Merge pull request #256 from Vijayaa21/main

Create kruskal.py

Author: Pradeepsingh61

Python/algorithms/graph_algorithms/kruskal.py

@@ -0,0 +1,79 @@
+"""
+Data Structure: Kruskal's Minimum Spanning Tree (MST) Algorithm
+
+Description:
+    Kruskal's algorithm finds the Minimum Spanning Tree of a graph by
+    sorting edges by weight and adding them one by one without creating cycles.
+
+Use Case:
+    Useful in network design (telecom, computer networks), clustering, 
+    and designing efficient transportation systems.
+
+Time Complexity:
+    O(E log E), where E = number of edges (due to sorting edges)
+
+Space Complexity:
+    O(V + E), where V = number of vertices, E = number of edges
+"""
+
+class DisjointSet:
+    """Union-Find data structure for cycle detection."""
+    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):
+        xroot, yroot = self.find(x), self.find(y)
+        if xroot == yroot:
+            return False
+        if self.rank[xroot] < self.rank[yroot]:
+            self.parent[xroot] = yroot
+        elif self.rank[xroot] > self.rank[yroot]:
+            self.parent[yroot] = xroot
+        else:
+            self.parent[yroot] = xroot
+            self.rank[xroot] += 1
+        return True
+
+
+def kruskal(vertices, edges):
+    """
+    Compute MST using Kruskal's algorithm.
+
+    Args:
+        vertices (int): Number of vertices.
+        edges (list of tuples): Each tuple = (weight, u, v)
+
+    Returns:
+        list: Edges in the MST
+    """
+    edges.sort()
+    ds = DisjointSet(vertices)
+    mst = []
+    for weight, u, v in edges:
+        if ds.union(u, v):
+            mst.append((u, v, weight))
+    return mst
+
+
+def main():
+    """Test Kruskal's MST algorithm."""
+    vertices = 4
+    edges = [
+        (10, 0, 1),
+        (6, 0, 2),
+        (5, 0, 3),
+        (15, 1, 3),
+        (4, 2, 3)
+    ]
+    mst = kruskal(vertices, edges)
+    print("Edges in MST:", mst)
+
+
+if __name__ == "__main__":
+    main()