number 3, no trace is required GRAPH ALGORITHMS 244 1. For the following graphs,
ID: 3715445 • Letter: N
Question
number 3, no trace is required
GRAPH ALGORITHMS 244 1. For the following graphs, give the order that when doing a breadth-first startin e order that the nodes will be EAFor the following g a bread 8.3.4 EXERCISES first traversal starting at the node labelo fr e labeled wi 6 d. will be first vi. at the node labeled with a 1, 2. For the graphs in Exercise 1, give the order that the nodes ited when doing a depth-first traversal starting at the node 3. Write a detailed algorithm for depth-first traversal usi matrix that just prints the node label as the visit operation. You should t it using the graphs in this section to make sure you get the same answer 4. Write a detailed algorithm for breadth-first traversal using an adiad matrix that just prints the node label as the visit operation. You should t it using the graphs in this section to make sure you get the same answ 5. Write a detailed algorithm for depth-first traversal using an adia cency lst that just prints the node label as the visit operation. the graphs in this section to make sure you get the same a You should trace it 6. Write a detailed algorithm for breadth-first traversal using an adjacency her that just prints the node label as the visit operation.You should trace it using the graphs in this section to make sure you get the same answer 7. Prove that each edge in a connected graph will be part of the depth-first traversal tree or will be an edge pointing to a predecessor in the tree. 8. Prove that each edge in a connected graph will be part of the breadth-fis traversal tree or will be an edge pointing to a node in the tree that is neither a predecessor nor a descendent.Explanation / Answer
Ques 3.
// arr is the adjacency matix
// visited is a boolean matix which tells is the
// node is visited or not, false means not visited
Function depth_first_search(arr , visited , i)
BEGIN
// display the current node
print(i);
// mark the current node as visited
visited[i] = true
// traverse the matrix
for j = 0 to arr.length()
BEGIN
// if the node j is not visited and there is an
// edge between I and j
if visited[j] == false and arr[i][j] == 1
BEGIN
depth_first_search( arr , visited , j );
END
END
END
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