Minimum Transfers Between Pin Boards

Problem Statement

At Pinterest, users organize content into boards. Each board contains a collection of unique pin IDs. You want to navigate from a starting pin source to a destination pin target by jumping between pins that share a common board.

Each time you switch to or take a board, it counts as using one board. You can transition freely between any pins located on the same board once you are on it.

Given a list of boards, where boards[i] is an array of pin IDs on the i-th board, return the minimum number of boards you must visit to travel from source to target. If it is impossible to reach target from source, return -1.

If source == target, you are already at the destination and need 0 boards.

Function Signature

def min_boards(boards: list[list[int]], source: int, target: int) -> int:
    pass

Input and Output

• boards: A list of lists of integers, where boards[i] represents all pins on board i.
• source: An integer representing the starting pin ID.
• target: An integer representing the target pin ID.
• Return: An integer representing the minimum number of boards used, or -1 if unreachable.

Constraints

• 1 <= len(boards) <= 1000
• 1 <= len(boards[i]) <= 1000
• The total number of pins across all boards does not exceed 10^5.
• All pin IDs are non-negative integers (0 <= pin_id <= 10^9).
• boards[i] contains distinct pin IDs.

Examples

Example 1

boards = [[1, 2, 7], [3, 6, 7]]
source = 1
target = 6
# Output: 2
# Explanation: You take board 0 to go from pin 1 to pin 7, then board 1 to reach pin 6.

Example 2

boards = [[7, 12], [4, 5, 15], [6], [15, 19], [9, 12, 13]]
source = 15
target = 12
# Output: -1
# Explanation: There is no board connection leading from pin 15 to pin 12.

Example 3

boards = [[1, 5], [5, 9]]
source = 5
target = 5
# Output: 0
# Explanation: You are already at pin 5.