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Minimax

Statement

 Goal

Difficulty: Medium
Topic: Minimax algorithm, Alpha–beta pruning, Zero-sum games, Negamax

We are given a 2-player, zero-sum game, where players alternate turns. The game always lasts D turns, and during its move, every player has to choose from B choices. Thus, D is the game tree depth, B its branching factor, and depending on players' choices, the game has B^D possible outcomes.

Assuming the game tree is small enough, we can check all outcomes and solve the game (i.e. compute the best strategy for every player) using the Minimax algorithm ( https://en.wikipedia.org/wiki/Minimax ).

To make our algorithm more efficient, we can skip some computations using the alpha-beta prunning technique ( https://en.wikipedia.org/wiki/Alpha-beta_pruning ).


Your task is to compute the minimum gain for the first player using Minimax with alpha-beta cutoffs. Moves should be examined in left-to-right order, as provided in the input.
Input
Line 1: 2 space-separated integers:
D - depth of the game tree (assuming root is depth 0)
B - the branching factor

Line 2: B^D space-separated integers - the leafs of the game tree containing scores of the first (max) player.
Output
Two space-separated numbers:
- the best score that the root player is guaranteed to obtain
- the number of visited tree nodes
Constraints
0 < D < 15
0 < B < 15
-1000 < game score < 1000
number of leafs < 3500
Example
Input
1 4
2 -1 3 0
Output
3 5
Solve it

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