Implement Kruskal's Minimum Spanning Tree Algorithm

graph.py

@@ -0,0 +1,62 @@
+import heapq
+
+class DisjointSetUnion:
+    def __init__(self, n):
+        self.parents = list(range(n))
+        self.ranks = [0] * n
+
+    def find(self, x):
+        if self.parents[x] != x:
+            self.parents[x] = self.find(self.parents[x])
+        return self.parents[x]
+
+    def union(self, x, y):
+        root_x = self.find(x)
+        root_y = self.find(y)
+
+        if root_x == root_y:
+            return
+
+        if self.ranks[root_x] > self.ranks[root_y]:
+            self.parents[root_y] = root_x
+        elif self.ranks[root_x] < self.ranks[root_y]:
+            self.parents[root_x] = root_y
+        else:
+            self.parents[root_y] = root_x
+            self.ranks[root_x] += 1
+
+def kruskal_mst(graph):
+    n = len(graph)
+    mst_weight = 0
+    visited = [False] * n
+    edges = []
+
+    # Add edges to the priority queue
+    for i in range(n):
+        for neighbor, weight in graph[i]:
+            if i < neighbor:
+                heapq.heappush(edges, (weight, i, neighbor))
+
+    # Process edges in the priority queue
+    dsu = DisjointSetUnion(n)
+    while edges:
+        weight, u, v = heapq.heappop(edges)
+
+        if not visited[u] and not visited[v]:
+            visited[u] = visited[v] = True
+            mst_weight += weight
+            dsu.union(u, v)
+
+    return mst_weight
+
+if __name__ == "__main__":
+    # Example graph
+    graph = [
+        [(1, 3), (2, 5)],
+        [(0, 3), (2, 1)],
+        [(0, 5), (1, 1)],
+        [],
+        [],
+    ]
+
+    print("Minimum Spanning Tree weight:", kruskal_mst(graph))

tests.py

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+import heapq
+
+class DisjointSetUnion:
+    def __init__(self, n):
+        self.parents = list(range(n))
+        self.ranks = [0] * n
+
+    def find(self, x):
+        if self.parents[x] != x:
+            self.parents[x] = self.find(self.parents[x])
+        return self.parents[x]
+
+    def union(self, x, y):
+        root_x = self.find(x)
+        root_y = self.find(y)
+
+        if root_x == root_y:
+            return
+
+        if self.ranks[root_x] > self.ranks[root_y]:
+            self.parents[root_y] = root_x
+        elif self.ranks[root_x] < self.ranks[root_y]:
+            self.parents[root_x] = root_y
+        else:
+            self.parents[root_y] = root_x
+            self.ranks[root_x] += 1
+
+def kruskal(n, edges):
+    dsu = DisjointSetUnion(n)
+    visited = [False] * n
+    edges.sort(key=lambda edge: edge[2])
+    mst_weight = 0
+
+    for edge in edges:
+        u, v, weight = edge
+        if not visited[u] and not visited[v]:
+            if dsu.find(u) != dsu.find(v):
+                dsu.union(u, v)
+                visited[u] = visited[v] = True
+                mst_weight += weight
+
+    return mst_weight
+
+def read_graph(file_name):
+    n, m = map(int, input().split())
+    edges = []
+    for _ in range(m):
+        u, v, w = map(int, input().split())
+        edges.append((u - 1, v - 1, w))
+    return n, edges
+
+if __name__ == "__main__":
+    file_name = "test.txt"
+    n, edges = read_graph(file_name)
+    print(kruskal(n, edges))