Added Prim's Algorithm to searches

src/main/java/com/thealgorithms/graph/Prims.java

@@ -0,0 +1,111 @@
+package com.thealgorithms.graph;
+
+import java.util.*;
+
+/**
+ * Implementation of Prim's Algorithm for finding the Minimum Spanning Tree (MST)
+ * of a connected, undirected, weighted graph.
+ *
+ * Prim’s algorithm builds the MST by always choosing the minimum weight edge 
+ * that connects a vertex in the MST to a vertex outside it.
+ *
+ * Time Complexity: O(E log V)
+ * Space Complexity: O(V)
+ *
+ * https://en.wikipedia.org/wiki/Prim%27s_algorithm
+ *
+ * Example:
+ *   Graph:
+ *     A - B (4)
+ *     A - C (3)
+ *     B - C (1)
+ *     B - D (2)
+ *     C - D (4)
+ *
+ *   MST edges:
+ *     B - C (1)
+ *     B - D (2)
+ *     A - C (3)
+ *
+ * @author OpenAI
+ */
+public final class Prims {
+
+    private Prims() {
+    }
+
+    /**
+     * Represents an edge in the graph.
+     */
+    private static class Edge {
+        String to;
+        int weight;
+
+        Edge(String to, int weight) {
+            this.to = to;
+            this.weight = weight;
+        }
+    }
+
+    /**
+     * Graph represented as adjacency list.
+     */
+    public static class Graph {
+        private final Map<String, List<Edge>> adj = new LinkedHashMap<>();
+
+        /**
+         * Adds an undirected weighted edge between u and v.
+         */
+        public void addEdge(String u, String v, int weight) {
+            adj.computeIfAbsent(u, k -> new ArrayList<>()).add(new Edge(v, weight));
+            adj.computeIfAbsent(v, k -> new ArrayList<>()).add(new Edge(u, weight));
+        }
+    }
+
+    /**
+     * Runs Prim’s Algorithm to compute the MST.
+     *
+     * @param graph  the input graph
+     * @param start  the starting vertex
+     * @return list of edges representing the MST
+     */
+    public static List<String> primsMST(Graph graph, String start) {
+        List<String> mstEdges = new ArrayList<>();
+        Set<String> visited = new HashSet<>();
+        PriorityQueue<Edge> pq = new PriorityQueue<>(Comparator.comparingInt(e -> e.weight));
+
+        visited.add(start);
+        pq.addAll(graph.adj.get(start));
+
+        while (!pq.isEmpty()) {
+            Edge edge = pq.poll();
+            if (visited.contains(edge.to)) continue;
+
+            visited.add(edge.to);
+            mstEdges.add(edge.to);
+
+            for (Edge next : graph.adj.get(edge.to)) {
+                if (!visited.contains(next.to)) {
+                    pq.offer(next);
+                }
+            }
+        }
+
+        return mstEdges;
+    }
+
+    /**
+     * Example usage.
+     */
+    public static void main(String[] args) {
+        Graph graph = new Graph();
+        graph.addEdge("A", "B", 4);
+        graph.addEdge("A", "C", 3);
+        graph.addEdge("B", "C", 1);
+        graph.addEdge("B", "D", 2);
+        graph.addEdge("C", "D", 4);
+
+        List<String> mst = primsMST(graph, "A");
+        System.out.println("MST vertices (order added): " + mst);
+    }
+}