# Shortest distance between objects in JavaScript

In this problem we have to calculate and find the shortest distance between two given objects in Javascript. So we will write a function to do this operation and also we will see its time and space complexity. We must consider the positions and coordinates of the objects in some way.

## Understanding the Problem

The problem says to find the shortest path between the two given objects. So we will use two coordinates. And define a function which will have four parameters. These parameters will represent the x and y coordinates of the two objects. Inside the function the differences in x and y coordinates between two objects will be calculated. So the distance between two objects will then be calculated using the distance formula.

## Logic for the given Problem

As we have understood, we have to calculate the distance between two objects. So we need to follow some steps to get the required output. First create an object with a coordinate array as the value and identifier as key. So we need to define a function to handle the object. And after that we will start an array and to hold the coordinates. Iterate over the object values and map them with object identifiers. Sort the coordinates based on the x coordinate and identifier. Calculate the distance using the distance formula and update the result if the current distance is shorter. At the end return the result array with selected coordinates for the shortest distance.

## Algorithm

Step 1: Define a function to calculate the distance between two objects x and y. We have given four parameters inside the function named x1, x2, y1 and y2.

Step 2: Calculate the difference between x1 and x2 and similarly y1 and y2. and store these differences in deltaX and deltaY respectively.

Step 3: Now we will calculate the square root of the multiplication of deltaX and deltaY.

Step 4: At the end we will return the distance which we have calculated in the above step.

### Example

//function to calculate the distance between two objects
function calculateDistance(x1, y1, x2, y2) {
const deltaX = x2 - x1;
const deltaY = y2 - y1;
const distance = Math.sqrt(deltaX * deltaX + deltaY * deltaY);
return distance;
}

// Example usage
const object1 = { x: 0, y: 1 };
const object2 = { x: 4, y: 6 };
const distance = calculateDistance(object1.x, object1.y, object2.x, object2.y);
console.log(distance);


### Output

6.4031242374328485


## Complexity

The time complexity for calculating the shortest distance between two objects with the help of the above function is O(1), which is constant because the solution performs a fixed number of arithmetic operations besides the size of the objects. And the formula we have used to calculate the distance uses basic mathematical operations like subtraction, multiplication and square root so these operations have constant time complexity.

## Conclusion

In the given problem statement we had to find the shortest distance between two given objects with the help of Javascript and basic mathematical operations. The given solution calculates the distance based on the coordinates of the objects and gives the result. It has a constant time complexity which ensures the execution time remains the same besides the size of the objects.

Updated on: 16-Aug-2023

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