2884. Pathfinding

Bessie is stranded on a deserted arctic island and wants to determine

all the paths she might take to return to her pasture. She has

tested her boat and knows she can travel from one island to another

island in 1 unit of time if a route with proper currents connects

the pair.

She has experimented to create a map of the ocean with valid

single-hop routes between each pair of the N (1 <= N <= 100) islands,

conveniently numbered 1..N. The routes are one-way (unidirectional),

owing to the way the currents push her boat in the ocean. It's

possible that a pair of islands is connected by two routes that use

different currents and thus provide a bidirectional connection. The

map takes care to avoid specifying that a route exists between an

island and itself.

Given her starting location M (1 <= M <= N) and a representation

of the map, help Bessie determine which islands are one 'hop' away,

two 'hops' away, and so on. If Bessie can take multiple different

paths to an island, consider only the path with the shortest distance.

By way of example, below are N=4 islands with connectivity as shown

(for this example, M=1):

start--> 1-------->2

|            |

|            |

V           V

4<--------3

Bessie can visit island 1 in time 0 (since M=1), islands 2 and 4

at time 1, and island 3 at time 2.

The input for this task is a matrix C where the element at row r,

column c is named C_rc (0 <= C_rc <= 1) and, if it has the value

1, means "Currents enable Bessie to travel directly from island r

to island c in one time unit". Row C_r has N elements, respectively

C_r1..C_rN, each one of which is 0 or 1.