815. Bus Routes

We have a list of bus routes. Each routes[i] is a bus route that the i-th bus repeats forever. For example if routes[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 stop S (initially not on a bus), and we want to go to bus stop T. 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.

 

https://www.youtube.com/watch?v=vEcm5farBls

 

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

[[1, : 0
2, : 0
7],: 0, 1
[3, : 1
6, : 1

 

class Solution {
    public int numBusesToDestination(int[][] routes, int S, int T) {
        if(S == T) return 0;
        HashMap<Integer, List<Integer>> map = new HashMap<>();
        // fill in the map, key: stop id, value : bus id
        for(int i = 0; i < routes.length; i++){
            for(int j = 0; j < routes[i].length; j++){
                // try get or default . if map.getKey(routes[i][j]) is null, then return new ArrayList<>(); 
                // if map.getKey(routes[i][j]) is not null, then return map.getKey(routes[i][j]) 
                List<Integer> buses = map.getOrDefault(routes[i][j], new ArrayList<>());
                // buses if the list of the buses that stop at this stop
                buses.add(i);
                map.put(routes[i][j], buses);
            }
        }
        
        // after done filling up the map, we want to start from the start pos, and get all the stops which are at the 
        // same level as start pos, see if there is destination among those, if yes, then the number of bus we used is just 1
        // otherwise, we put all of them into the queue and expand 
        
        // if after queue is empty and we haven't returned anything , then no path exists , return -1 
        
        // use an int level to represent how many buses we used so far, the level 
        // use a set visited to mark the visited bus as visited, so we don't come back to count it again to
        // guarentee the minimum number 
        HashSet<Integer> visited = new HashSet<>();
        int level = 0;
        Queue<Integer> queue = new LinkedList<>();
        queue.offer(S);
        while(!queue.isEmpty()){
            int size = queue.size();
            level++;
            for(int i = 0; i < size; i++){
                int cur = queue.poll(); // 1 
            // get all the bus that stop at 1, and then get all the stop same level as 1 
                List<Integer> buses = map.get(cur); // buses = [0]
            // get all the stops same level as 1
                for(int bus : buses){
                //List<Integer> stops = routes[bus];
                    if(visited.contains(bus)) continue;
                    visited.add(bus);
                    for(int stop : routes[bus]){
                        if(stop == T){
                           return level; 
                        }else{
                          queue.offer(stop);  
                        }             
                    }        
                }
            }
        }
        return -1;
    }
}