Calculate Distance Between Two Points in C++

Problem Description

In this problem, we are given coordinate points of a 2-dimensional plane and a 3-dimensional plane, and we have to find the distance between these two points. In this article, we are going to discuss how we can find the distance between two points in C++.

Approaches to Calculate Distance Between Two Points

To solve this problem, here are the two approaches that can you use:

• Using 2D Coordinates
• Using 3D Coordinates

Using 2D Coordinates

In this approach, we use the direct distance formula to calculate the distance between two points. The formula for calculating the distance between two points in 2D space is derived from the Pythagorean theorem:

Distance between two points = ?((x2 - x1)² + (y2 - y1)²)

We use the above formula. We create a function and directly apply the distance formula using the sqrt() and pow() inbuilt functions. The sqrt() function is used to find the square root, and the pow() function is used to calculate power on numbers.

Example

Input:

x1 = 3, y1 = 4

x2 = 7, y2 = 1

Output:

The distance between the two points is: 5

Explanation:

We use the distance formula to calculate the distance between two points:

Distance = ?((x2 - x1)² + (y2 - y1)²)

= ?((7 - 3)² + (1 - 4)²)

= ?(16 + 9) = ?25 = 5

Implementation Code

#include<bits/stdc++.h>
using namespace std;

// Function to calculate the distance between two points
double calculateDistance(double x1, double y1, double x2, double y2) {
    double distance = sqrt(pow(x2 - x1, 2) + pow(y2 - y1, 2));
    return distance;
}

// Main function to apply the distance formula
int main() {
    double x1 = 3;
    double y1 = 4;
    double x2 = 7;
    double y2 = 1;

    // Calculate and display the distance
    double distance = calculateDistance(x1, y1, x2, y2);
    cout << "The distance between the two points is: " << distance << endl;

    return 0;
}

Output

The distance between the two points is: 5

Using 3D Coordinates

In this problem, we are given three coordinates of the plane. For 3-dimensional space, one additional coordinate z is included for each point. We can find the distance between two points (x1, y1, z1) and (x2, y2, z2) in the 3D coordinate system using the formula:

Distance = ?((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

This formula is derived from the Pythagorean theorem and is used to calculate the direct distance between two points in 3D space.

Example

Input:

x1 = 1, y1 = 2, z1 = 3

x2 = 4, y2 = 6, z2 = 8

Output:

The distance between the two points is: 7.07107

Explanation:

We use the distance formula to calculate the distance between two points in 3D space:

Distance = ?((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

= ?((4 - 1)² + (6 - 2)² + (8 - 3)²)

= ?(9 + 16 + 25) = ?50 ? 7.07107

Implementation Code

#include<bits/stdc++.h>
using namespace std;

// Function to calculate the distance between two points in 3D
double calculateDistance3D(double x1, double y1, double z1, double x2, double y2, double z2) {
    // Apply the distance formula
    return sqrt(pow(x2 - x1, 2) + pow(y2 - y1, 2) + pow(z2 - z1, 2));
}

int main() {
    double x1 = 1;
    double y1 = 2;
    double z1 = 3;
    double x2 = 4;
    double y2 = 6;
    double z2 = 8;

    // Calculate and display the distance
    double distance = calculateDistance3D(x1, y1, z1, x2, y2, z2);
    cout << "The distance between the two points in 3D is: " << distance << endl;

    return 0;
}

Output

The distance between the two points in 3D is: 7.07107

Time Complexity: O(1)
Space Complexity: O(1)