Operator Precedence in C++

In C++, operator precedence determines the order in which operators are evaluated in a complex expression. Understanding this is important for writing (and interpreting) expressions correctly and avoiding unexpected errors in your programs.

Operators with higher precedence are evaluated before operators with lower precedence. If two operators have the same precedence, their evaluation is determined by the operator’s associativity *(left to right or right to left).

Operator Precedence Table

Here is a table with the precedence of operators in C++, from highest to lowest. The highest precedence is evaluated first:

How Operator Precedence Works

Expression Evaluation

Operator precedence determines the order in which operators are evaluated in an expression. For example, consider the following expression:

int result = 3 + 4 * 2; // equivalent to 3 + (4 * 2) = 11

Here, the multiplication operator (*) has a higher precedence than the addition operator (+). Therefore, 4 * 2 is evaluated first, resulting in 8, and then 3 is added, resulting in 11.

Using Parentheses

To change the order of evaluation, you can use parentheses. Parentheses have the highest precedence and force the evaluation of the expression they contain first:

int result = (3 + 4) * 2;

In this case, 3 + 4 is evaluated first due to the parentheses, resulting in 7, and then multiplied by 2, resulting in 14.

Associativity

When operators have the same precedence, associativity is applied to determine the order of evaluation. Most operators in C++ have left-to-right associativity.

int a = 1;
int b = 2;
int c = 3;
int result = a + b - c; // Evaluated as ((a + b) - c)

Here, both + and - have the same precedence and left-to-right associativity, so a + b is evaluated first and then c is subtracted.

Complex Example

Let’s consider the following expression:

int result = 5 + 2 * 3 - 4 / 2 + (1 + 3);

We will evaluate it step by step according to precedence and associativity:

1. Evaluate the expression in parentheses: (1 + 3), which results in 4.
2. Evaluate the multiplication: 2 * 3, which results in 6.
3. Evaluate the division: 4 / 2, which results in 2.
4. Evaluate the remaining operations from left to right:
   • 5 + 6 results in 11.
   • 11 - 2 results in 9.
   • 9 + 4 results in 13.

Thus, the final result of the expression is 13.

int result = (5 + 2) * (3 - 1);