Question

Let us consider an unweighted graph G . Let a breadth-first traverse of G be done from a node r . Let $\mathrm{d}(\mathrm{r}, \mathrm{u})$ and $\mathrm{d}(\mathrm{r}, \mathrm{v})$ be the lengths of the shortest paths from $r$ to $u$ and $v$ respectively, in G . of $u$ is visited before $v$ during the breadth-first traversal, which of the following statements is correct? A. $d(r, u)<d(r, v)$ B. $d(r, u)>d(r, v)$ C. $\mathbf{d}(\mathbf{r}, \mathbf{u})<=\mathbf{d}(\mathbf{r}, \mathbf{v})$ D. None of the above

   Let us consider an unweighted graph G . Let a breadth-first traverse of G be done from a node r . Let $\mathrm{d}(\mathrm{r}, \mathrm{u})$ and $\mathrm{d}(\mathrm{r}, \mathrm{v})$ be the lengths of the shortest paths from $r$ to $u$ and $v$ respectively, in G . of $u$ is visited before $v$ during the breadth-first traversal, which of the following statements is correct?
A. $d(r, u)<d(r, v)$
B. $d(r, u)>d(r, v)$
C. $\mathbf{d}(\mathbf{r}, \mathbf{u})<=\mathbf{d}(\mathbf{r}, \mathbf{v})$
D. None of the above

Data Structures Using C

Amol M. Jagtap, Ajit… 1st Edition

Chapter 6, Problem 1

Instant Answer

Step 1

BFS explores a graph level by level, starting from a source node (in this case, r). It first visits all nodes at distance 1 from r, then all nodes at distance 2, and so on. Show more…

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Let us consider an unweighted graph G . Let a breadth-first traverse of G be done from a node r . Let $\mathrm{d}(\mathrm{r}, \mathrm{u})$ and $\mathrm{d}(\mathrm{r}, \mathrm{v})$ be the lengths of the shortest paths from $r$ to $u$ and $v$ respectively, in G . of $u$ is visited before $v$ during the breadth-first traversal, which of the following statements is correct? A. $d(r, u)<d(r, v)$ B. $d(r, u)>d(r, v)$ C. $\mathbf{d}(\mathbf{r}, \mathbf{u})<=\mathbf{d}(\mathbf{r}, \mathbf{v})$ D. None of the above

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