By Charles Stein

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**Extra info for Approximate computation of expectations**

**Sample text**

A data structure consists of a storage structure to hold the data, and methods for creating, modifying, and accessing the data. More formally, a data structure consists of these three components: 23 Chap. 3: 24 Data Structures 1. A set of operations for manipulating specific types of abstract objects 2. A storage structure in which the abstract objects are stored 3. An implementation of each of the operations in terms of the storage structure. Component 1 of the definition-a set of operations on abstract objects-is called an abstract data type, or ADT.

Another approach is needed if we are to escape this infinite regress. How can we determine whether an algorithm is optimal? More generally, how can we determine how much time any solution to a given problem is bound to require? Problem complexity expresses the amount of time that is both necessary and sufficient to solve a problem. Knowing how much time is necessary to solve a problem informs us that any approach that takes less time is bound to fail. And knowing how much time is sufficient indicates how efficient a particular solution is and to what extent it can be improved on.

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