From e385da26d9ea2936ef24a5e361c6d19596ad1247 Mon Sep 17 00:00:00 2001
From: Richa Kiran <64418209+richk21@users.noreply.github.com>
Date: Wed, 1 Oct 2025 18:29:15 +0530
Subject: [PATCH] Implemented PrismAlgorithm

---
 .../thealgorithms/graph/PrismAlgorithm.java   | 59 +++++++++++++++++++
 1 file changed, 59 insertions(+)
 create mode 100644 src/main/java/com/thealgorithms/graph/PrismAlgorithm.java

diff --git a/src/main/java/com/thealgorithms/graph/PrismAlgorithm.java b/src/main/java/com/thealgorithms/graph/PrismAlgorithm.java
new file mode 100644
index 000000000000..584dfd6ee965
--- /dev/null
+++ b/src/main/java/com/thealgorithms/graph/PrismAlgorithm.java
@@ -0,0 +1,59 @@
+package com.thealgorithms.graph;
+
+import java.util.*;
+
+
+
+/**
+ * This class provides a method to compute the Minimum Spanning Tree (MST)
+ * weight using Prim's Algorithm without any custom helper class.
+ */
+public class PrismAlgorithm {
+
+    /**
+     * Computes the total weight of the Minimum Spanning Tree (MST)
+     * for a given undirected, weighted graph using Prim's Algorithm.
+     *
+     * @param V   Number of vertices in the graph.
+     * @param adj Adjacency list representation of the graph.
+     *            Each entry: {adjacentNode, edgeWeight}.
+     * @return The sum of the edge weights in the MST.
+     *
+     * <p>Time Complexity: O(E log V)</p>
+     * <p>Space Complexity: O(V + E)</p>
+     */
+    static int spanningTree(int V, ArrayList<ArrayList<ArrayList<Integer>>> adj) {
+
+        // Min-heap storing {weight, node}
+        PriorityQueue<int[]> pq = new PriorityQueue<>((a, b) -> a[0] - b[0]);
+
+        int[] visited = new int[V]; // visited array
+        int mstWeightSum = 0;
+
+        // Start from node 0, with weight = 0
+        pq.add(new int[]{0, 0});
+
+        while (!pq.isEmpty()) {
+            int[] current = pq.poll();
+            int weight = current[0];
+            int node = current[1];
+
+            if (visited[node] == 1) continue;
+
+            visited[node] = 1;
+            mstWeightSum += weight;
+
+            // Explore adjacent edges
+            for (ArrayList<Integer> edge : adj.get(node)) {
+                int adjNode = edge.get(0);
+                int edgeWeight = edge.get(1);
+
+                if (visited[adjNode] == 0) {
+                    pq.add(new int[]{edgeWeight, adjNode});
+                }
+            }
+        }
+
+        return mstWeightSum;
+    }
+}