There are some principles and techniques for constructing algorithms.

**Algorithmic Problems**

There are some principles and
techniques for constructing algorithms. We usually say that a problem is
algorithmic in nature when its solution involves the construction of an
algorithm. Some types of problems can be immediately recognized as algorithmic.

**Example 6.2. Consider the well-known Goat, grass and wolf
problem: **A farmer** **wishes
to take a goat, a grass bundle and a wolf across a river. However, his boat can
take only one of them at a time. So several trips are necessary across the
river. Moreover, the goat should not be left alone with the grass (otherwise,
the goat would eat the grass), and the wolf should not be left alone with the
goat (otherwise, the wolf would eat the goat). How can the farmer achieve the
task? Initially, we assume that all the four are at the same side of the river,
and finally, all the four must be in the opposite side. The farmer must be in
the boat when crossing the river. A solution consists of a sequence of
instructions indicating who or what should cross. Therefore, this is an
algorithmic problem. Instructions may be like.

Let the farmer cross with the
wolf.

Or

Let the farmer cross alone.

However, some algorithmic problems
do not require us to construct algorithms. Instead, an algorithm is provided
and we are required to prove some of its properties.

**Example 6.3. Consider The Chameleons of Chromeland problem: **On the island** **of
Chromeland there are three different types of chameleons: red chameleons, green
chameleons, and blue chameleons. Whenever two chameleons of different colors
meet, they both change color to the third color. For which number of red, green
and blue chameleons is it possible to arrange a series of meetings that results
in all the chameleons displaying the same color? This is an algorithmic
problem, because there is an algorithm to arrange meetings between chameleons.
Using some properties of the algorithm, we can find out for which initial
number of chameleons, the goal is possible.

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11th Computer Science : Chapter 6 : Specification and Abstraction : Algorithmic Problems |

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