feat(graph): add Prim's Minimum Spanning Tree Visualizer with frontier and visited panels

src/algorithms/graph/prim.js

@@ -0,0 +1,96 @@
+// src/algorithms/graph/prim.js
+
+// Build adjacency list from list of edges
+function buildAdjacency(edges, n) {
+  const adj = Array.from({ length: n }, () => []);
+  for (const e of edges) {
+    const u = e.from - 1;
+    const v = e.to - 1;
+    const w = e.weight;
+
+    adj[u].push({ u, v, w });
+    adj[v].push({ u: v, v: u, w }); // undirected graph
+  }
+  return adj;
+}
+
+/**
+ * Prim's Algorithm – Step Generator
+ * Yields one step at a time:
+ *  type: "consider" | "add" | "skip" | "done"
+ *  edge: {from, to, weight}
+ *  visited: boolean[]
+ *  frontier: edge[]
+ *  mst: collected MST edges
+ */
+export function* primSteps(edges, nodeCount, startNode = 1) {
+  if (nodeCount === 0) {
+    yield { type: "done", mst: [], visited: [], frontier: [] };
+    return;
+  }
+
+  const adj = buildAdjacency(edges, nodeCount);
+  const visited = Array(nodeCount).fill(false);
+  const mst = [];
+  const frontier = [];
+
+  const pushEdges = (u) => {
+    for (const { v, w } of adj[u]) {
+      if (!visited[v]) {
+        frontier.push({ from: u + 1, to: v + 1, weight: w });
+      }
+    }
+  };
+
+  const startIdx = Math.max(1, Math.min(startNode, nodeCount)) - 1;
+  visited[startIdx] = true;
+  pushEdges(startIdx);
+
+  while (mst.length < nodeCount - 1 && frontier.length > 0) {
+    frontier.sort((a, b) => a.weight - b.weight);
+    const edge = frontier.shift();
+
+    yield {
+      type: "consider",
+      edge,
+      visited: [...visited],
+      frontier: [...frontier],
+      mst: [...mst],
+    };
+
+    const u = edge.from - 1;
+    const v = edge.to - 1;
+
+    if (visited[u] && visited[v]) {
+      yield {
+        type: "skip",
+        edge,
+        visited: [...visited],
+        frontier: [...frontier],
+        mst: [...mst],
+      };
+      continue;
+    }
+
+    const nextNode = visited[u] ? v : u;
+    visited[nextNode] = true;
+
+    mst.push(edge);
+    pushEdges(nextNode);
+
+    yield {
+      type: "add",
+      edge,
+      visited: [...visited],
+      frontier: [...frontier],
+      mst: [...mst],
+    };
+  }
+
+  yield {
+    type: "done",
+    mst: [...mst],
+    visited: [...visited],
+    frontier: [...frontier],
+  };
+}