Minimum Link Reallocation to Connect Repositories

Given `link_nodes` repositories and existing undirected sync links, compute the minimum number of existing links that must be reassigned so every repository becomes connected. If there are fewer than `n - 1` links, return `-1`. Requirements Input: link_nodes: number of repositories, numbered from 1 to link_nodes. link_from[]: start endpoints of existing undirected links. link_to[]: end endpoints of existing undirected links. Reassignment operation: delete one existing link and reconnect it between any two repositories. Output: the minimum number of reassignments required to make all repositories part of one connected component. If the number of links is less than link_nodes - 1, return -1. Examples link_nodes = 4 link_from = [1, 1, 3] link_to = [2, 3, 2] Output: 1 The initial components are {1,2,3} and {4}; one redundant edge can be reassigned. link_nodes = 4 link_from = [1, 2] link_to = [3, 4] Output: -1 There are only two links, fewer than 4 - 1. Notes The core answer is component_count - 1 when there are enough edges. Use DFS/BFS or union-find to count connected components. The impossibility check must happen before relying on duplicate or cycle edges: any connected graph on n nodes needs at least n - 1 edges. Preparation Implement both union-find and DFS/BFS versions, including 1-index to 0-index conversion tests. Memorise the proof: with at least n - 1 edges, every extra edge inside a component can be repurposed, so the only remaining count is components - 1.