The Glowcap Warrens of Umbersett

Commission of the Lampless Guild, Umbersett

Beneath the hill-town of Umbersett lies a warren of caverns joined by narrow tunnels. Things that hate the light have nested in the dark ones. The Guild means to flood the whole warren with the pale light of glowcap fungus. Spores are planted in a few caverns, and the glow creeps outward through the tunnels night by night. Before the delvers go down, the Guild must know how many nights to wait, or whether some cavern will stay dark forever.

The rules of the spread are exact:

• On night 0, every seeded cavern glows, and no other cavern does.
• On each following night, every cavern joined by a tunnel to a cavern that was already glowing begins to glow.
• A glowing cavern never goes dark.

Write glowNights(n, tunnels, seeds).

• n is an integer, n >= 1. It is the number of caverns, numbered 0 to n - 1.
• tunnels is a list of pairs [a, b]. Each pair is a tunnel joining caverns a and b, with a != b. A tunnel can be crossed in both directions. The same pair may appear more than once, in either order. The list may be empty.
• seeds is a list of cavern numbers where spores are planted. Numbers may repeat. The list may be empty.

Return an integer:

• the smallest night number on which every cavern is glowing, or
• -1 if some cavern never comes to glow.

If every cavern is seeded, the answer is 0.