Merge pull request 7oSkaaa#1108 from LamaSalah32/main

add 19- Is Graph Bipartite? (Lama Salah).cpp

05- May/19- Is Graph Bipartite?/19- Is Graph Bipartite? (Lama Salah).cpp

@@ -0,0 +1,49 @@
+// Author: Lama Salah
+
+class Solution {
+public:
+    vector<vector<int>> adj; // Adjacency list to represent the graph.
+    vector<int> vis; // Array to keep track of node colors.
+
+    // Recursive function to check if the graph is not bipartite.
+    bool isNotBipartite(int node, int color) {
+        vis[node] = color; // Assign the current node the specified color (0 or 1).
+
+        bool ans = false; // Variable to store the result.
+
+        for (auto& i : adj[node]) {
+            if (vis[i] == -1) {
+                // If the neighbor hasn't been visited, recursively call the function with the opposite color.
+                ans |= isNotBipartite(i, color ^ 1);
+            } else if ((color ^ 1) != vis[i]) {
+                // If the neighbor has been visited and has the same color as the current node, the graph is not bipartite.
+                return true;
+            }
+        }
+
+        return ans;
+    }
+
+    bool isBipartite(vector<vector<int>>& graph) {
+        adj.assign(graph.size(), vector<int>()); // Initialize the adjacency list.
+        vis.assign(graph.size(), -1); // Initialize the vis array.
+
+        // Build the adjacency list based on the given graph.
+        for (int i = 0; i < graph.size(); i++) {
+            for (auto& j : graph[i]) {
+                adj[i].push_back(j);
+                adj[j].push_back(i);
+            }
+        }
+
+        // Iterate over each node in the graph.
+        for (int i = 0; i < graph.size(); i++) {
+            if (vis[i] == -1 && isNotBipartite(i, 0)) {
+                // If the node hasn't been visited and the graph is not bipartite, return false.
+                return false;
+            }
+        }
+
+        return true; // The graph is bipartite.
+    }
+};