2155 - All Divisions With the Highest Score of a Binary Array.

Medium

You are given a 0-indexed binary array nums of length n. nums can be divided at index i (where 0 <= i <= n) into two arrays (possibly empty) <code>nums_left</code> and <code>nums_right</code>:

• <code>nums_left</code> has all the elements of nums between index 0 and i - 1 (inclusive) , while <code>nums_right</code> has all the elements of nums between index i and n - 1 (inclusive).

• If i == 0, <code>nums_left</code> is empty , while <code>nums_right</code> has all the elements of nums.

• If i == n, <code>nums_left</code> has all the elements of nums, while <code>nums_right</code> is empty.

The division score of an index i is the sum of the number of 0's in <code>nums_left</code> and the number of 1's in <code>nums_right</code>.

Return all distinct indices that have the highest possible division score. You may return the answer in any order.

Example 1:

Input: nums = 0,0,1,0

Output: 2,4

Explanation: Division at index

• 0: nums_left is []. nums_right is 0,0, **1** ,0. The score is 0 + 1 = 1.

• 1: nums_left is **0** . nums_right is 0, **1** ,0. The score is 1 + 1 = 2.

• 2: nums_left is **0** , **0** . nums_right is **1** ,0. The score is 2 + 1 = 3.

• 3: nums_left is **0** , **0** ,1. nums_right is 0. The score is 2 + 0 = 2.

• 4: nums_left is **0** , **0** ,1, **0** . nums_right is []. The score is 3 + 0 = 3.

Indices 2 and 4 both have the highest possible division score 3.

Note the answer 4,2 would also be accepted.

Example 2:

Input: nums = 0,0,0

Output: 3

Explanation: Division at index

• 0: nums_left is []. nums_right is 0,0,0. The score is 0 + 0 = 0.

• 1: nums_left is **0** . nums_right is 0,0. The score is 1 + 0 = 1.

• 2: nums_left is **0** , **0** . nums_right is 0. The score is 2 + 0 = 2.

• 3: nums_left is **0** , **0** , **0** . nums_right is []. The score is 3 + 0 = 3.

Only index 3 has the highest possible division score 3.

Example 3:

Input: nums = 1,1

Output: 0

Explanation: Division at index

• 0: nums_left is []. nums_right is **1** , **1** . The score is 0 + 2 = 2.

• 1: nums_left is 1. nums_right is **1** . The score is 0 + 1 = 1.

• 2: nums_left is 1,1. nums_right is []. The score is 0 + 0 = 0.

Only index 0 has the highest possible division score 2.

Constraints:

• n == nums.length

• <code>1 <= n <= 10⁵</code>

• nums[i] is either 0 or 1.