Added Bellman Ford Negative Cycle implementation and test file with prettier code

Author: Mayank29903

Graphs/BellmanFordNegativeCycle.js

@@ -0,0 +1,32 @@
+/*
+ * Author: Mayank
+ * Bellman-Ford Algorithm implementation in JavaScript
+ * Detects shortest paths and checks for negative weight cycles in a graph.
+ */
+
+// Bellman-Ford with negative cycle detection
+
+function bellmanFordNegativeCycle(graph, vertices, start) {
+  const dist = new Array(vertices).fill(Infinity)
+  dist[start] = 0
+
+  // relax all edges (V - 1) times
+  for (let i = 0; i < vertices - 1; i++) {
+    for (let [u, v, w] of graph) {
+      if (dist[u] !== Infinity && dist[u] + w < dist[v]) {
+        dist[v] = dist[u] + w
+      }
+    }
+  }
+
+  // check for negative cycle
+  for (let [u, v, w] of graph) {
+    if (dist[u] !== Infinity && dist[u] + w < dist[v]) {
+      return { hasNegativeCycle: true, dist }
+    }
+  }
+
+  return { hasNegativeCycle: false, dist }
+}
+
+export { bellmanFordNegativeCycle }

Graphs/test/BellmanFordNegativeCycle.test.js

@@ -0,0 +1,29 @@
+/*
+ * Test file for Bellman-Ford Negative Cycle Detection
+ */
+
+import { bellmanFordNegativeCycle } from '../BellmanFordNegativeCycle.js'
+
+test('should find shortest distance without negative cycle', () => {
+  const graph = [
+    [0, 1, 4],
+    [0, 2, 5],
+    [1, 2, -3],
+    [2, 3, 4]
+  ]
+  const result = bellmanFordNegativeCycle(graph, 4, 0)
+
+  expect(result.hasNegativeCycle).toBe(false)
+  expect(result.dist[3]).toBe(6) // shortest distance from 0 to 3
+})
+
+test('should detect negative cycle', () => {
+  const graph = [
+    [0, 1, 1],
+    [1, 2, -1],
+    [2, 0, -1]
+  ]
+  const result = bellmanFordNegativeCycle(graph, 3, 0)
+
+  expect(result.hasNegativeCycle).toBe(true)
+})