**Problem Crocodile.**You have a weighted undirected graph with a start node and

*k*designated target nodes. Two players play a full-information game, taking turns:

- Player 1 moves on the nodes of the graph, starting at the designated start node, and aiming to reach a target node. In each turn, she can traverse any edge out of her current node [except the blocked edge / see below], incurring a cost equal to the weight of the edge.
- Player 2 can block one edge at every turn. When an edge is blocked, Player 1 cannot traverse it in the next turn. An edge can be blocked multiple times, and any past edge is "unblocked" when a new edge is blocked.

*B*,

*regardless*of what Play 2 does. Running time: O~(

*n*+

*m*).

**Problem Elephants**. You have

*n*elephants on the line at given coordinates. The elephants make

*n*moves: in each unit of time, some elephant moves to another position. You have cameras that can photograph any interval of length L of the line. After each move, output the minimum number of cameras needed to phtograph all elephants in the current configuration.

*n*.

**Problem Parrots.**You are given a message of

*M*bytes (0..255) to transmit over a weird channel. The channel can carry elements between 1 and

*R*, but elements don't arrive in order (they are permuted adversarially). Send the message, minimizing the number L of elements sent across the channel.