feat-prim_mst

Author: ArpitaHanjagi

Desktop/open-source/R/graph_algorithms/prim_mst.r

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+# Prim's Minimum Spanning Tree Algorithm
+#
+# The Prim algorithm finds the Minimum Spanning Tree (MST) of a connected, undirected, weighted graph.
+# It starts from a source vertex and grows the MST by adding the smallest-weight edge connecting
+# the MST to a new vertex.
+#
+# Time Complexity: O(V^2) with adjacency matrix, can be O(E log V) with priority queue
+# Space Complexity: O(V)
+#
+# Input: graph as an adjacency list where each entry is a list of edges with fields
+#        `vertex` and `weight`, and `source` vertex index (integer)
+# Output: A list containing MST edges, total weight
+
+prim_mst <- function(graph, source = 1) {
+  all_vertices <- unique(c(names(graph), unlist(lapply(graph, function(x) sapply(x, function(e) e$vertex)))))
+  all_vertices <- as.numeric(all_vertices)
+  num_vertices <- max(all_vertices)
+
+  in_mst <- rep(FALSE, num_vertices)
+  key <- rep(Inf, num_vertices)
+  parent <- rep(-1, num_vertices)
+
+  key[source] <- 0
+
+  for (i in 1:num_vertices) {
+    # Pick the minimum key vertex not in MST
+    u <- which.min(ifelse(in_mst, Inf, key))
+
+    in_mst[u] <- TRUE
+
+    # Update keys and parents for adjacent vertices
+    for (edge in graph[[as.character(u)]]) {
+      v <- edge$vertex
+      w <- edge$weight
+      if (!in_mst[v] && w < key[v]) {
+        key[v] <- w
+        parent[v] <- u
+      }
+    }
+  }
+
+  # Build MST edges
+  mst_edges <- list()
+  total_weight <- 0
+  for (v in 1:num_vertices) {
+    if (parent[v] != -1) {
+      mst_edges <- append(mst_edges, list(list(from = parent[v], to = v, weight = key[v])))
+      total_weight <- total_weight + key[v]
+    }
+  }
+
+  return(list(
+    edges = mst_edges,
+    total_weight = total_weight
+  ))
+}
+
+# Example usage
+cat("=== Prim's Minimum Spanning Tree Algorithm ===\n")
+
+# Example undirected graph
+# Graph structure:
+# 1 --2--> 2
+# 1 --3--> 3
+# 2 --1--> 3
+# 2 --4--> 4
+# 3 --5--> 4
+prim_graph <- list(
+  "1" = list(list(vertex = 2, weight = 2), list(vertex = 3, weight = 3)),
+  "2" = list(list(vertex = 1, weight = 2), list(vertex = 3, weight = 1), list(vertex = 4, weight = 4)),
+  "3" = list(list(vertex = 1, weight = 3), list(vertex = 2, weight = 1), list(vertex = 4, weight = 5)),
+  "4" = list(list(vertex = 2, weight = 4), list(vertex = 3, weight = 5))
+)
+
+cat("Graph (adjacency list):\n")
+for (v in names(prim_graph)) {
+  edges <- prim_graph[[v]]
+  edge_strs <- sapply(edges, function(e) paste0(e$vertex, "(", e$weight, ")"))
+  cat("Vertex", v, "-> [", paste(edge_strs, collapse = ", "), "]\n")
+}
+
+cat("\nRunning Prim's MST from vertex 1:\n")
+mst_result <- prim_mst(prim_graph, 1)
+cat("MST edges:\n")
+for (edge in mst_result$edges) {
+  cat(edge$from, "--", edge$weight, "-->", edge$to, "\n")
+}
+cat("Total weight of MST:", mst_result$total_weight, "\n")