Pebbling a checkerboard. we are given a checkerboard which has 4 rows and n columns, and has an integer written in each square. we are also given a set of 2n pebbles, and we want to place some or all of these on the checkerboard (each pebble can be placed on exactly one square) so as to maximize the sum of the integers in the squares that are covered by pebbles. there is one constraint: for a placement of pebbles to be legal, no two of them can be on horizontally or vertically adjacent squares (diagonal adjacency is fine). (a) determine the number of legal patterns that can occur in any column (in isolation, ignoring the pebbles in adjacent columns) and describe these patterns. call two patterns compatible if they can be placed on adjacent columns to form a legal placement. let us consider subproblems consisting of the first k columns 1 ? k ? n. each subproblem can be assigned a type, which is the pattern occurring in the last column. (b) using the notions of compatibility and type, give an o(n)-time dynamic programming algorithm for computing an optimal placement

Ihave a music player on my phone. i can buy songs, add them to playlists and play them. obviously it would be redundant to store each song in each playlist; each playlist is just a list of pointers to the songs. for this lab you will simulate this behavior. your program will need to have options to: add songs to the system library (you will store the text of the first line of the song, rather than the audio) add playlists add songs to a playlist list playlists play a playlist list all of the songs in the library with a count of how many times each song has been played remove a song from a playlist remove a playlist remove a song from the library (and thus from all playlists that contain it) note that we will not be checking many error cases. in real programming this would be bad, you should usually try to recognize and respond to as many types of errors as you can. in the context of class we are trying to acquaint you with as many concepts as possible, so for the sake of educational efficiency we will not be checking most errors in this lab, you may assume that your user provides correct input. you may add all appropriate error testing if you wish, but we will not be testing for it.

You need a reliable network for about twenty-five computers that will be distributed across a large building. it is important that the network be relatively cheap. which topology should you use?

Hyperactive media sales has 10 windows 7 laptop computers used by sales-people in the organization. each laptop computer has several customized applications that are used during the sales process as well as customer relationship management software. all of the applications on the laptops are difficult to configure and have large data files. if all of the laptops have current hardware, what is the easiest way to install windows 10 on them?