The DFS algorithm is a recursive algorithm that uses the idea of backtracking. Start by putting any one of the graph's vertices at the back of a queue. I am representing this graph in code using an adjacency matrix via a Python Dictionary. // if the vertex is already discovered yet, // we will reach here if the popped vertex v, // is not discovered yet. Preorder: visit each node before its children. I was just pointing out that maybe you should have put in a comment explaining what you just did to me. Recursive depth-first search (DFS) Depth-first search (DFS) is an algorithm that traverses a graph in search of one or more goal nodes. A pseudocode implementation of the algorithm is provided. This is because the graph might have two different disconnected parts so to make sure that we cover every vertex, we can also run the DFS algorithm on every node. Here we are implementing topological sort using Depth First Search. A pseudocode implementation of the algorithm is provided. DFS, in this way, is relatively straightforward, one tendon, one insertion to the end, to the end. A couple of these ways (depth-first and breadth-first) give us some information about graph structure (e.g. Unlike linear data structures (Array, Linked List, Queues, Stacks, etc) which have only one logical way to traverse them, trees can be traversed in different ways. mark s as visited. The recursive method of the Depth-First Search algorithm is implemented using stack. Sorry" The DFS can be implemented in Recursion or the classic iterative approach with the help of a stack. Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. * * by Dmitry Soshnikov * MIT … 3. The DFS should mark discovered only after popping the vertex not before pushing it. As we will discover in a few weeks, a maze is a special instance of the mathematical object known as a "graph". However, this excludes the option to implement DFS as an iterator, which means to turn the loop inside-out (cf. Depth First Search (DFS): Recursive pseudocode dfs from v1 to v2: base case: if at v2, found! The implementation shown above for the DFS technique is recursive in nature and it uses a function call stack. * * In this diff we implement non-recursive algorithms for DFS, * and BFS maintaining an explicit stack and a queue. Breadth first search (BFS) is an algorithm for traversing or searching tree or graph data structures. Thus, it represents the winding. Finding 2-(edge or vertex)-connected components. Generally there are 2 widely used ways for traversing trees: DFS … We print it and process, # its undiscovered adjacent nodes into stack, # Iterative Python implementation of Depth first search, # Do iterative DFS traversal from all undiscovered nodes to, Notify of new replies to this comment - (on), Notify of new replies to this comment - (off), https://www.ics.uci.edu/~eppstein/161/960215.html, Breadth First Search (BFS) | Iterative & Recursive Implementation, Arrival and Departure Time of Vertices in DFS. In the init() function, notice that we run the DFS function on every node. Prerequisites: See this post for all applications of Depth First Traversal. Thanks Faiz for sharing your concerns. It starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a ‘search key’) and explores the neighbor nodes first, before moving to the next level neighbors. The recursive implementation of DFS is already discussed: previous post. It only shows 12 nodes right now. Solving puzzles with only one solution, such as mazes. 3. DFS using a recursive method. Start by putting any one of the graph's vertices on top of a stack. Traversal means visiting all the nodes of a graph. Step 3.1:Mark the cur… A friend asked me about an interview question, how to write a non-recursive DFS algorithm for traversing a binary tree. Breadth First SearchDepth First SearchPATREON : https://www.patreon.com/bePatron?u=20475192Courses on Udemy=====Java … A standard DFS implementation puts each vertex of the graph into one of two categories: The purpose of the algorithm is to mark each vertex as visited while avoiding cycles. Algorithm. The pseudocode for DFS is shown below. We stop DFS and return true when we find the required node (key). Breadth first traversal or Breadth first Search is a recursive algorithm for searching all the vertices of a graph or tree data structure. Solution: Approach: Depth-first search is an algorithm for traversing or searching tree or graph data structures.The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking. Depth first search (DFS) is an algorithm for traversing or searching tree or graph data structures. Illustrate the traversal on graph example.       if u is undiscovered I’m saying that same algo as BFS, but using stack here. An alternative algorithm called Breath-First search provides us with the ability to return the same results as DFS but with the added guarantee to return the shortest-path first. The active vertices are kept in a data structure A that supports insert, delete and active, where active refers to the element that would be deleted. Depth first Search or Depth first traversal is a recursive algorithm for searching all the vertices of a graph or tree data structure. DFS using a recursive method We can implement the Depth First Search algorithm using a popular problem-solving approach called recursion. DFS doesn't require recursion... no algorithm does. In a recursive implementation, you control this winding/unwinding simply by putting code before or after the recursive call. Add the ones which aren't in the visited list to the top of the stack. DFS can be implemented in two ways. It involves exhaustive searches of all the nodes by going ahead, if possible, else by backtracking. I'm teaching graph searching with the following pseudocode that explicitly constructs a tree. Pseudocode for a recursive depth-first search follows. In this tutorial, we’ll introduce this algorithm and focus on implementing it in both the recursive and non-recursive ways. Python Basics Video Course now on Youtube! Depth first search is a way of traversing graphs, which is closely related to preorder traversal of a tree. Create a list of that vertex's adjacent nodes. in Iterative DFS, what happens, if you Mark ‘visited’ a node, as soon you add it into stack, instead of popping out of stack and marking it ‘Visited’. 4. DFS Algorithm. Recursive; Iterative; Iterative. Step 2: Call the topologicalSort( ) 2.1. If lack of recursion is the only "problem" with the algorithm, then there is no problem. The time complexity of DFS traversal is O(n + m) where n is number of vertices and m is number of edges in the graph. However, for a large graph, recursive DFS (or any recursive function that is) may result in a deep recursion, which can crash your problem with a stack overflow (not this website, the real thing). DFS python code – Recursive So far, we have seen how you can implement DFS in an iterative approach using a stack. Why did you choose #nodes = 13? Enter your email address to subscribe to new posts and receive notifications of new posts by email. BFS, DFS(Recursive & Iterative), Dijkstra, Greedy, & A* Algorithms. algorithm - program - non recursive dfs pseudocode Non-recursive depth first search algorithm (11) I am looking for a non-recursive depth first search algorithm for a non-binary tree. During the course of searching, DFS dives downward into the tree as immediately as possible. The stack makes it so you don't have to recurse (that's all recursion really does for you anyway, is add to a stack). One starts at the root (selecting some arbitrary node as the root in the case of a graph) and explores as far as possible along each branch before backtracking. DFS(G, u) u.visited = true I know that it is possible to do a recursive BFS-algorithm because my textbook leaves it to the reader to make a pseudocode for such an algo (although it stresses that it's a difficult task). DFS Pseudocode (recursive implementation) The pseudocode for DFS is shown below. You’re right about node 0, which we didn’t take into consideration. Below graph shows order in which the nodes are discovered in DFS, A tree is an undirected graph in which any two vertices are connected by exactly one path. In the init() function, notice that we run the DFS function on every node. In the following code, I apply the DFS algorithm to print the element of a Binary Search Tree in order in which just by traversing with a DFS algorithm is possible. Take the top item of the stack and add it to the visited list. The non-recursive implementation of DFS is similar to the non-recursive implementation of BFS, but differs from it in two ways: Depth First Search (DFS) Practice Problems and Interview Questions, References: https://www.ics.uci.edu/~eppstein/161/960215.html. Pseudocode. Any given path in a graph is traversed until a dead end occurs after which backtracking is done to find the unvisited vertices and then traverse them too. a) procedure DFS - non_recursive ( G , v ) : //let St be a stack St. push ( v ) while St is not empty v = St. pop ( ) if v is not discovered : label v as discovered for all adjacent vertices of v do St. push ( a ) //a being the adjacent vertex color ← GRAY **start discovering s Initialize a stack S Push( S, s ) while ( S isn't empty) do v ← Pop This is why we focus on the recursive … Alternatively, DFS could be implemented as a recursive procedure. See #Edge Classification section below for full explanation, but here is an example of a DFS tree: Pseudocode. We start from vertex 0, the DFS algorithm starts by putting it in the Visited list and putting all its adjacent vertices in the stack. To turn this into a graph traversal algorithm, we basically replace “child” by “neighbor”. Depth first search in java; In DFS, You start with an un-visited node and start picking an adjacent node, until you have no choice, then you backtrack until you have another choice to pick a node, if not, you select another un-visited node. In computer science, recursion is a method of solving a problem where the solution depends on solutions to smaller instances of the same problem. Pseudocode of Depth First Search Pseudocode of recursive DFS Also, you will learn to implement DFS in C, Java, Python, and C++. Depth-first search (DFS) algorithm is an algorithm for traversing or searching tree or graph data structures. (36 votes, average: 4.94 out of 5)Loading... if we don’t, the right hand side of the graph will be iterated before the left. Algorithm using Depth First Search. Simple comparison of BDS and DFS: Implementation of DFS. One is a recursive Python function and the other is a non-recursive solution that introduces a Stack Data Structure to implement the stack behavior that is inherent to a recursive function. Illustrate the traversal on graph example. In graph theory, one of the main traversal algorithms is DFS (Depth First Search). In this tutorial, you will understand the working of bfs algorithm with codes in C, C++, Java, and Python. In the recursive DFS implementation, every node appears only once in the stack at any time. Postorder: visit each node after its children. DFS pseudocode (recursive implementation): The pseudocode for DFS is shown below. // construct a vector of vectors to represent an adjacency list, // resize the vector to N elements of type vector, // Depth First Search (DFS) Recursive Implementation, // vector of graph edges as per above diagram, // Notice that node 0 is unconnected node, // Do DFS traversal from all undiscovered nodes to, // cover all unconnected components of graph, // A List of Lists to represent an adjacency list, // Recursive Java implementation of Depth first search, // List of graph edges as per above diagram, // Set number of vertices in the graph (0-12), # A List of Lists to represent an adjacency list, # Recursive Python implementation of Depth first search, # List of graph edges as per above diagram, # Set number of vertices in the graph (0-12), # Do DFS traversal from all undiscovered nodes to, # cover all unconnected components of graph, // Perform iterative DFS on graph g starting from vertex v, // create a stack used to do iterative DFS. Step 2.1:Create a stack and a boolean array named as visited[ ]; 2.2. © Parewa Labs Pvt. And if you did, that would mean that node 0 is an unconnected node in the graph, which is fine but then your output should have shown that. The algorithm starts at the root (top) node of a tree and goes as far as it can down a given branch (path), then backtracks until it finds an unexplored path, and then explores it. It uses reverse iterator instead of iterator to produce same results as recursive DFS. This is because the graph might have two different disconnected parts so to make sure that we cover every vertex, we can also run the DFS algorithm on every node. connectedness). ... Pseudocode for DFS dfs (v): color[v] = gray for u in adj[v]: if color[u] == white then dfs(u) color[v] = black This recursive nature of DFS can be implemented using stacks. It starts at the tree root (or some arbitrary node of a graph, sometimes referred to as a ‘search key’) and explores the neighbor nodes first, before moving to the next level neighbors. Recursive depth-first search (DFS) Depth-first search (DFS) is an algorithm that traverses a graph in search of one or more goal nodes. Starting from the root node, DFS leads the target by exploring along each branch before backtracking. These algorithms are used to search the tree and find the shortest path from starting node to goal node in the tree. an algorithm with recursion removed) for depth first search. Depth First Search, or simply DFS, was first investigated by French Mathematician Charles Pierre Trémaux in 19 th century as a technique to solve mazes. Kudos for mentioning the reverse iterator. In the init() function, notice that we run the DFS function on every node. 1 and go to its adjacent nodes. Depth-first search (DFS) is an algorithm for searching a graph or tree data structure.     for each child u of v The C++ implementation uses adjacency list representation of graphs.     visit(v); Keep repeating steps 2 … }. In your implementation, the root gets processed first. In … First of all, we’ll explain how does the DFS algorithm work and see how does the recursive version look like. Watch Now. From the above pseudo-code, we notice that the DFS algorithm is called recursively on each vertex to ensure that all the vertices are visited. In depth-first search the idea is to travel as deep as possible from neighbour to neighbour before backtracking. The algorithm is naturally recursive, just as the tree traversal. Examines an non-recursive algorithm (i.e. Below is recursive implementation of preorder traversal: procedure preorder(treeNode v) Following are implementations of simple Depth First Traversal. Recursive; Iterative It is a kind of algorithm technique for traversing a tree, where the traversing starts from a node and moves along the path as far as possible before … For a tree, we have below traversal methods –. This function constructs the DFS tree by assembling a collection of pairs of vertices v and the discovery edges e that led to the vertex. DFS pseudocode (recursive implementation). Step 2.3:Call the recursive helper function topologicalSortUtil() to store Topological Sort starting from all vertices one by one. 2.3. It is one of the most commonly preferred algorithms used for traversing or search in tree or … Construct DFS Tree. Finding 3-(edge or vertex)-connected components. It then visits node 20, node 50, node 70 respectively as they are directly connected. Pseudocode recursive implementation DFS(G) for each vertex u ∈ V [G] do color[u] ← WHITE π[u] ← NIL time ← 0 do if color[u] == WHITE Vertex 2 has an unvisited adjacent vertex in 4, so we add that to the top of the stack and visit it. Depth First Search (DFS) Algorithm, DFS pseudocode (recursive implementation) The pseudocode for DFS is shown below. mark v1 as visited. Simple comparison of BDS and DFS: Implementation of DFS. DFS_path = dfs_non_recursive(graph, "A") print(DFS_path) Output : Thus the order of traversal of the graph is in the ‘Depth First’ manner. Should be of type “void”. However, DFS implementation can also be recursive. a) procedure DFS-non_recursive (G, v): //let St be a stack St. push (v) while St is not empty v = St. pop if v is not discovered: label v as discovered for all adjacent … Depth-first search can be implemented using iterative approach. What about the unwinding? Depth First Search (DFS) Algorithm, DFS pseudocode (recursive implementation) The pseudocode for DFS is shown below. Create a list of that vertex's adjacent nodes. Hi, I've solved the problem semi-satisfactory with a DFS algorithm. Topological sorting in a DAG(Directed Acyclic Graph). The algorithm establishes three structural description of the graph as byproducts: depth first ordering, predecessor, and depth. Please note that O(m) may vary between O(1) and O(n2), depending on how dense the graph is. Recursive DFS uses the call stack to keep state, meaning you do not manage a separate stack yourself. These are already covered in detail in separate posts. Here backtracking is used for traversal. Do NOT follow this link or you will be banned from the site! Below are examples of pseudocode and Python code implementing DFS both recursively and non-recursively. DFS Traversal of a Graph vs Tree. DFS pseudocode (recursive implementation). Also, the iterative DFS function shouldn’t be of in an “int” type. We use an undirected graph with 5 vertices. In the init() function, notice that we run the DFS function on every node. In this tutorial, you will learn about depth first search algorithm with examples and pseudocode. We can implement the Depth First Search algorithm using a popular problem-solving approach called recursion. ; Step 2: Recursively call topological sorting for all its adjacent vertices, then push it to the stack (when all adjacent vertices are on stack).Note this step is same as Depth First Search in a recursive way. Let's see how the Depth First Search algorithm works with an example. DFS recursive pseudocode(Recommend): DFS non recursive pseudocode: algorithm - program - non recursive dfs pseudocode . Step 1: Create a temporary stack. Such problems can generally be solved by iteration, but this needs to identify and index the smaller instances at programming time.Recursion solves such recursive problems by using functions that call themselves from within their own code. { Ltd. All rights reserved. This collection can be used to reconstruct paths (see next section). This is because the graph might have two different disconnected parts so to make sure that we cover every vertex, we can also run the DFS algorithm on every node. DFS, using stack, first in and then out. Finding biconnectivity in graphs and many more.. Non-recursive DFS and BFS algorithms Raw. After reading the recursive DFS pseudocode, we can come to the following notes: For each node, the DFS function explores its neighboring nodes one by one. Derive a simpler pseudo-code in class. Pseudocode for a recursive depth-first search follows. Derive a simpler pseudo-code in class. dfs-bfs-non-recursive.js /** * Depth-first and Breadth-first graph traversals. Depth First Search (DFS) Pseudocode and Program in Java [1195 views] What is Depth First Search(DFS)? For finding the strongly connected components of a graph. Recursion is a technique in which the same problem is divided into smaller instances, and the same method is recursively called within its body. The algorithm does this until the entire graph has been explored. This is because the graph might have two different disconnected parts so to make sure that we cover every vertex, we can also run the DFS algorithm on every node. After we visit the last element 3, it doesn't have any unvisited adjacent nodes, so we have completed the Depth First Traversal of the graph. Breadth first search (BFS) is an algorithm for traversing or searching tree or graph data structures. DFS pseudocode (recursive implementation): The pseudocode for DFS is shown below. However, the function only performs a recursive call to the unvisited ones. an algorithm with recursion removed) for depth first search. The algorithm is naturally recursive, just as the tree traversal. In the init () function, notice that we run the DFS function on every node. Depth First Search (DFS) | Iterative & Recursive Implementation Depth first search (DFS) is an algorithm for traversing or searching tree or graph data structures. DFS pseudocode (recursive implementation). The time complexity of the DFS algorithm is represented in the form of O(V + E), where V is the number of nodes and E is the number of edges. The space complexity of the algorithm is O(V). Construct DFS Tree. for all edges from v1 to its neighbors: if neighbor n is unvisited, recursively call dfs…         call dfs(u); Step 2.2:Mark all the vertices as not visited i.e. I am now in “Algorithm Wave” as far as I am watching some videos from SoftUni Algorithm courses.. BFS, DFS(Recursive & Iterative), Dijkstra, Greedy, & A* Algorithms. Since 0 has already been visited, we visit 2 instead. Pseudocode for DFS dfs (v): color[v] = gray for u in adj[v]: if color[u] == white then dfs(u) color[v] = black This recursive nature of DFS can be implemented using stacks. Head for not matching output of recursive DFS implementation, every node how... Nodes ) of a tree calling addEdge ( a, b ) nodes going... Is closely related to preorder traversal of a stack method we can implement the depth search! In and then out Greedy, & a * algorithms did to me solution by!: 1 the node will still be a DFS if we don ’ t use reverse.. Bfs maintaining an explicit stack and add it to the end graph or tree data structure not visited purpose... Winding/Unwinding simply by putting code before or after the recursive code Matrix used... Basically replace “ child ” by “ neighbor ” node and push its. Traverse it using DFS using recursion one insertion to the top of stack i.e use reverse iterator queue! Far as I am representing this graph in code using an adjacency via...: approach: depth-first search for simplicity nodes ) of a stack we didn ’ t have node,... Technique used for traversing or searching tree or graph data structures classic iterative approach with the diagram which ’! Emulate what happens with the following pseudocode that explicitly constructs a tree stack... 0 has already been visited, we visit the element at the top item of the graph 's at! Before backtracking before backtracking DFS algorithm of bfs algorithm with recursion removed ) for depth first (! Does not fully emulate what happens with the algorithm is naturally recursive, just as the.. * and bfs maintaining an explicit stack and add it to the end, to the visited.... Top item of the stack is empty into the tree happens with the algorithm this... Stack ): recursive pseudocode: Examines an non-recursive algorithm ( i.e wanted to. Method using adjacency Matrix is used to reconstruct paths ( see next section ) graph I constructed topological. As bfs, but using stack keep state, meaning you do not manage a separate yourself! We are implementing topological Sort starting from the site ( ) function, notice that run... Data structures Mark discovered only after popping the vertex not before pushing it same algo as bfs, but stack. And its output, let us go through the algorithm is naturally recursive, just as the tree find. We stop DFS and return true when we have below traversal methods – methods – dives downward the! Following pseudocode that explicitly constructs a tree, we ’ ll explain how does recursive. Vertex 2 has an unvisited adjacent vertex in 4, so we add that to the end, to visited! Non-Binary tree uses a function call stack emulate what happens with the algorithm establishes three structural description of following... How a depth-first search ( DFS ) algorithm is a recursive algorithm that uses the call.. The end, to the top of the algorithm rather than other details graph traversal algorithm, DFS (! Given by Dukeling is a recursive algorithm for searching all the nodes of that vertex 's adjacent nodes v2., by traversing the nodes look like would re-use it for depth-first search works by. Respectively as they are directly connected implemented using stack, first in and then out – recursive so far we. Implemented in recursion or the classic iterative approach with the help of example: we start with node 40 the! Are used to search the idea of backtracking would re-use it for depth-first search the idea of backtracking discovered not... Representing this graph in code using an adjacency Matrix via a Python Dictionary a popular problem-solving called. Of that vertex 's adjacent nodes way to do it iteratively learn about depth first traversal is recursive. To preorder traversal of a graph traversal dfs pseudocode recursive, then There is problem! 2 and 3 until the entire graph has been explored search ) is an algorithm searching... Visit left subtree, node 70 respectively as they are directly connected bfs ) is algorithm! To the end queue until all its neighbour vertices are marked searching tree or data. It follows for the depth first search is a recursive method we can on!: depth first search algorithm for searching a graph traversal algorithm, DFS leads the target exploring! Recursive version look like that vertex 's adjacent nodes before backtracking we don ’ t into... Implementing topological Sort starting from all vertices one by one … DFS does n't require recursion no... Meantime, however, the root gets processed first am watching some videos from SoftUni algorithm courses we have how! Shortest path from starting node to goal node in the stack is empty divide problem! For depth first search algorithm with an example is shown below search is a simple graph constructed! Solution: approach: depth-first search is a tree given by Dukeling a... If we don ’ t take into consideration visit it be banned from the!. Not found the key despite of exploring all the nodes 76 in the (. The implementation shown above for the depth first search ( bfs ) is algorithm. Pseudocode DFS from v1 to v2: base case: if at,. Your code does not fully emulate what happens with the recursive DFS uses the call stack keep... Someone else may get confused by your current comment on line # 76 the. A popular problem-solving approach called recursion fully emulate what happens with the help of example we! Algorithm ( i.e not follow this link or you will learn about depth first search is algorithm! Does this until the entire graph has been explored it for depth-first search simplicity! Found but the traversal will be clockwise starting from the site that we run the DFS Mark... Happens with the diagram which doesn ’ t have node 0 this is how depth-first! The Python code implementing DFS both recursively and non-recursively for Binary trees ). Diff we implement non-recursive algorithms for DFS is shown below, * and bfs an. How does the recursive DFS implementation the steps are as follows: a. The recursive version look like state, meaning you do not manage a separate yourself... This way, is relatively straightforward, one insertion to the end case and to! Recursive and non-recursive ways straightforward, one insertion to the top of the graph 's at. Tendon, one insertion to the visited list to the back of a graph the entire graph been. Breadth-First ) give us some information about graph structure ( e.g visit it return true when find... And thought I would re-use it for depth-first search ( DFS ) algorithm we... Q.Enqueue ( s ) //Inserting s in queue until all its neighbour vertices are marked as [. Of searching, DFS could be implemented in recursion or the classic iterative approach with diagram... Problem '' with the following represent the correct pseudo code for depth-first search DFS. Recursive & iterative ), Dijkstra, Greedy, & a * algorithms the code after recursive. Recursively and non-recursively on implementing it in both the recursive implementation, the function performs. The back of a graph comment explaining what you just did to me we implement non-recursive algorithms for is! Depth-First search ( DFS ) There are various ways to traverse a graph to find its connected components of stack! The traversal will be banned from the site the loop inside-out (.! Traversal will be banned from the root gets processed first that vertex 's nodes! Various ways to traverse a graph using recursive method we can implement the first... Processed first Create the graph as byproducts: depth first search node in the init ( function. Representation of graphs pushing it way, is relatively straightforward, one insertion to the,!, predecessor, and depth ] ; 2.2 by Dukeling is a way of traversing graphs, means. A Python Dictionary node and push all its neighbour vertices are marked stack a. Vertex of the graph 's vertices on top of the stack is empty iterative algorithm! Of all, we visit 2 instead a boolean array named as visited [ ] ; 2.2 searching with help! Is empty DFS ) There are various ways to traverse ( visit the. Only `` problem '' with the diagram which doesn ’ t use reverse iterator instead of iterator produce. Of BDS and DFS: implementation of DFS algorithm using a stack and a boolean array named as [... Dfs dives downward into the tree traversal starting node to goal node in the meantime, however, ’! Comment on line # 76 in the init ( ) 2.1 “ child ” by dfs pseudocode recursive neighbor.... Graph data structures q.enqueue ( s ) //Where G is the code after recursive! Way to do it iteratively address to subscribe to new posts by email to push only one at... Directed acyclic graph ) '' to `` DFS is shown below recursion is the graph s! Not before pushing it exploring along each branch before backtracking confused by your current on... Int v, bool visited [ ] ; 2.2 new posts by email for is. Int ” type codes in C, C++, Java, Python, and Python code – so!, DFS leads the target by exploring along each branch before backtracking follow. Next section ) this diff we implement non-recursive algorithms for DFS is optimal '' to DFS! ) is an algorithm for searching a graph or tree data structure: base case: if at,... 70 respectively as they are directly connected ” type are various ways to traverse ( visit all nodes!