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C++ operator overloading

Give a Vec2 class natural arithmetic, comparison, and output operators.

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Before you start

C++ classes and const member functions.

Give a Vec2 class natural arithmetic, comparison, and output operators.
Predict the sample output and explain the state changes.
Complete the practice task and check the boundary cases.

The concept

Operator overloading lets a user-defined type work with the usual operators. A 2D vector class can define + and - for vectors, * for scaling, == for comparison, and << for printing. Done well, code such as a + b * 2 reads like the mathematics.

Binary arithmetic operators are usually written as const member functions or as free functions that return a new object. The stream operator << must be a free function because its left operand is the stream. Overload only when the meaning is obvious; an operator that surprises its readers is worse than a named function.

Code example

C++

#include <iostream>

struct Vec2 {
  int x;
  int y;

  Vec2 operator+(const Vec2& other) const { return {x + other.x, y + other.y}; }
  Vec2 operator-(const Vec2& other) const { return {x - other.x, y - other.y}; }
  Vec2 operator*(int k) const { return {x * k, y * k}; }
  bool operator==(const Vec2& other) const { return x == other.x && y == other.y; }
};

std::ostream& operator<<(std::ostream& out, const Vec2& v) {
  return out << "(" << v.x << ", " << v.y << ")";
}

int main() {
  Vec2 a{1, 2};
  Vec2 b{3, 4};
  std::cout << a + b << "\n";
  std::cout << b - a << "\n";
  std::cout << a * 3 << "\n";
  std::cout << (a + b == Vec2{4, 6}) << " " << (a == b) << "\n";
}

Output

(4, 6)
(2, 2)
(3, 6)
1 0

Example details

Follow the code

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Guided walkthroughReady

1#include <iostream>

3struct Vec2 {

4 int x;

5 int y;

7 Vec2 operator+(const Vec2& other) const { return {x + other.x, y + other.y}; }

8 Vec2 operator-(const Vec2& other) const { return {x - other.x, y - other.y}; }

9 Vec2 operator*(int k) const { return {x * k, y * k}; }

10 bool operator==(const Vec2& other) const { return x == other.x && y == other.y; }

11};

13std::ostream& operator<<(std::ostream& out, const Vec2& v) {

14 return out << "(" << v.x << ", " << v.y << ")";

15}

17int main() {

18 Vec2 a{1, 2};

19 Vec2 b{3, 4};

20 std::cout << a + b << "\n";

21 std::cout << b - a << "\n";

22 std::cout << a * 3 << "\n";

23 std::cout << (a + b == Vec2{4, 6}) << " " << (a == b) << "\n";

24}

Follow the example

Start to inspect the source, values, and output. These prepared steps explain the published sample; grouped loop steps describe multiple iterations.

View the complete dry-run table

Prepared trace of the published program. Some rows group repeated iterations.
What happens	State after step	Output so far
a + b calls a.operator+(b) and returns a new vector. const says that a is not changed.	`—`	—
A free function so that std::cout << v works. It returns the stream so that calls can be chained.	`—`	—
(1,2) + (3,4).	`—`	(4, 6)
(3,4) − (1,2).	`—`	(4, 6) (2, 2)
Scaling by an int.	`—`	(4, 6) (2, 2) (3, 6)
== compares both fields; a bool prints as 1 or 0.	`—`	(4, 6) (2, 2) (3, 6) 1 0

Behind the scenes

How C++ processes this code

The C++ compiler produces a native executable. Execution enters main, where objects and function calls perform the work.

Cost and common mistakes

Each operator is O(1).

3 * a does not compile with a member operator*(int), because the left operand is an int. Add a free function for that order.
Define == and != together, and keep them consistent. Since C++20, defining == also gives !=, and <=> can generate the comparison operators.
Do not overload && or ||, and avoid the comma operator: the overloaded versions lose short-circuit behaviour.

Try it yourself

How do you support 3 * a?

Reveal answer and reasoning

Add a free function Vec2 operator*(int k, const Vec2& v) { return v * k; }.