Task

You receive:

• A: a binary array where 1 denotes a cake and 0 denotes anything else.
• start: the index occupied by the person.

Return the minimum distance from start to a cake. Return -1 when the array contains no cakes.

Example

A = [0, 0, 0, 1, 0, 0, 1]
start = 1

Output:

2

Explanation: the nearest cake appears at position 3, which is two positions away.

A = [0, 0, 0, 1, 0, 0, 1]
start = 1

2

Task

The array now includes both people and cakes:

• 1 identifies a person.
• 2 identifies a cake.
• 0 identifies an empty slot.

Give every person exactly one distinct cake, while allowing each cake to serve no more than one person, subject to these requirements:

• The sum of all person-to-cake distances must be minimized across the entire assignment.
• If the number of people exceeds the number of cakes, signal that no assignment can be made.
• Given one requested person index, return the cake index assigned to that person by the globally best matching.
• Test inputs do not contain tied assignments with equal distances.

Consequently, a question about one person can still require determining the complete optimal matching first.

Example

line = [1, 0, 2, 0, 1, 0, 0, 0, 2]
# people at [0, 4], cakes at [2, 8]

Considering each person separately:

• person 0 would choose cake 2 (distance 2).
• person 4 would also choose cake 2 (distance 2).

The optimal one-to-one result is instead:

• person 0 -> cake 2 (distance 2)
• person 4 -> cake 8 (distance 4)

The total distance is 6.

Therefore, a query for person index 4 must return cake index 8, rather than that person's individually closest cake, index 2.