some small updates

Author: jsgoller1

implementations/Data Structure - Graphs.ipynb

@@ -65,12 +65,55 @@
     "    print(node.value, [child.value for child in node.children])"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Example: [Graph Valid Tree](https://leetcode.com/problems/graph-valid-tree/)\n",
+    "\n",
+    "A graph is a tree with no cycles; for this problem, we need to find cycles from a list of edges. We can do this with a regular BFS, quitting if we visit the same node twice. "
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "from collections import deque\n",
+    "\n",
+    "class Solution:\n",
+    "    def validTree(self, n: int, edges: List[List[int]]) -> bool:\n",
+    "        if not edges:\n",
+    "            return n < 2\n",
+    "        adj_list = {i:set() for i in range(0, n)}\n",
+    "        for n1,n2 in edges:\n",
+    "            adj_list[n1].add(n2)\n",
+    "            adj_list[n2].add(n1)\n",
+    "        \n",
+    "        visited = set()\n",
+    "        q = deque([(edges[0][0], None)])\n",
+    "        while q:\n",
+    "            curr, parent = q.popleft()\n",
+    "            visited.add(curr)\n",
+    "            for child in adj_list[curr]:\n",
+    "                if child == parent:\n",
+    "                    continue\n",
+    "                if child in visited:\n",
+    "                    return False\n",
+    "                q.append((child,curr))\n",
+    "        return len(visited) == n\n",
+    "\n",
+    "s = Solution()\n",
+    "cases = [\n",
+    "    (5, [[0,1], [0,2], [0,3], [1,4]], True),\n",
+    "    (5, [[0,1], [1,2], [2,3], [1,3], [1,4]], False),\n",
+    "]\n",
+    "for n, edges, expected in cases:\n",
+    "    actual = s.validTree(n, edges)\n",
+    "    assert actual == expected, f\"{n, edges}\"\n",
+    "            "
+   ]
   }
  ],
  "metadata": {

implementations/Technique - Topological Sorting.ipynb

@@ -276,20 +276,6 @@
     "    print(s.findOrder(n_courses, prereqs))"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Example: [Graph Valid Tree](https://leetcode.com/problems/graph-valid-tree/)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -324,7 +310,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -375,11 +361,6 @@
     "        only return top ordering if we visit every \n",
     "        node without hitting a cycle.\n",
     "        \"\"\"\n",
-    "        # Instead of taking the complement\n",
-    "        # of the union of all successors and the\n",
-    "        # set of all nodes, we cumulative take\n",
-    "        # the complement of each successor with\n",
-    "        # the set of all letters.\n",
     "        dag = create_letter_dag(words)\n",
     "        roots = set(dag.keys())\n",
     "        for successors in dag.values():\n",
@@ -407,13 +388,6 @@
     "    actual = s.alienOrder(word_list)\n",
     "    assert actual == expected, f\"{word_list}: {expected} != {actual}\""
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {