From 5a986000cd9b4e16c5b824af1b160947e4e31afc Mon Sep 17 00:00:00 2001
From: Srishti Soni <92056170+shimmer12@users.noreply.github.com>
Date: Sun, 12 Oct 2025 02:36:54 +0530
Subject: [PATCH 1/3] Implement Kruskal's Minimum Spanning Tree algorithm

---
 graph_algorithms/kruskalMST.r | 50 +++++++++++++++++++++++++++++++++++
 1 file changed, 50 insertions(+)
 create mode 100644 graph_algorithms/kruskalMST.r

diff --git a/graph_algorithms/kruskalMST.r b/graph_algorithms/kruskalMST.r
new file mode 100644
index 00000000..83d79d01
--- /dev/null
+++ b/graph_algorithms/kruskalMST.r
@@ -0,0 +1,50 @@
+# Kruskal's Minimum Spanning Tree (base R, small)
+# edges: data.frame or matrix with columns u, v, w (1-based node ids)
+# n: number of vertices
+kruskalMST <- function(edges, n) {
+  edges <- as.data.frame(edges)
+  names(edges) <- c("u", "v", "w")
+  edges <- edges[order(edges$w), ]
+
+  parent <- seq_len(n)
+  rank <- integer(n)
+
+  find <- function(x) {
+    while (parent[x] != x) {
+      parent[x] <<- parent[parent[x]]  # path compression
+      x <- parent[x]
+    }
+    x
+  }
+  unite <- function(a, b) {
+    ra <- find(a); rb <- find(b)
+    if (ra == rb) return(FALSE)
+    if (rank[ra] < rank[rb]) parent[ra] <<- rb
+    else if (rank[ra] > rank[rb]) parent[rb] <<- ra
+    else { parent[rb] <<- ra; rank[ra] <<- rank[ra] + 1L }
+    TRUE
+  }
+
+  mst <- edges[0, ]
+  total <- 0
+  for (i in seq_len(nrow(edges))) {
+    if (unite(edges$u[i], edges$v[i])) {
+      mst <- rbind(mst, edges[i, ])
+      total <- total + edges$w[i]
+      if (nrow(mst) == n - 1) break
+    }
+  }
+  list(total_weight = total, edges = mst)
+}
+
+# --- tiny demo ---
+# Graph: 1--(1)--2, 1--(3)--3, 2--(2)--3, 2--(4)--4, 3--(5)--4
+set.seed(1)
+E <- data.frame(
+  u = c(1, 1, 2, 2, 3),
+  v = c(2, 3, 3, 4, 4),
+  w = c(1, 3, 2, 4, 5)
+)
+res <- kruskalMST(E, n = 4)
+print(res$total_weight)  # expected 1 + 2 + 4 = 7
+print(res$edges)

From 86f6b385f0d7380da71421450b5447edc4f714af Mon Sep 17 00:00:00 2001
From: Srishti Soni <92056170+shimmer12@users.noreply.github.com>
Date: Sun, 12 Oct 2025 02:41:29 +0530
Subject: [PATCH 2/3] Update graph_algorithms/kruskalMST.r

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
---
 graph_algorithms/kruskalMST.r | 1 -
 1 file changed, 1 deletion(-)

diff --git a/graph_algorithms/kruskalMST.r b/graph_algorithms/kruskalMST.r
index 83d79d01..cc5c9d8e 100644
--- a/graph_algorithms/kruskalMST.r
+++ b/graph_algorithms/kruskalMST.r
@@ -39,7 +39,6 @@ kruskalMST <- function(edges, n) {
 
 # --- tiny demo ---
 # Graph: 1--(1)--2, 1--(3)--3, 2--(2)--3, 2--(4)--4, 3--(5)--4
-set.seed(1)
 E <- data.frame(
   u = c(1, 1, 2, 2, 3),
   v = c(2, 3, 3, 4, 4),

From 5e30bf8266d6b0119c2b65923201e1b8652eedfa Mon Sep 17 00:00:00 2001
From: Srishti Soni <92056170+shimmer12@users.noreply.github.com>
Date: Sun, 12 Oct 2025 02:44:30 +0530
Subject: [PATCH 3/3] Update graph_algorithms/kruskalMST.r

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
---
 graph_algorithms/kruskalMST.r | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/graph_algorithms/kruskalMST.r b/graph_algorithms/kruskalMST.r
index cc5c9d8e..dbf60fce 100644
--- a/graph_algorithms/kruskalMST.r
+++ b/graph_algorithms/kruskalMST.r
@@ -25,7 +25,7 @@ kruskalMST <- function(edges, n) {
     TRUE
   }
 
-  mst <- edges[0, ]
+  mst <- data.frame(u = integer(0), v = integer(0), w = numeric(0))
   total <- 0
   for (i in seq_len(nrow(edges))) {
     if (unite(edges$u[i], edges$v[i])) {