From 4f2285ad9dcb422b58c7c8ccb08d94e8efb405f0 Mon Sep 17 00:00:00 2001
From: koushitha-30734 <2400030734@kluniversity.in>
Date: Sun, 23 Nov 2025 20:08:17 +0530
Subject: [PATCH] Create MinimumSpanningTree
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This PR adds a simple and clean implementation of Kruskal’s MST algorithm using Union-Find in Go. It includes edge sorting, DSU, and returns the MST edges with total weight. Useful for graph algorithm practice and future extensions.
---
 MinimumSpanningTree | 95 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 95 insertions(+)
 create mode 100644 MinimumSpanningTree

diff --git a/MinimumSpanningTree b/MinimumSpanningTree
new file mode 100644
index 000000000..7750ddf5a
--- /dev/null
+++ b/MinimumSpanningTree
@@ -0,0 +1,95 @@
+package main
+
+import (
+	"fmt"
+	"sort"
+)
+
+type Edge struct {
+	u, v int
+	w    int
+}
+
+type ByWeight []Edge
+
+func (a ByWeight) Len() int           { return len(a) }
+func (a ByWeight) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
+func (a ByWeight) Less(i, j int) bool { return a[i].w < a[j].w }
+
+type UnionFind struct {
+	parent []int
+	rank   []int
+}
+
+func NewUnionFind(n int) *UnionFind {
+	p := make([]int, n)
+	r := make([]int, n)
+	for i := 0; i < n; i++ {
+		p[i] = i
+		r[i] = 0
+	}
+	return &UnionFind{parent: p, rank: r}
+}
+
+func (dsu *UnionFind) Find(x int) int {
+	if dsu.parent[x] != x {
+		dsu.parent[x] = dsu.Find(dsu.parent[x])
+	}
+	return dsu.parent[x]
+}
+
+func (dsu *UnionFind) Union(a, b int) bool {
+	ra := dsu.Find(a)
+	rb := dsu.Find(b)
+	if ra == rb {
+		return false
+	}
+	if dsu.rank[ra] < dsu.rank[rb] {
+		dsu.parent[ra] = rb
+	} else if dsu.rank[ra] > dsu.rank[rb] {
+		dsu.parent[rb] = ra
+	} else {
+		dsu.parent[rb] = ra
+		dsu.rank[ra]++
+	}
+	return true
+}
+
+func KruskalMST(n int, edges []Edge) ([]Edge, int) {
+	sort.Sort(ByWeight(edges))
+	dsu := NewUnionFind(n)
+
+	var mst []Edge
+	totalWeight := 0
+	for _, e := range edges {
+		if dsu.Union(e.u, e.v) {
+			mst = append(mst, e)
+			totalWeight += e.w
+			// early stop: if we already have n-1 edges
+			if len(mst) == n-1 {
+				break
+			}
+		}
+	}
+	return mst, totalWeight
+}
+
+func main() {
+	
+	n := 4
+	edges := []Edge{
+		{u: 0, v: 1, w: 1},
+		{u: 0, v: 2, w: 4},
+		{u: 1, v: 2, w: 2},
+		{u: 1, v: 3, w: 3},
+		{u: 2, v: 3, w: 5},
+	}
+
+	mst, total := KruskalMST(n, edges)
+
+	fmt.Println("MST edges (u - v : weight):")
+	for _, e := range mst {
+		fmt.Printf("%d - %d : %d\n", e.u, e.v, e.w)
+	}
+	fmt.Printf("Total weight: %d\n", total)
+}