Maximize distance to closest person [Next Array]

Time: O(N); Space: O(1); easy

In a row of seats, 1 represents a person sitting in that seat, and 0 represents that the seat is empty. There is at least one empty seat, and at least one person sitting. Alex wants to sit in the seat such that the distance between him and the closest person to him is maximized. Return that maximum distance to closest person.

Example 1:

Input: seats = [1,0,0,0,1,0,1]

Output: 2

Explanation:

  • If Alex sits in the second open seat (seats[2]), then the closest person has distance 2.

  • If Alex sits in any other open seat, the closest person has distance 1.

  • Thus, the maximum distance to the closest person is 2.

Example 2:

Input: seats = [1,0,0,0]

Output: 3

Explanation:

  • If Alex sits in the last seat, the closest person is 3 seats away.

  • This is the maximum distance possible, so the answer is 3.

Notes:

  • 1 <= seats.length <= 20000

  • seats contains only 0s or 1s, at least one 0, and at least one 1.

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.

[1]:

class Solution1(object):
    def maxDistToClosest(self, seats):
        """
        :type seats: List[int]
        :rtype: int
        """
        N = len(seats)
        left, right = [N] * N, [N] * N

        for i in range(N):
            if seats[i] == 1:
                left[i] = 0
            elif i > 0:
                left[i] = left[i-1] + 1

        for i in range(N-1, -1, -1):
            if seats[i] == 1:
                right[i] = 0
            elif i < N-1:
                right[i] = right[i+1] + 1

        return max(min(left[i], right[i])
                   for i, seat in enumerate(seats) if not seat)

[2]:

s = Solution1()
seats = [1,0,0,0,1,0,1]
assert s.maxDistToClosest(seats) == 2

[3]:

class Solution2(object):
    def maxDistToClosest(self, seats):
        """
        :type seats: List[int]
        :rtype: int
        """
        prev, result = -1, 1
        for i in range(len(seats)):
            if seats[i]:
                if prev < 0:
                    result = i
                else:
                    result = max(result, (i-prev)//2)
                prev = i
        return max(result, len(seats)-1-prev)

[4]:

s = Solution2()
seats = [1,0,0,0,1,0,1]
assert s.maxDistToClosest(seats) == 2