Create HamiltonianPath.js

02. Algorithms/07. Backtracking/Hamilton Path/HamiltonianPath.js

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+/// A hamiltonian path is simply a path that visits all the nodes exectly once.
+
+// Backtracking | Recursion
+// Time O(n) | Space O(n)
+const makeGraph = (edges) => {
+
+    const graph = {};
+
+    for(let i = 0; i < edges.length; i++) {
+        const node0 = edges[i][0];
+        const node1 = edges[i][1];
+        const node0Neighbor = graph[node0] || [];
+        const node1Neighbor = graph[node1] || [];
+        node0Neighbor.push(node1);
+        node1Neighbor.push(node0);
+        graph[node0] = node0Neighbor;
+        graph[node1] = node1Neighbor;
+    }
+    return graph;
+}
+
+const hamiltonianPath = (edges, src) => {
+
+    const graph = makeGraph(edges);
+    const totalNodes = Object.keys(graph).length;
+
+    const visited = new Set();
+
+    const dfs = (node) => {
+        const neighbors = graph[node] || [];
+        if(visited.size === totalNodes) return true;
+
+        for(let i = 0; i < neighbors.length; i++) {
+            if(visited.has(neighbors[i])) continue;
+            visited.add(neighbors[i]);
+            if(dfs(neighbors[i])) return true;
+            visited.delete(neighbors[i]);
+        }
+
+        return false;
+    }
+    // adding src node becase we're considering it as visited.
+    visited.add(src);
+    return dfs(src);
+}
+
+const edges = [[0,1],[1,2],[1,3],[1,4]];
+
+console.log(hamiltonianPath(edges,0));