feat: bipartite graph (#190)

graph/bipartite_graph.ts

@@ -0,0 +1,46 @@
+const dfs = (
+  graph: number[][],
+  colors: number[],
+  node: number,
+  color: number
+): boolean => {
+  if (colors[node] !== 0) {
+    return colors[node] === color;
+  }
+
+  colors[node] = color;
+
+  for (const neighbor of graph[node]) {
+    if (!dfs(graph, colors, neighbor, -color)) {
+      return false;
+    }
+  }
+
+  return true;
+};
+
+
+/**
+ * Determines if a given graph is bipartite.
+ *
+ * A Bipartite Graph is a graph whose vertices can be divided into two independent sets, 
+ * U and V such that every edge (u, v) either connects a vertex from U to V or a vertex from 
+ * V to U
+ *
+ * @param {number[][]} graph - The graph represented as an adjacency list.
+ * @returns {boolean} - `true` if the graph is bipartite, `false` otherwise.
+ */
+
+
+export const isBipartite = (graph: number[][]): boolean => {
+  const n: number = graph.length;
+  const colors: number[] = new Array(n).fill(0);
+
+  for (let i = 0; i < n; i++) {
+    if (colors[i] === 0 && !dfs(graph, colors, i, 1)) {
+      return false;
+    }
+  }
+
+  return true;
+};

graph/test/bipartite_graph.test.ts

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+import { isBipartite } from "../bipartite_graph";
+
+describe('isBipartite', () => {
+    it('should return true for a bipartite graph', () => {
+      const graph = [[1, 3], [0, 2], [1, 3], [0, 2]];
+      const result = isBipartite(graph);
+      expect(result).toBe(true);
+    });
+
+    it('should return true for an empty graph', () => {
+      const graph: number[][] = [];
+      const result = isBipartite(graph);
+      expect(result).toBe(true);
+    });
+
+    it('should return true for a single node graph', () => {
+      const graph = [[]];
+      const result = isBipartite(graph);
+      expect(result).toBe(true);
+    });
+
+    it('should return false for a non-bipartite graph', () => {
+      const graph = [[1, 2, 3], [0, 2], [0, 1, 3], [0, 2]];
+      const result = isBipartite(graph);
+      expect(result).toBe(false);
+    });
+
+    it('should return true for a disconnected bipartite graph', () => {
+      const graph = [[1, 2], [0], [0], [4], [3]];
+      const result = isBipartite(graph);
+      expect(result).toBe(true);
+    });
+  });