849-max-dist-to-closest.js

/*
Leetcode
849. Maximize Distance to Closest Person
medium

You are given an array representing a row of seats where seats[i] = 1 represents 
a person sitting in the ith seat, and seats[i] = 0 represents that the ith seat 
is empty (0-indexed).

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 the closest person.


Example 1:
Input: seats = [1,0,0,0,1,0,1]
Output: 2
Explanation: 
If Alex sits in the second open seat (i.e. 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 (i.e. seats[3]), the closest person is 3 seats away.
This is the maximum distance possible, so the answer is 3.

Example 3:
Input: seats = [0,1]
Output: 1

Constraints:
2 <= seats.length <= 2 * 104
seats[i] is 0 or 1.
At least one seat is empty.
At least one seat is occupied.
*/

/*
Approach Next Array

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: O(N), where N is the length of seats.
Space Complexity: O(N), the space used by left and right.
*/

/**
 * @param {number[]} seats
 * @return {number}
 */
var maxDistToClosest = function(seats) {
  const N = seats.length;
  let left = new Array(N).fill(N);
  let right = new Array(N).fill(N);


  for (let i = 0; i < N; i++) {
    if (seats[i] == 1) left[i] = 0;
    else if (i > 0) {
      left[i] = left[i-1] + 1;
    }
  }
  //console.log('left', left)

  for (let i = N-1; i >= 0; i--) {
    if (seats[i] == 1) right[i] = 0;
    else if (i < N - 1) {
      right[i] = right[i+1] + 1;
    }
  }
  //console.log('right', right);

  let ans = 0;
  for (let i = 0; i < N; i++) {
    if (seats[i] == 0) {
      ans = Math.max(ans, Math.min(left[i], right[i]));
    }
  }
  
  //console.log('ans', ans);
  return ans;
}

// tests
//console.log('maxDistToClosest', maxDistToClosest([1,0,0,0,1,0,1]));
//console.log('maxDistToClosest', maxDistToClosest([1,0,0,0,0,0,0,0]));
//console.log('maxDistToClosest', maxDistToClosest([0,1]));

/*
todo 2 pointers solution
https://leetcode.com/problems/maximize-distance-to-closest-person/solution/
*/

export {
  maxDistToClosest
}