Breadth First Search Visualization
Breadth-First Search (BFS) explores a graph much like finding connections in a social network. Starting from a source node, it first visits all of its direct friends (neighbors), then all of their friends, and so on, level by level. It uses a queue to keep track of who to visit next, ensuring it doesn't go too deep down one path. This makes it perfect for finding the shortest path in an unweighted graph.
Pseudocode
queue = new Queue()
queue.enq(src)
mark src as visited
while queue is not empty:
u = queue.deq()
for each neighbor v of u:
if v is not visited:
queue.enq(v)
mark v as visited
AI Summary
(5 credits)
Common Interview Questions
Why does BFS guarantee the shortest path in an unweighted graph while DFS does not?
BFS explores nodes level-by-level in increasing order of distance from the source using a FIFO queue. The first time a target vertex is reached, the path taken must be the minimum edge distance path. DFS delves deep down single branches without distance guarantees.
What is 0-1 BFS and when should it be used instead of Dijkstra's Algorithm?
When graph edge weights are restricted to only 0 or 1, 0-1 BFS uses a Double-Ended Queue (Deque). Weight-0 edges push to the front of the deque (push_front), and weight-1 edges push to the back (push_back). This runs in O(V + E) time, faster than Dijkstra's O((V + E) log V).
Compare Bidirectional BFS with standard BFS for searching web graph relationships.
Standard BFS searches outwards from source up to distance d, expanding O(bd) nodes (where b is branching factor). Bidirectional BFS runs two simultaneous searches from source and target. They meet in the middle, expanding O(2 * bd/2) nodes, exponentially saving memory and time.
How can memory consumption in BFS become a critical bottleneck for dense graphs?
The queue size in BFS reaches the maximum width of the graph (the frontier layer). For complete or dense graphs, the queue can hold O(V) nodes concurrently, consuming high memory compared to DFS which holds only O(H) height nodes.
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