Implement Kruskal's Minimum Spanning Tree algorithm

graph_algorithms/kruskalMST.r

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+# 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$w), ]
+
+  parent <- seq_len(n)
+  rank <- integer(n)
+
+  find <- function(x) {
+    while (parent[x] != x) {
+      parent[x] <<- parent[parent[x]]  # path compression
+      x <- parent[x]
+    }
+    x
+  }
+  unite <- function(a, b) {
+    ra <- find(a); rb <- find(b)
+    if (ra == rb) return(FALSE)
+    if (rank[ra] < rank[rb]) parent[ra] <<- rb
+    else if (rank[ra] > rank[rb]) parent[rb] <<- ra
+    else { parent[rb] <<- ra; rank[ra] <<- rank[ra] + 1L }
+    TRUE
+  }
+
+  mst <- data.frame(u = integer(0), v = integer(0), w = numeric(0))
+  total <- 0
+  for (i in seq_len(nrow(edges))) {
+    if (unite(edges$u[i], edges$v[i])) {
+      mst <- rbind(mst, edges[i, ])
+      total <- total + edges$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
+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)