Consider the undirected graph below and Kruskal's algorithm for computing a minimum spanning tree. In which order are the edges added to the solution?

Consider the undirected graph below and Prim's algorithm for computing a minimum spanning tree using node S as the source node. In which order are the edges added to the solution?

Consider the undirected graph below and Kruskal's algorithm for computing a minimum spanning tree. In which order are the edges added to the solution?

Consider the undirected graph below and Prim's algorithm for computing a minimum spanning tree using node S as the source node. In which order are the edges added to the solution?

Consider the undirected, unweighted graph below. Assuming that node S is the starting point (i.e., first node to be visited) and that whenever a node has multiple neighbours that need to be processed by the algorithm the neighbours would be processed in lexicographical order, answer the following questions regarding the order in which the nodes are visited in a Depth-First Search (DFS) run.

Consider the undirected, unweighted graph below. Assuming that node S is the starting point (i.e., first node to be visited) and that whenever a node has multiple neighbours that need to be processed by the algorithm the neighbours would be processed in lexicographical order, answer the following questions regarding the order in which the nodes are visited in a Breadth-First Search (BFS) run.

Consider the undirected, unweighted graph below. Assuming that node S is the starting point (i.e., first node to be visited) and that whenever a node has multiple neighbours that need to be processed by the algorithm the neighbours would be processed in lexicographical order, answer the following questions regarding the order in which the nodes are visited in a Depth-First Search (DFS) run.

Consider the undirected, unweighted graph below. Assuming that node S is the starting point (i.e., first node to be visited) and that whenever a node has multiple neighbours that need to be processed by the algorithm the neighbours would be processed in lexicographical order, answer the following questions regarding the order in which the nodes are visited in a Breadth-First Search (BFS) run.

Solve, in big-θ, the following recurrence relation

T(n) = T(n/4) + c, where n >= 4
T(n) = b, where n = 1

for constants b and c.

Given the following pseudocode, derive the recurrence relation that represents its time complexity. 

def count_digits(n):
    if n < 10: 
        return 1 
    return 1 + count_digits(n // 10)

Let b and c represent constant values. What is the base case and recurrence step?