3 One implementation for the sparse matrix is described in Section 12.3 Another im-plementation is a hash table whose search key is a concatenation of the matrix coor-dinates. 1.7 Every problem certainly does not have an algorithm. As discussed in Chapter 15, there are a number of reasons why this might be the case. Some problems don’t have a suf f ciently clear de f nition. Some problems, such as the halting problem, are non-computable. For some problems, such as one typically studied by arti f cial intelligence researchers, we simply don’t know a solution. 1.8 We must assume that by “algorithm” we mean something composed of steps are of a nature that they can be performed by a computer. If so, than any algorithm can be expressed in C ++ . In particular, if an algorithm can be expressed in any other computer programming language, then it can be expressed in C ++ , since all (suf f ciently general) computer programming languages compute the same set of functions. 1.9
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