2037. Minimum Number of Moves to Seat Everyone
Description
There are n
seats and n
students in a room. You are given an array seats
of length n
, where seats[i]
is the position of the i^{th}
seat. You are also given the array students
of length n
, where students[j]
is the position of the j^{th}
student.
You may perform the following move any number of times:
 Increase or decrease the position of the
i^{th}
student by1
(i.e., moving thei^{th}
student from positionx
tox + 1
orx  1
)
Return the minimum number of moves required to move each student to a seat such that no two students are in the same seat.
Note that there may be multiple seats or students in the same position at the beginning.
Example 1:
Input: seats = [3,1,5], students = [2,7,4] Output: 4 Explanation: The students are moved as follows:  The first student is moved from from position 2 to position 1 using 1 move.  The second student is moved from from position 7 to position 5 using 2 moves.  The third student is moved from from position 4 to position 3 using 1 move. In total, 1 + 2 + 1 = 4 moves were used.
Example 2:
Input: seats = [4,1,5,9], students = [1,3,2,6] Output: 7 Explanation: The students are moved as follows:  The first student is not moved.  The second student is moved from from position 3 to position 4 using 1 move.  The third student is moved from from position 2 to position 5 using 3 moves.  The fourth student is moved from from position 6 to position 9 using 3 moves. In total, 0 + 1 + 3 + 3 = 7 moves were used.
Example 3:
Input: seats = [2,2,6,6], students = [1,3,2,6] Output: 4 Explanation: Note that there are two seats at position 2 and two seats at position 6. The students are moved as follows:  The first student is moved from from position 1 to position 2 using 1 move.  The second student is moved from from position 3 to position 6 using 3 moves.  The third student is not moved.  The fourth student is not moved. In total, 1 + 3 + 0 + 0 = 4 moves were used.
Constraints:
n == seats.length == students.length
1 <= n <= 100
1 <= seats[i], students[j] <= 100
Solutions
Solution 1: Sorting
Sort both arrays, then traverse the two arrays, calculate the distance between each student’s seat and their actual seat, and add all the distances to get the answer.
The time complexity is $O(n \times \log n)$, and the space complexity is $O(\log n)$. Here, $n$ is the length of the arrays seats
and students
.













