Question

Suppose you treat the integers as a graph. In other words, there are an infinite number of vertices; 0 is adjacent to -1 and 1; 1 is adjacent to 0 and 2; and so on. This representation is similar to the ""number line"" that is sometimes used to teach basic arithmetic. If you were to perform a breadth-first search, starting at 0 and with a goal of 3, in what order would the integers be visited? Assume that the neighbors of each integer are returned in their natural order (for example, the neighbors of 0 are -1 and 1, in that order).

Answer 1

In a breadth-first search starting at 0 with the goal of reaching 3, the integers visited would be in the sequence: 0, -1, 1, 2, 3.

Step-by-step explanation:

When performing a breadth-first search (BFS) starting from the integer 0 with the goal of reaching the integer 3, the order in which the integers would be visited is determined by the BFS algorithm, which explores neighbors level by level. The neighbors of each integer are explored in their natural order, so for 0 they are -1 and 1, in that order.

The sequence visited starting from 0 would be:

1. 0
2. -1 (as 0's neighbor)
3. 1 (also 0's neighbor)
4. 2 (as 1's neighbor)
5. 3 (as 2's neighbor, and the goal)

This BFS traversal ensures that we visit nodes in the order of their distance from the starting point, in this case, the integer 0.