815 Bus Routes

815. Bus Routes

1. Question

We have a list of bus routes. Eachroutes[i]is a bus route that the i-th bus repeats forever. For example ifroutes[0] = [1, 5, 7], this means that the first bus (0-th indexed) travels in the sequence 1->5->7->1->5->7->1->... forever.

We start at bus stopS(initially not on a bus), and we want to go to bus stopT. Travelling by buses only, what is the least number of buses we must take to reach our destination? Return -1 if it is not possible.

Example:
Input:
routes = [[1, 2, 7], [3, 6, 7]]
S = 1
T = 6

Output: 2

Explanation:
The best strategy is take the first bus to the bus stop 7, then take the second bus to the bus stop 6.

Note:

• 1 <= routes.length <= 500.

• 1 <= routes[i].length <= 500.

• 0 <= routes[i][j] < 10 ^ 6.

2. Implementation

(1) BFS

class Solution {
    public int numBusesToDestination(int[][] routes, int S, int T) {
        if (S == T) {
            return 0;
        }

        Map<Integer, Set<Integer>> graph = new HashMap();

        for (int i = 0; i < routes.length; i++) {
            for (int stop : routes[i]) {
                graph.putIfAbsent(stop, new HashSet());
                graph.get(stop).add(i);
            }
        }

        Queue<Integer> queue = new LinkedList();
        queue.add(S);

        Set<Integer> visited = new HashSet();
        int buses= 1;

        while (!queue.isEmpty()) {
            int size = queue.size();

            while (size-- > 0) {
                int curStop = queue.remove();

                for (int bus : graph.get(curStop)) {
                    if (visited.contains(bus)) continue;

                    visited.add(bus);
                    for (int nextStop : routes[bus]) {
                        if (nextStop == T) {
                            return buses;
                        }
                        queue.add(nextStop);
                    }
                }
            }
            ++buses;
        }
        return -1;
    }
}

3. Time & Space Complexity

BFS: 时间复杂度O(mn), m是公交车数量，n是每个公交车经过的stop数量。空间复杂度O(mn)