A subsequence is called palindromic if it results in the same sequence when read from left-to-right and right-to-left. For example, in the sequence: A, A,A, T,G, G,T, A,C, G,A
The subsequences A, A,A and A, T,G, G,T, A are palindromic, while A, C,G is not. Give an algorithm to find the length of the longest palindromic subsequence in a sequence a[1 ...n]. Your algorithm should run in O(n2) time. Show the proof of correctness and proof of running time, respectively.

You will be given two character arrays of the same size, one will contain a number of ships. ships will move around the character array based on which way they are facing and the route they are on. routes are given in the other array. the route consists of '-' and '|' for straight paths, '\' and '/' for curves, and '+' for intersections. there are ships on these routes. ships always face a direction, '^' for up, '> ' for right, 'v' for down, and '< ' for left. any time the ships hit a '\' or a '/' it will turn as you would expect a ship to turn (e.g. a '^' that moves into a '/' will turn right). at an intersection, ships will always continue straight through. all ships move at the same speed, ships take turns moving and all ships move during one 'tick'. the one in the most top left goes first, followed by those to its right, then the ones in the next row. it iterates along the rows and then down the columns. each ship moves one space on its turn moving along the route. your function needs to return the position of the first collision between two ships and the number of ticks before the crash occurred.

Johnson enterprises uses a computer to handle its sales invoices. lately, business has been so good that it takes an extra 3 hours per night, plus every third saturday, to keep up with the volume of sales invoices. management is considering updating its computer with a faster model that would eliminate all of the overtime processing.

A. in packet tracer, only the server-pt device can act as a server. desktop or laptop pcs cannot act as a server. based on your studies so far, explain the client-server model.