- Under what condition BFS is optimal?
- What is BFS and DFS with example?
- Why is BFS V E?
- Why do we use DFS?
- When the DFS of a graph is unique?
- Does Dijkstra use DFS?
- Which between DFS and BFS can find a vertex first?
- How do you implement DFS?
- Which has the lowest worst case complexity?
- Does DFS have a path graph?
- What is the time complexity of DFS?
- Why is DFS faster than BFS?
- Does DFS find shortest path?
- What is Dijkstra shortest path algorithm?
- What is the time complexity of Dijkstra algorithm?
- What is the advantage of using DFS over BFS?
- Why is DFS not optimal?
- Where is DFS used?
- Is DFS tree unique?
- Which is better DFS or BFS?
- Is Dijkstra a BF?

## Under what condition BFS is optimal?

BFS is optimal if the path cost is a non-decreasing function of d(depth).

Normally, BFS is applied when all the actions have the same cost.

Optimal as in “produces the optimal path”, not “is the fastest algorithm possible”..

## What is BFS and DFS with example?

The full form of BFS is Breadth-First Search while the full form of DFS is Depth First Search. BFS uses a queue to keep track of the next location to visit. whereas DFS uses a stack to keep track of the next location to visit. BFS traverses according to tree level while DFS traverses according to tree depth.

## Why is BFS V E?

3 Answers. Overall, BFS accesses (and processes) each edge constant times (twice actually; we assume an undirected graph), costing O(E) total time in edge processing. … The overhead for initialization is O(V). Thus the total running time of BFS is O(V+E).

## Why do we use DFS?

BFS can be used to find the shortest path, with unit weight edges, from a node (origional source) to another. Whereas, DFS can be used to exhaust all the choices because of its nature of going in depth, like discovering the longest path between two nodes in an acyclic graph.

## When the DFS of a graph is unique?

7. When the Depth First Search of a graph is unique? Explanation: When Every node will have one successor then the Depth First Search is unique. In all other cases, when it will have more than one successor, it can choose any of them in arbitrary order.

## Does Dijkstra use DFS?

2 Answers. DFS keeps jumping along nodes until it finds a path, While Dijkstra is more similar to a BFS except it keeps track of weights (not all paths have equal cost) and will keep checking the shortest path not already checked until it gets to the target.

## Which between DFS and BFS can find a vertex first?

BFS vs DFSS.NOBFS1.BFS stands for Breadth First Search.2.BFS(Breadth First Search) uses Queue data structure for finding the shortest path.3.BFS can be used to find single source shortest path in an unweighted graph, because in BFS, we reach a vertex with minimum number of edges from a source vertex.3 more rows•Jul 3, 2020

## How do you implement DFS?

DFS algorithmStart by putting any one of the graph’s vertices on top of a stack.Take the top item of the stack and add it to the visited list.Create a list of that vertex’s adjacent nodes. Add the ones which aren’t in the visited list to the top of the stack.Keep repeating steps 2 and 3 until the stack is empty.

## Which has the lowest worst case complexity?

______ sorting algorithms has the lowest worst-case complexity.Selection Sort.Bubble Sort.Merge Sort.Quick Sort.

## Does DFS have a path graph?

Approach: Either Breadth First Search (BFS) or Depth First Search (DFS) can be used to find path between two vertices. Take the first vertex as source in BFS (or DFS), follow the standard BFS (or DFS). If the second vertex is found in our traversal, then return true else return false.

## What is the time complexity of DFS?

The time complexity of DFS if the entire tree is traversed is O ( V ) O(V) O(V) where V is the number of nodes. In the case of a graph, the time complexity is O ( V + E ) O(V + E) O(V+E) where V is the number of vertexes and E is the number of edges.

## Why is DFS faster than BFS?

Comparing BFS and DFS, the big advantage of DFS is that it has much lower memory requirements than BFS, because it’s not necessary to store all of the child pointers at each level. … Then, a BFS would usually be faster than a DFS. So, the advantages of either vary depending on the data and what you’re looking for.

## Does DFS find shortest path?

Both BFS and DFS will give the shortest path from A to B if you implemented right.

## What is Dijkstra shortest path algorithm?

Dijkstra’s algorithm (or Dijkstra’s Shortest Path First algorithm, SPF algorithm) is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. … For a given source node in the graph, the algorithm finds the shortest path between that node and every other.

## What is the time complexity of Dijkstra algorithm?

Time Complexity of Dijkstra’s Algorithm is O ( V 2 ) but with min-priority queue it drops down to O ( V + E l o g V ) .

## What is the advantage of using DFS over BFS?

For a complete/perfect tree, DFS takes a linear amount of space with respect to the depth of the tree whereas BFS takes an exponential amount of space with respect to the depth of the tree. This is because for BFS the maximum number of nodes in the queue is proportional to the number of nodes in one level of the tree.

## Why is DFS not optimal?

DFS is non-optimal in nature. … In DFS, we need to store only the nodes which are present in the path from the root to the current node and their unexplored successors. For state space with branching factor b and maximum depth m, DFS has space complexity of O(bm), a much better improvement over that of BFS.

## Where is DFS used?

Depth-first search is often used as a subroutine in network flow algorithms such as the Ford-Fulkerson algorithm. DFS is also used as a subroutine in matching algorithms in graph theory such as the Hopcroft–Karp algorithm. Depth-first searches are used in mapping routes, scheduling, and finding spanning trees.

## Is DFS tree unique?

1 Answer. The fact that DFS does not determine uniquely the resulting labeling is due to the fact that there is no order in which the children of a node are visited. To my understanding, checking whether a tree T of a given graph G is a DFS tree can be done as follows.

## Which is better DFS or BFS?

BFS uses Queue to find the shortest path. DFS uses Stack to find the shortest path. BFS is better when target is closer to Source. … DFS is faster than BFS.

## Is Dijkstra a BF?

You can implement Dijkstra’s algorithm as BFS with a priority queue (though it’s not the only implementation). Dijkstra’s algorithm relies on the property that the shortest path from s to t is also the shortest path to any of the vertices along the path. This is exactly what BFS does.