{ "id": "graphs/graph-dfs", "version": 1, "deterministic": true, "url": "/dsa/graphs/graph-dfs", "topic": { "slug": "graphs", "title": "Graphs" }, "title": "Depth-First Search", "tagline": "Plunge down one path to the end, then back up and try the next.", "vizKind": "graph", "complexity": { "time": { "best": "O(V + E)", "average": "O(V + E)", "worst": "O(V + E)" }, "space": "O(V)", "growth": "linear", "note": "Same cost as BFS: every node once, every edge once, so V + E. The space is the stack — O(V) in the worst case. With recursive DFS, that stack is the call stack, which is why very deep graphs can overflow it." }, "code": { "javascript": "function dfs(graph, start) {\n const stack = [start];\n const seen = new Set([start]);\n while (stack.length > 0) {\n const node = stack.pop();\n visit(node);\n for (const next of graph[node]) {\n if (!seen.has(next)) {\n seen.add(next);\n stack.push(next);\n }\n }\n }\n}", "python": "def dfs(graph, start):\n stack = [start]\n seen = {start}\n while stack:\n node = stack.pop()\n visit(node)\n for nxt in graph[node]:\n if nxt not in seen:\n seen.add(nxt)\n stack.append(nxt)\n", "java": "void dfs(Map> graph, String start) {\n Deque stack = new ArrayDeque<>(List.of(start));\n Set seen = new HashSet<>(List.of(start));\n while (!stack.isEmpty()) {\n String node = stack.pop();\n visit(node);\n for (String next : graph.get(node)) {\n if (!seen.contains(next)) {\n seen.add(next);\n stack.push(next);\n }\n }\n }\n}", "cpp": "void dfs(map>& graph, string start) {\n vector stack{start};\n set seen{start};\n while (!stack.empty()) {\n string node = stack.back(); stack.pop_back();\n visit(node);\n for (auto& next : graph[node]) {\n if (!seen.count(next)) {\n seen.insert(next);\n stack.push_back(next);\n }\n }\n }\n}" }, "defaultInput": [ 1 ], "defaultTarget": null, "inputHint": "Pick a start node: 1 = A, up to 8 = H. Watch it dive deep first.", "pitfalls": [ { "wrong": "Using a queue instead of a stack.", "right": "A queue makes it explore in rings — that's BFS. DFS needs last-in-first-out so it dives into the newest node: a stack (or recursion)." }, { "wrong": "Recursing on a huge graph without thinking about the call stack.", "right": "Recursive DFS uses the call stack, and a very deep graph can overflow it. For deep graphs, use an explicit stack, like the code here does." }, { "wrong": "Not tracking visited nodes.", "right": "Without a 'seen' set, a cycle sends DFS around forever. Mark nodes as you discover them, just like BFS." } ], "quiz": [ { "q": "What data structure gives DFS its 'go deep first' behaviour?", "options": [ "A queue", "A stack", "A sorted list", "A heap" ], "answer": 1, "why": "A stack is last-in-first-out, so DFS always continues from the most recently discovered node — plunging deeper before it spreads sideways." }, { "q": "How do the nodes visited by DFS and BFS compare on the same graph?", "options": [ "DFS visits fewer nodes", "They visit the same nodes, in a different order", "BFS visits fewer nodes", "They visit completely different nodes" ], "answer": 1, "why": "Both reach every node connected to the start, exactly once, at the same O(V + E) cost. Only the order differs — and that order is what makes each suited to different problems." }, { "q": "Why can a recursive DFS crash on a very deep graph?", "options": [ "It runs out of nodes", "Each level of depth adds a frame to the call stack, which can overflow", "Recursion is always slow", "It visits nodes twice" ], "answer": 1, "why": "Recursive DFS rides the call stack — one frame per level of depth. A long enough path fills the stack and overflows it, which is why deep graphs often use an explicit stack instead." } ], "problems": [ { "name": "Flood Fill", "difficulty": "Easy", "url": "https://leetcode.com/problems/flood-fill/" }, { "name": "Number of Islands", "difficulty": "Medium", "url": "https://leetcode.com/problems/number-of-islands/" }, { "name": "Max Area of Island", "difficulty": "Medium", "url": "https://leetcode.com/problems/max-area-of-island/" } ], "trace": { "note": "Each frame is one immutable step: data snapshot, pointers, per-index roles, executing code line, and a one-sentence explanation.", "length": 20, "frames": [ { "data": { "nodes": [ { "id": "A", "label": "A", "x": 0.5, "y": 0.12, "role": "pivot" }, { "id": "B", "label": "B", "x": 0.24, "y": 0.37 }, { "id": "C", "label": "C", "x": 0.76, "y": 0.37 }, { "id": "D", "label": "D", "x": 0.12, "y": 0.66 }, { "id": "E", "label": "E", "x": 0.4, "y": 0.66 }, { "id": "F", "label": "F", "x": 0.6, "y": 0.66 }, { "id": "G", "label": "G", "x": 0.88, "y": 0.66 }, { "id": "H", "label": "H", "x": 0.5, "y": 0.92 } ], "edges": [ { "from": "A", "to": "B" }, { "from": "A", "to": "C" }, { "from": "B", "to": "D" }, { "from": "B", "to": "E" }, { "from": "C", "to": "F" }, { "from": "C", "to": "G" }, { "from": "E", "to": "H" }, { "from": "F", "to": "H" } ], "directed": false, "frontier": { "label": "stack", "ids": [ "A" ] }, "visited": [] }, "pointers": [], "highlights": [], "codeLine": 2, "variables": { "start": "A", "stack": "A" }, "explanation": "Depth-first search plunges as deep as it can from A, using a stack. A stack is last-in-first-out, so it always dives into the most recently found node — that's why DFS goes deep before wide.", "stats": { "comparisons": 0, "swaps": 0 }, "accent": "active" }, { "data": { "nodes": [ { "id": "A", "label": "A", "x": 0.5, "y": 0.12, "role": "active" }, { "id": "B", "label": "B", "x": 0.24, "y": 0.37 }, { "id": "C", "label": "C", "x": 0.76, "y": 0.37 }, { "id": "D", "label": "D", "x": 0.12, "y": 0.66 }, { "id": "E", "label": "E", "x": 0.4, "y": 0.66 }, { "id": "F", "label": "F", "x": 0.6, "y": 0.66 }, { "id": "G", "label": "G", "x": 0.88, "y": 0.66 }, { "id": "H", "label": "H", "x": 0.5, "y": 0.92 } ], "edges": [ { "from": "A", "to": "B" }, { "from": "A", "to": "C" }, { "from": "B", "to": "D" }, { "from": "B", "to": "E" }, { "from": "C", "to": "F" }, { "from": "C", "to": "G" }, { "from": "E", "to": "H" }, { "from": "F", "to": "H" } ], "directed": false, "frontier": { "label": "stack", "ids": [] }, "visited": [ "A" ] }, "pointers": [], "highlights": [], "codeLine": 6, "variables": { "visiting": "A", "order": "A" }, "explanation": "Pop A off the top of the stack and visit it. 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