Question

What is a loop invariant? How is a loop invariant used?

Short answer

A loop invariant is a property that remains true during every traversal of a loop.

The use of a loop invariant is illustrated in the program to find the factorial of a number.

Step-by-step solution

Defining loop invariant

A loop invariant is a feature of a computer program that is always true during every traversal of a loop. Loop invariants are generally shown by conditional logic but both are not the same. For understanding the effect of any loop in programming, an understanding of loop invariant is needed.

The loop invariant is often checked before the program begins, before each iteration of the loop, and after the loop has been completed for a partially valid program.

Determine how a loop invariant is used

The use of a loop invariant is illustrated in the following program

\(\begin{array}{l}j: = 1\\factorial\,: = 1\\{\rm{while}}\,j < n\\j\,: = j + 1\\factorial\,\,: = \,\,factorial \cdot j\end{array}\)

Here, a loop invariant is used for verifying that this program terminates with \(factorial = n!\),where \(n\)is a positive integer.[a1]

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