How should I practice Minimum Fuel Car Alignment?

Start by reading the full statement, solve the visible examples, then compare the pattern against related Fivetran phone screen problems in FastPrep.

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Problem · Array

Minimum Fuel Car Alignment

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Problem statement

You are given the integer coordinates of n cars in parallel arrays xCoordinates and yCoordinates.

Move every car so that the final positions form one horizontal row with no gaps. You may choose any integer row y, any integer starting position s, and any assignment of cars to the distinct positions (s, y), (s + 1, y), ..., (s + n - 1, y).

Moving a car from (x1, y1) to (x2, y2) costs |x1 - x2| + |y1 - y2| units of fuel.

Return the minimum possible total fuel cost. The result is a 64-bit integer.

Function

minimumFuelCost(xCoordinates: int[], yCoordinates: int[]) → long

Examples

Example 1

xCoordinates = [1,4]yCoordinates = [1,4]return = 5

Choose row y = 1 and final x-coordinates [1, 2]. The cars cost 0 and |4 - 2| + |4 - 1| = 5, for a minimum total of 5.

Example 2

xCoordinates = [0,5,2]yCoordinates = [2,2,2]return = 3

Keep the common row at y = 2 and use x-coordinates [1, 2, 3]. Matching sorted car x-coordinates [0, 2, 5] to them costs 1 + 0 + 2 = 3.

Example 3

xCoordinates = [4,1,3,2]yCoordinates = [3,0,2,1]return = 4

The x-coordinates already occupy four consecutive positions. Choosing y = 1 gives vertical cost 2 + 1 + 1 + 0 = 4.

Constraints

1 <= n <= 2 * 10^5
xCoordinates.length == yCoordinates.length == n
-10^9 <= xCoordinates[i], yCoordinates[i] <= 10^9
Every final coordinate is an integer, and each of the n consecutive final positions is occupied by exactly one car.
The minimum total cost fits in a signed 64-bit integer.