2134 - Minimum Swaps to Group All 1's Together II.

Medium

A swap is defined as taking two distinct positions in an array and swapping the values in them.

A circular array is defined as an array where we consider the first element and the last element to be adjacent.

Given a binary circular array nums, return the minimum number of swaps required to group all 1's present in the array together at any location.

Example 1:

Input: nums = 0,1,0,1,1,0,0

Output: 1

Explanation: Here are a few of the ways to group all the 1's together:

0,0,1,1,1,0,0 using 1 swap.

0,1,1,1,0,0,0 using 1 swap.

1,1,0,0,0,0,1 using 2 swaps (using the circular property of the array).

There is no way to group all 1's together with 0 swaps.

Thus, the minimum number of swaps required is 1.

Example 2:

Input: nums = 0,1,1,1,0,0,1,1,0

Output: 2

Explanation: Here are a few of the ways to group all the 1's together:

1,1,1,0,0,0,0,1,1 using 2 swaps (using the circular property of the array).

1,1,1,1,1,0,0,0,0 using 2 swaps.

There is no way to group all 1's together with 0 or 1 swaps.

Thus, the minimum number of swaps required is 2.

Example 3:

Input: nums = 1,1,0,0,1

Output: 0

Explanation: All the 1's are already grouped together due to the circular property of the array.

Thus, the minimum number of swaps required is 0.

Constraints:

• <code>1 <= nums.length <= 10⁵</code>

• nums[i] is either 0 or 1.