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This section presents four applications, each with a new idea in the implementation of dynamic programming. As you study each application, pay special attention to the three basic elements of the DP model:

**SELETED DP APPLICATIONS**

This section presents four applications, each with a new idea in the
implementation of dynamic programming. As you study each application, pay special
attention to the three basic elements of the DP model:

1. Definition of the *stages*

2. Definition of the *alternatives*
at each stage

3. Definition of the *states* for
each stage

Of the three elements, the definition of the *state* is usually the most subtle. The applications presented here
show that the definition of the state varies depending on the situation being
modeled. Nevertheless, as you investigate each application, you will find it
helpful to consider the following questions:

1. What relationships bind the stages together?

2. What information is needed to make feasible decisions at the current
stage with-out reexamining the decisions made at previous stages?

My teaching experience indicates that understanding the concept of the *state* can be enhanced by questioning the
validity of the way it is defined in the book. Try a dif-ferent definition that
may appear "more logical" to you, and use it in the recursive
computations. You will eventually discover that the definitions presented here
provide the correct way for solving the problem. Meanwhile, the proposed mental
process should enhance your understanding of the concept of the state.

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