(10 points) Suppose you have been sent back in time and have arrived at the scene of an ancient Roman battle. It is your job to assign n spears to n Roman soldiers so that each soldier has a spear. It is best if your assignments minimize the difference in heights between the height of the man and the height of his spear. That is, if the ith man has height mi, and his spear has height s,, then you want to minimize : Imi-sil (a) Design algorithm to find the optimal, or near optimal, solution without evaluating all possible combinations. Include an explanation and pseudocode showing how your al gorithm works. (b) Compare the runtime complexity of your algorithm with the complexity of a brute force solution