Add Dijkstra's shortest path algorithm (#153)

Author: piyushkumar0707

DIRECTORY.md

@@ -35,6 +35,7 @@
   * [Lasso](https://github.com/TheAlgorithms/R/blob/HEAD/data_preprocessing/lasso.r)
 
 ## Graph Algorithms
+  * [Dijkstra Shortest Path](https://github.com/TheAlgorithms/R/blob/HEAD/graph_algorithms/dijkstra_shortest_path.r)
   * [Breadth First Search](https://github.com/TheAlgorithms/R/blob/HEAD/graph_algorithms/breadth_first_search.r)
   * [Depth First Search](https://github.com/TheAlgorithms/R/blob/HEAD/graph_algorithms/depth_first_search.r)
 

graph_algorithms/dijkstra_shortest_path.r

@@ -0,0 +1,258 @@
+# Dijkstra's Shortest Path Algorithm
+#
+# Dijkstra's algorithm finds the shortest path between a source vertex and all other vertices
+# in a weighted graph with non-negative edge weights. It uses a greedy approach with a priority queue.
+#
+# Time Complexity: O((V + E) log V) with binary heap, O(V^2) with simple array
+# Space Complexity: O(V) for distance and visited arrays
+#
+# Input: A weighted graph represented as adjacency list with weights, and a source vertex
+# Output: Shortest distances from source to all vertices and the paths
+
+# Priority queue implementation using simple vector (for educational purposes)
+# In production, use more efficient data structures
+create_priority_queue <- function() {
+  list(
+    elements = data.frame(vertex = integer(0), distance = numeric(0)),
+    size = 0
+  )
+}
+
+# Insert element into priority queue
+pq_insert <- function(pq, vertex, distance) {
+  pq$elements <- rbind(pq$elements, data.frame(vertex = vertex, distance = distance))
+  pq$size <- pq$size + 1
+  return(pq)
+}
+
+# Extract minimum element from priority queue
+pq_extract_min <- function(pq) {
+  if (pq$size == 0) {
+    return(list(pq = pq, min_element = NULL))
+  }
+  
+  min_idx <- which.min(pq$elements$distance)
+  min_element <- pq$elements[min_idx, ]
+  pq$elements <- pq$elements[-min_idx, ]
+  pq$size <- pq$size - 1
+  
+  return(list(pq = pq, min_element = min_element))
+}
+
+# Check if priority queue is empty
+pq_is_empty <- function(pq) {
+  return(pq$size == 0)
+}
+
+# Main Dijkstra's algorithm implementation
+dijkstra_shortest_path <- function(graph, source) {
+  # Get all vertices in the graph
+  all_vertices <- unique(c(names(graph), unlist(lapply(graph, function(x) x$vertex))))
+  num_vertices <- max(all_vertices)
+  
+  # Initialize distances and previous vertices
+  distances <- rep(Inf, num_vertices)
+  previous <- rep(-1, num_vertices)
+  visited <- rep(FALSE, num_vertices)
+  
+  # Set source distance to 0
+  distances[source] <- 0
+  
+  # Create priority queue and add source
+  pq <- create_priority_queue()
+  pq <- pq_insert(pq, source, 0)
+  
+  while (!pq_is_empty(pq)) {
+    # Extract vertex with minimum distance
+    result <- pq_extract_min(pq)
+    pq <- result$pq
+    current <- result$min_element
+    
+    if (is.null(current)) break
+    
+    u <- current$vertex
+    
+    # Skip if already visited
+    if (visited[u]) next
+    
+    # Mark as visited
+    visited[u] <- TRUE
+    
+    # Update distances to neighbors
+    if (as.character(u) %in% names(graph)) {
+      for (edge in graph[[as.character(u)]]) {
+        v <- edge$vertex
+        weight <- edge$weight
+        
+        # Relaxation step
+        if (!visited[v] && distances[u] + weight < distances[v]) {
+          distances[v] <- distances[u] + weight
+          previous[v] <- u
+          pq <- pq_insert(pq, v, distances[v])
+        }
+      }
+    }
+  }
+  
+  return(list(
+    distances = distances,
+    previous = previous
+  ))
+}
+
+# Reconstruct shortest path from source to target
+get_shortest_path <- function(dijkstra_result, source, target) {
+  previous <- dijkstra_result$previous
+  distances <- dijkstra_result$distances
+  
+  # Check if target is reachable
+  if (distances[target] == Inf) {
+    return(list(
+      path = NULL,
+      distance = Inf
+    ))
+  }
+  
+  # Reconstruct path by backtracking
+  path <- c()
+  current <- target
+  
+  while (current != -1) {
+    path <- c(current, path)
+    current <- previous[current]
+  }
+  
+  return(list(
+    path = path,
+    distance = distances[target]
+  ))
+}
+
+# Find shortest paths to all vertices
+get_all_shortest_paths <- function(dijkstra_result, source) {
+  distances <- dijkstra_result$distances
+  previous <- dijkstra_result$previous
+  paths <- list()
+  
+  for (target in 1:length(distances)) {
+    if (distances[target] != Inf) {
+      path_result <- get_shortest_path(dijkstra_result, source, target)
+      paths[[as.character(target)]] <- path_result
+    }
+  }
+  
+  return(paths)
+}
+
+# Example usage and testing
+cat("=== Dijkstra's Shortest Path Algorithm ===\n")
+
+# Create a weighted graph as adjacency list
+# Graph structure with weights:
+#       1
+#     /   \
+#   4/     \2
+#   /       \
+#  2         3
+#  |3      /1
+#  |      /
+#  4-----5
+#     2
+weighted_graph <- list(
+  "1" = list(
+    list(vertex = 2, weight = 4),
+    list(vertex = 3, weight = 2)
+  ),
+  "2" = list(
+    list(vertex = 4, weight = 3)
+  ),
+  "3" = list(
+    list(vertex = 5, weight = 1)
+  ),
+  "4" = list(
+    list(vertex = 5, weight = 2)
+  ),
+  "5" = list()
+)
+
+cat("Weighted graph structure:\n")
+for (vertex in names(weighted_graph)) {
+  edges <- weighted_graph[[vertex]]
+  if (length(edges) > 0) {
+    edge_strs <- sapply(edges, function(e) paste0(e$vertex, "(", e$weight, ")"))
+    cat("Vertex", vertex, "-> [", paste(edge_strs, collapse = ", "), "]\n")
+  } else {
+    cat("Vertex", vertex, "-> []\n")
+  }
+}
+
+# Run Dijkstra's algorithm from vertex 1
+cat("\nRunning Dijkstra's algorithm from vertex 1:\n")
+result <- dijkstra_shortest_path(weighted_graph, 1)
+
+# Display shortest distances
+cat("Shortest distances from vertex 1:\n")
+for (i in 1:length(result$distances)) {
+  if (result$distances[i] != Inf) {
+    cat("To vertex", i, ": distance =", result$distances[i], "\n")
+  }
+}
+
+# Get shortest path to specific vertex
+cat("\nShortest path from 1 to 5:\n")
+path_to_5 <- get_shortest_path(result, 1, 5)
+if (!is.null(path_to_5$path)) {
+  cat("Path:", paste(path_to_5$path, collapse = " -> "), "\n")
+  cat("Distance:", path_to_5$distance, "\n")
+}
+
+# Get all shortest paths
+cat("\nAll shortest paths from vertex 1:\n")
+all_paths <- get_all_shortest_paths(result, 1)
+for (target in names(all_paths)) {
+  path_info <- all_paths[[target]]
+  cat("To vertex", target, ": ", paste(path_info$path, collapse = " -> "), 
+      " (distance:", path_info$distance, ")\n")
+}
+
+# Example with a more complex graph
+cat("\n=== More Complex Weighted Graph Example ===\n")
+complex_weighted_graph <- list(
+  "1" = list(
+    list(vertex = 2, weight = 7),
+    list(vertex = 3, weight = 9),
+    list(vertex = 6, weight = 14)
+  ),
+  "2" = list(
+    list(vertex = 3, weight = 10),
+    list(vertex = 4, weight = 15)
+  ),
+  "3" = list(
+    list(vertex = 4, weight = 11),
+    list(vertex = 6, weight = 2)
+  ),
+  "4" = list(
+    list(vertex = 5, weight = 6)
+  ),
+  "5" = list(),
+  "6" = list(
+    list(vertex = 5, weight = 9)
+  )
+)
+
+cat("Complex weighted graph from vertex 1:\n")
+complex_result <- dijkstra_shortest_path(complex_weighted_graph, 1)
+
+cat("Shortest distances:\n")
+for (i in 1:length(complex_result$distances)) {
+  if (complex_result$distances[i] != Inf) {
+    cat("To vertex", i, ": distance =", complex_result$distances[i], "\n")
+  }
+}
+
+# Shortest path to vertex 5
+path_to_5_complex <- get_shortest_path(complex_result, 1, 5)
+if (!is.null(path_to_5_complex$path)) {
+  cat("Shortest path from 1 to 5:", paste(path_to_5_complex$path, collapse = " -> "), "\n")
+  cat("Distance:", path_to_5_complex$distance, "\n")
+}