[yroot]:
+            parent[yroot] = xroot
+        else:
+            parent[yroot] = xroot
+            rank[xroot] += 1
+
+    # main function to construct MST using Kruskal's algorithm
+    def kruskal_mst(self):
+        result = []
+        i, e = 0, 0
+
+        # sort all edges in non-decreasing order of their weight
+        self.graph = sorted(self.graph, key=lambda item: item[2])
+
+        parent = []
+        rank = []
+
+        # create V subsets with single elements
+        for node in range(self.V):
+            parent.append(node)
+            rank.append(0)
+
+        # number of edges to be taken is equal to V-1
+        while e < self.V - 1:
+            u, v, w = self.graph[i]
+            i = i + 1
+            x = self.find(parent, u)
+            y = self.find(parent, v)
+
+            # if including this edge does not cause cycle, include it in result
+            if x != y:
+                e = e + 1
+                result.append([u, v, w])
+                self.union(parent, rank, x, y)
+
+        return result, sum([e[2] for e in result])

kruskal.py

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+ ```python
+import heapq
+
+class Edge:
+    def __init__(self, u, v, w):
+        self.u = u
+        self.v = v
+        self.w = w