Iteration and recursion
There are several problems which
can be solved by doing the same action repeatedly. Both iteration and recursion
are algorithm design techniques to execute the same action repeatedly. What is
the use of repeating the same action again and again? Even though the action is
the same, the state in which the action is executed is not the same. Each time
we execute the action, the state changes. Therefore, the same action is
repeatedly executed, but in different states. The state changes in such a way
that the process progresses to achieve the desired input-output relation.
Iteration: In
iteration, the loop body is repeatedly executed as long as the
loop condition is true. Each time the loop body is executed, the variables are
updated. However, there is also a property of the variables which remains
unchanged by the execution of the loop body. This unchanging property is called
the loop invariant. Loop invariant is the key to construct and to reason about
iterative algorithms.
Recursion: Recursion
is another algorithm design technique, closely related
to iteration, but more powerful.Using recursion, we solve a problem with a
given input, by solving the same problem with a part of the input, and
constructing a solution to the original problem from the solution to the
partial input.
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