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Precedence and Associativity

Operator precedence and associativity

  • The sequence of operators and operands that reduces to a single value after the evaluation is called an expression
  • If 2*3 is evaluated nothing great ,it gives 6 but if 2*3+2 is 6+2 =8 or 2*6=12.To avoid this confusion rules of precedence and associativity are used

Precedence: Operator precedence gives priorities to operators while evaluating an expression

Example: when 2*3+2 is evaluated  output is 8 but not 12 because the * operator is having more priority than + hence 2*3 is  evaluated first followed by 6+2

Operator precedence table

  • Operator precedence table gives the detail list of priorities for each and every operator
  • Operators are listed from higher priority to lower
Precedence Operator Description Associativity
1 :: Scope resolution Left-to-right
2 ++   -- Suffix/postfix increment and decrement
type() type{} Function-style typecast
() Function call
[] Array subscripting
. Element selection by reference
-> Element selection through pointer
3 ++   -- Prefix increment and decrement Right-to-left
+   - Unary plus and minus
!   ~ Logical NOT and bitwise NOT
(type) C-style type cast
* Indirection (dereference)
& Address-of
sizeof Size-of
newnew[] Dynamic memory allocation
deletedelete[] Dynamic memory deallocation
4 .*   ->* Pointer to member Left-to-right
5 *   /   % Multiplication, division, and remainder
6 +   - Addition and subtraction
7 <<   >> Bitwise left shift and right shift
8 <   <= For relational operators < and ≤ respectively
>   >= For relational operators > and ≥ respectively
9 ==   != For relational = and ≠ respectively
10 & Bitwise AND
11 ^ Bitwise XOR (exclusive or)
12 | Bitwise OR (inclusive or)
13 && Logical AND
14 || Logical OR
15 ?: Ternary conditional operator Right-to-left
= Direct assignment (provided by default for C++ classes)
+=   -= Assignment by sum and difference
*=   /=   %= Assignment by product, quotient, and remainder
<<=   >>= Assignment by bitwise left shift and right shift
&=   ^=   |= Assignment by bitwise AND, XOR, and OR
16 throw Throw operator (for exceptions)
17 , Comma Left-to-right

Example1

Evaluate 5*4+(3+2)

  • Parenthesis is having the highest priority
    5*4+5
  • Among * and +,* is having the highest priority
    20 + 5= 25 is the final output

Example 2

Arithmetic operators for having higher priority than relational operators

Observe the difference With Parenthesis  and without Parenthesis

5<4+5<4 
5<9<4// 5<9 gives 1
1<4 =1
(5>4)+(5>4)//5>4 is true 
1+1
2

Associativity

Associativity determines in which direction operators  are to be evaluated if they are under the same priority i.e

  1. Left to Right
  2. Right to Left

Example

5*3/2
15/2
7

Here * and / are having the same level of priority but it associativity is given as left to right. hence evaluate* followed by /

Note

From the Operator precedence table, we can conclude  except for   group 3 and group 15 all the remaining operators are having associativity as,left to right

C plus plus program to demonstrate operator precedence and associativity

main() 
{

int a = 20,b = 10,c = 15 d = 5,e;

e = (a + b) * c / d; // ( 30 * 15 ) / 5
cout << "Value of (a + b) * c / d is :" << e << endl ;


e = ((a + b) * c) / d; // (30 * 15 ) / 5
cout << "Value of ((a + b) * c) / d is :" << e << endl ;


e = (a + b) * (c / d); // (30) * (15/5)
cout << "Value of (a + b) * (c / d) is :" << e << endl ;


e = a + (b * c) / d; // 20 + (150/5)
cout << "Value of a + (b * c) / d is :" << e << endl ;

}

​Using the rules of precedence and associativity evaluate the following expressions post your outputs and doubts in the comments

  1. 5*3/2-1
  2. (2+3)&&5+1/2
  3. int a=2;
    ++a*++a*++a;
    what is the value of’ a ‘after evaluating the above statement?

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