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Expression Evaluation
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Introduction


Evaluating an expression is one of the most common tasks in programming.For example a+b+c is an expression. Here + is an operator. The variables a, b and c are operands.The value of the expression is the sum of a, b and c. An expression may be often evaluated to assign a variable a new value or to verify the truthfulness of a test condition. For example the operator can be unary( Ex:~,++ etc), binary(Ex: +,* etc) or ternary (Ex: (a>b)?p:q)

 

Examples of expressions:

 

To compute the area of a triangle from base b and height h

 

Area=1/2.0*base*height

 

Note that this expression will be evaluated left to right, that is the division opeartor will be evaluated, followed by two multiplication operators. The 2.0 is used to make sure that the division is carried out as a floating point operation.

 



To compute the area of a triangle from the three sides, a, b and c

 

s=(a+b+c)/2.0

 

area = s*(s-a)*(s-b)*(s-c)

 

Here area is calculated in two steps. The first step, s is computed from the three sides a, b and c. Note that, the paranthesis is used so that evaluation within the paranthesis takes first. Without paranthesis, we would have obtained the value of s as sum of a, b and half of c. Similarly, paranthesis are very important in evaluating the second expression.

To find the nth term of an arithmetic progression, we can use the following expression

tn= a+(n-1)*d

where a is the first term and d is the common difference.

Here also, the use of paranthesis has helped us in evaluating the expression the way we need it.


An expression used in a computer program is very similar to an algebraic expression and when many operators are specified in an expression, then the evaluation takes place according to the precedence of operators.The order of the precedence is given by a table of precedence.

A paranthesis can be used to override the precedence of operators and force the evalutation of a sub-expression within an expression.Expression is evaluated according to assosciativity of the operator. The assosciativity of the operator is a property that determines how operators of the same precedence are grouped in the absence of paranthesis. The objective in evaluating an expression is to consider the precedence and aasosciativity of the individual operators and compute the value of the sub-expressions.

 

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