Shortest Path in Unweighted Graph Using BFS in DSA C - Execution Trace

Concept Flow - Shortest Path in Unweighted Graph Using BFS

Start at source node

↓

Initialize queue with source

↓

While queue not empty

↓

Dequeue current node

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For each neighbor

↓

If neighbor not visited

↓

Mark visited, set distance, set parent

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Enqueue neighbor

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Repeat until queue empty

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Build shortest path using parent pointers

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Done

Start from the source node, explore neighbors level by level using a queue, track distances and parents to find shortest paths.

Execution Sample

DSA C

void bfs_shortest_path(int graph[][5], int n, int src, int dest) {
  int visited[5] = {0};
  int dist[5];
  int parent[5];
  int INF = 999;
  for(int i = 0; i < n; i++) {
    dist[i] = INF;
    parent[i] = -1;
  }
  dist[src] = 0;
  int q[5];
  int front = 0;
  int rear = -1;
  q[++rear] = src;
  visited[src] = 1;
  while(front <= rear) {
    int u = q[front++];
    for(int v = 0; v < n; v++) {
      if(graph[u][v] && !visited[v]) {
        visited[v] = 1;
        dist[v] = dist[u] + 1;
        parent[v] = u;
        q[++rear] = v;
      }
    }
  }
  // TODO: Reconstruct path from src to dest using parent array
}

This code runs BFS on an unweighted graph to find the shortest path from src to dest.

Execution Table

Step	Operation	Current Node	Queue State	Visited Nodes	Distance Array	Parent Array	Visual State
1	Initialize	-	[0]	[0,0,0,0,0]	[0,∞,∞,∞,∞]	[-1,-1,-1,-1,-1]	Start with source node 0 in queue
2	Dequeue	0	[]	[1,0,0,0,0]	[0,∞,∞,∞,∞]	[-1,-1,-1,-1,-1]	Visit node 0
3	Visit neighbors of 0	0	[1,3]	[1,1,0,1,0]	[0,1,∞,1,∞]	[-1,0,-1,0,-1]	Neighbors 1 and 3 enqueued
4	Dequeue	1	[3]	[1,1,0,1,0]	[0,1,∞,1,∞]	[-1,0,-1,0,-1]	Visit node 1
5	Visit neighbors of 1	1	[3,2]	[1,1,1,1,0]	[0,1,2,1,∞]	[-1,0,1,0,-1]	Neighbor 2 enqueued
6	Dequeue	3	[2]	[1,1,1,1,0]	[0,1,2,1,∞]	[-1,0,1,0,-1]	Visit node 3
7	Visit neighbors of 3	3	[2,4]	[1,1,1,1,1]	[0,1,2,1,2]	[-1,0,1,0,3]	Neighbor 4 enqueued
8	Dequeue	2	[4]	[1,1,1,1,1]	[0,1,2,1,2]	[-1,0,1,0,3]	Visit node 2
9	Visit neighbors of 2	2	[4]	[1,1,1,1,1]	[0,1,2,1,2]	[-1,0,1,0,3]	No new neighbors to enqueue
10	Dequeue	4	[]	[1,1,1,1,1]	[0,1,2,1,2]	[-1,0,1,0,3]	Visit node 4
11	Visit neighbors of 4	4	[]	[1,1,1,1,1]	[0,1,2,1,2]	[-1,0,1,0,3]	No new neighbors to enqueue
12	Queue empty	-	[]	[1,1,1,1,1]	[0,1,2,1,2]	[-1,0,1,0,3]	BFS complete, shortest paths found

💡 Queue is empty, BFS traversal finished

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 5	After Step 7	Final
visited	[0,0,0,0,0]	[1,0,0,0,0]	[1,1,0,1,0]	[1,1,1,1,0]	[1,1,1,1,1]	[1,1,1,1,1]
dist	[0,∞,∞,∞,∞]	[0,∞,∞,∞,∞]	[0,1,∞,1,∞]	[0,1,2,1,∞]	[0,1,2,1,2]	[0,1,2,1,2]
parent	[-1,-1,-1,-1,-1]	[-1,-1,-1,-1,-1]	[-1,0,-1,0,-1]	[-1,0,1,0,-1]	[-1,0,1,0,3]	[-1,0,1,0,3]
queue	[]	[]	[1,3]	[3,2]	[2,4]	[]

Key Moments - 3 Insights

Why do we mark a node as visited only when we enqueue it, not when we dequeue it?

Marking visited when enqueuing (see step 3) prevents adding the same node multiple times to the queue, ensuring BFS explores each node once.

How do we know the distance array holds shortest distances?

Distances are set when first visiting a node (step 3, 5, 7), and BFS explores nodes in order of increasing distance, so first distance set is shortest.

Why do we keep a parent array?

Parent array (step 3, 5, 7) helps reconstruct the shortest path from destination back to source after BFS finishes.

Visual Quiz - 3 Questions

Look at the execution table at step 3, which nodes are added to the queue?

A Nodes 1 and 3

B Nodes 2 and 4

C Node 0 only

D No nodes added

💡 Hint

Check the 'Queue State' and 'Operation' columns at step 3 in the execution table

At which step does the BFS queue become empty?

A Step 10

B Step 12

C Step 8

D Step 5

💡 Hint

Look at the 'Queue State' column and 'exit_note' in the execution table

If node 2 was connected to node 4, how would the queue change after visiting node 2?

A Node 4 would be added to the queue after node 2

B Node 4 would be added to the queue after node 3

C No change, node 4 is already visited

D Node 2 would be removed from the queue earlier

💡 Hint

Check 'visited' array in variable_tracker after step 7 to see if node 4 is already visited

Concept Snapshot

Shortest Path in Unweighted Graph Using BFS:
- Use a queue to explore nodes level by level
- Mark nodes visited when enqueued to avoid repeats
- Track distance and parent for each node
- BFS guarantees shortest path in unweighted graphs
- Reconstruct path using parent array after BFS

Full Transcript

This visualization shows how BFS finds the shortest path in an unweighted graph. We start from the source node, add it to a queue, and mark it visited. Then we repeatedly dequeue nodes, visit their neighbors, and enqueue unvisited neighbors while recording their distance and parent. This process continues until the queue is empty. The distance array holds the shortest distance from the source to each node, and the parent array helps reconstruct the shortest path. Key points include marking nodes visited when enqueued to avoid duplicates and BFS's level-by-level exploration ensuring shortest paths.