#### Approach #1: Next Array [Accepted]

Intuition

Let left[i] be the distance from seat i to the closest person sitting to the left of i. Similarly, let right[i] be the distance to the closest person sitting to the right of i. This is motivated by the idea that the closest person in seat i sits a distance min(left[i], right[i]) away.

Algorithm

To construct left[i], notice it is either left[i-1] + 1 if the seat is empty, or 0 if it is full. right[i] is constructed in a similar way.

Complexity Analysis

• Time Complexity: , where is the length of seats.

• Space Complexity: , the space used by left and right.

#### Approach #2: Two Pointer [Accepted]

Intuition

As we iterate through seats, we'll update the closest person sitting to our left, and closest person sitting to our right.

Algorithm

Keep track of prev, the filled seat at or to the left of i, and future, the filled seat at or to the right of i.

Then at seat i, the closest person is min(i - prev, future - i), with one exception. i - prev should be considered infinite if there is no person to the left of seat i, and similarly future - i is infinite if there is no one to the right of seat i.

Complexity Analysis

• Time Complexity: , where is the length of seats.

• Space Complexity: .

#### Approach #3: Group by Zero [Accepted]

Intuition

In a group of K adjacent empty seats between two people, the answer is (K+1) / 2.

Algorithm

For each group of K empty seats between two people, we can take into account the candidate answer (K+1) / 2.

For groups of empty seats between the edge of the row and one other person, the answer is K, and we should take into account those answers too.

Complexity Analysis

• Time Complexity: , where is the length of seats.

• Space Complexity: . (In Python, seats[::-1] uses space, but this can be remedied.)

Analysis written by: @awice.