Understanding how iterative DFS explores graphs depth-first using an explicit stack
Iterative Depth-First Search (DFS) is a graph traversal algorithm that explores a graph by going as deep as possible along each branch before backtracking. Unlike recursive DFS, it uses an explicit stack data structure instead of the call stack.
Key Characteristics:
Think of it like exploring a maze with a stack of breadcrumbs - push nodes onto the stack as you explore, and pop them when you backtrack!
Iterative DFS explores nodes by going deep first:
Iterative DFS uses an explicit stack, while recursive DFS uses the call stack. Both achieve the same result with O(V+E) complexity, but iterative avoids recursion limits and gives more control over the stack.
Start with the source node in a stack. The stack maintains the order of nodes to be explored (Last-In-First-Out).
While the stack is not empty, pop a node from the stack, visit it, and mark it as visited. This ensures depth-first exploration.
Push all unvisited neighbors of the current node onto the stack. Since we push and pop from the same end, the last neighbor pushed will be explored first (depth-first).
Iterative DFS visits each vertex once and checks each edge once:
Code Example:
// DFS Iterative - O(V+E) where V=vertices, E=edges
function dfsIterative(graph, start) {
const visited = new Set();
const stack = [start]; // Explicit stack
while (stack.length > 0) {
const node = stack.pop(); // Pop from stack
if (visited.has(node)) continue; // Skip if already visited
visited.add(node); // Mark as visited
console.log(node); // Process node
// Push unvisited neighbors to stack
for (const neighbor of graph[node]) {
if (!visited.has(neighbor)) {
stack.push(neighbor); // Push to stack
}
}
}
}Iterative DFS visits each vertex exactly once. With V vertices, this is O(V) time. The visited set ensures no vertex is processed twice.
When visiting a vertex, iterative DFS checks all its outgoing edges to find neighbors:
Combining both operations:
Both have O(V+E) time complexity. Iterative uses an explicit stack, while recursive uses the call stack. Iterative avoids stack overflow issues and gives more control, but recursive is often simpler to implement.
| Algorithm | Time Complexity | Space | Finds Shortest Path | Stack Overflow Risk |
|---|---|---|---|---|
| DFS Iterative | O(V+E) | O(V) | No | Low |
| DFS Recursive | O(V+E) | O(V) | No | Medium |
| BFS | O(V+E) | O(V) | Yes (unweighted) | Low |
| Dijkstra's | O((V+E) log V) | O(V) | Yes (weighted) | Low |
Iterative DFS is used for tree structures when you want to avoid recursion limits. File system navigation, DOM tree traversal, and expression tree evaluation all use iterative DFS.
Iterative DFS is perfect for solving mazes in systems with limited stack space. It maintains an explicit stack of paths to explore, avoiding recursion depth limits.
Iterative DFS can detect cycles by tracking nodes in the current path using the stack. This is useful in dependency resolution and deadlock detection.
Iterative DFS is used for topological sorting in build systems and task schedulers. The explicit stack makes it easier to handle large dependency graphs without hitting recursion limits.
In embedded systems with limited stack space, iterative DFS is preferred over recursive DFS. The explicit stack can be managed more carefully and avoids stack overflow risks.
Visits each vertex once (O(V)) and checks each edge once (O(E)), resulting in optimal linear complexity
Maintains a stack data structure instead of using the call stack, avoiding recursion limits
No recursion means no call stack limits - safer for deep graphs or systems with limited stack space
Produces the same depth-first traversal as recursive DFS, just with explicit stack management