- useful operation in databases is the natural join if we view database as list of ordered pairs of objectsthen the natural join of databases and is the list of all ordered triples (xyzsuch that the pair (xyis in and the pair (yzis in describe and analyze an efficient algorithm for computing the natural join of list of pairs and list of pairs - when bob wants to send alice message on the internethe breaks into data packetsnumbers the packets consecutivelyand injects them into the network when the packets arrive at alice' computerthey may be out of orderso alice must assemble the sequence of packets in order before she can be sure she has the entire message describe an efficient scheme for alice to do thisassuming that she knows the value of what is the running time of this algorithmc- describe way to use recursion to add all the numbers in an data setrepresented as list of lists projects - write python function that takes two three-dimensional numeric data sets and adds them componentwise - write python program for matrix class that can add and multiply twodimensional arrays of numbersassuming the dimensions agree appropriately for the operation - write program that can perform the caesar cipher for english messages that include both upperand lowercase characters - implement classsubstitutioncipherwith constructor that takes string with the uppercase letters in an arbitrary order and uses that for the forward mapping for encryption (akin to the self forward string in our caesarcipher class of code fragment you should derive the backward mapping from the forward version - redesign the caesarcipher class as subclass of the substitutioncipher from the previous problem - design randomcipher class as subclass of the substitutioncipher from exercise - so that each instance of the class relies on random permutation of letters for its mapping notes the fundamental data structures of arrays belong to the folklore of computer science they were first chronicled in the computer science literature by knuth in his seminal book on fundamental algorithms [