Chapter 11.2, Problem 35E

Suppose that m is a positive integer with m>2 An m-ary Huffman code for a set of N symbols can be constructed analogously to the construction of a binary Huffman code. At the initial step, ((N - i) mod (m — 1)) + 1 trees consisting of a single vertex with least weights are combined into a rooted tree with these vertices as leaves. At each subsequent step, the m trees of least weight are combined into an mary tree.

3. Suppose that we vary the payoff to the winning player in the game of nim so that the payoff is n dollars

when n is the number of legal moves made before a terminal position is reached. Find the payoff to the first

player if the initial position consists of

a) two piles with one and three stones, respectively.

b) two piles with two and four stones, respectively.

c) three piles with one, two, and three stones, respectively.