Tactical Removal

The final score of an array $A$ is calculated by repeatedly performing the following operation until the array is empty (initially, score is zero): - Add the median$^{\dagger}$ of the array to the score. - Remove any element from the array. Bob is given a permutation $P$ of length $N$. Bob wants to minimise the final score of the permutation, while Alice wants to maximise Bob's final score. To ac