algorithm design techniques search the result is even more pruning than one would expect from random ordering of the nodes other techniquessuch as searching deeper in more active lines of playare also employed in practicea- pruning limits the searching to only onnodeswhere is the size of the full game tree this is huge savings and means that searches using - pruning can go twice as deep as compared to an unpruned tree our tic-tac-toe example is not idealbecause there are so many identical valuesbut even sothe initial search of , nodes is reduced to , nodes (these counts include nonterminal nodes in many gamescomputers are among the best players in the world the techniques used are very interestingand can be applied to more serious problems more details can be found in the references summary this illustrates five of the most common techniques found in algorithm design when confronted with problemit is worthwhile to see if any of these methods apply proper choice of algorithmcombined with judicious use of data structurescan often lead quickly to efficient solutions exercises show that the greedy algorithm to minimize the mean completion time for multiprocessor job scheduling works the input is set of jobs jn each of which takes one time unit to complete each job ji earns di dollars if it is completed by the time limit ti but no money if completed after the time limit give an ( greedy algorithm to solve the problem  modify your algorithm to obtain an ( log ntime bound (hintthe time bound is due entirely to sorting the jobs by money the rest of the algorithm can be implementedusing the disjoint set data structurein ( log file contains only colonsspacesnewlinescommasand digits in the following frequencycolon ( )space ( )newline ( )comma ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( construct the huffman code part of the encoded file must be header indicating the huffman code give method for constructing the header of size at most ( (in addition to the symbols)where is the number of symbols complete the proof that huffman' algorithm generates an optimal prefix code show that if the symbols are sorted by frequencyhuffman' algorithm can be implemented in linear time write program to implement file compression (and uncompressionusing huffman' algorithm