[LeetCode] 815. Bus Routes 公交路线

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.

有一个表示公交路线的二维数组，每一行routes[i]代表一辆公交车循环运行的环形路线，求最少需要坐多少辆公交车才能从巴士站S到达T。

解法：BFS，先对原来的二维数组进行处理，二维数组的每一行代表这辆公交车能到达的站点，用HashMap记录某站点有哪个公交经过。这样处理完以后就知道每一个站点都有哪个公交车经过了。然后用一个queue记录当前站点，对于当前站点的所有经过的公交循环，每个公交又有自己的下一个站点。可以想象成一个图，每一个公交站点 被多少个公交经过,也就是意味着是个中转站,可以连通到另外一个公交上, 因为题目求的是经过公交的数量而不关心经过公交站点的数量，所以在BFS的时候以公交(也就是routes的下标)来扩展。

Java:

class Solution {
    public int numBusesToDestination(int[][] routes, int S, int T) {
       HashSet<Integer> visited = new HashSet<>();
       Queue<Integer> q = new LinkedList<>();
       HashMap<Integer, ArrayList<Integer>> map = new HashMap<>();
       int ret = 0; 
        
       if (S==T) return 0; 
        
       for(int i = 0; i < routes.length; i++){
            for(int j = 0; j < routes[i].length; j++){
                ArrayList<Integer> buses = map.getOrDefault(routes[i][j], new ArrayList<>());
                buses.add(i);
                map.put(routes[i][j], buses);                
            }       
        }
                
       q.offer(S); 
       while (!q.isEmpty()) {
           int len = q.size();
           ret++;
           for (int i = 0; i < len; i++) {
               int cur = q.poll();
               ArrayList<Integer> buses = map.get(cur);
               for (int bus: buses) {
                    if (visited.contains(bus)) continue;
                    visited.add(bus);
                    for (int j = 0; j < routes[bus].length; j++) {
                        if (routes[bus][j] == T) return ret;
                        q.offer(routes[bus][j]);  
                   }
               }
           }
        }
        return -1;
    }
}　　

Java:

public int numBusesToDestination(int[][] routes, int S, int T) {
        HashMap<Integer, HashSet<Integer>> to_routes = new HashMap<>();
        for (int i = 0; i < routes.length; ++i)
            for (int j : routes[i]) {
                if (!to_routes.containsKey(j)) to_routes.put(j, new HashSet<Integer>());
                to_routes.get(j).add(i);
            }
        Queue<Point> bfs = new ArrayDeque();
        bfs.offer(new Point(S, 0));
        HashSet<Integer> seen = new HashSet<>();
        seen.add(S);
        while (!bfs.isEmpty()) {
            int stop = bfs.peek().x, bus = bfs.peek().y;
            bfs.poll();
            if (stop == T) return bus;
            for (int route_i : to_routes.get(stop))
                for (int next_stop : routes[route_i])
                    if (!seen.contains(next_stop)) {
                        seen.add(next_stop);
                        bfs.offer(new Point(next_stop, bus + 1));
                    }
        }
        return -1;
    }

Python:

def numBusesToDestination(self, routes, S, T):
        to_routes = collections.defaultdict(set)
        for i,route in enumerate(routes):
            for j in route: to_routes[j].add(i)
        bfs = [(S,0)]
        seen = set([S])
        for stop, bus in bfs:
            if stop == T: return bus
            for route_i in to_routes[stop]:
                for next_stop in routes[route_i]:
                    if next_stop not in seen:
                        bfs.append((next_stop, bus+1))
                        seen.add(next_stop)
                routes[route_i] = []
        return -1

Python:

# Time:  O(|V| + |E|)
# Space: O(|V| + |E|)

import collections


class Solution(object):
    def numBusesToDestination(self, routes, S, T):
        """
        :type routes: List[List[int]]
        :type S: int
        :type T: int
        :rtype: int
        """
        if S == T:
            return 0

        to_route = collections.defaultdict(set)
        for i, route in enumerate(routes):
            for stop in route:
                to_route[stop].add(i)

        result = 1
        q = [S]
        lookup = set([S])
        while q:
            next_q = []
            for stop in q:
                for i in to_route[stop]:
                    for next_stop in routes[i]:
                        if next_stop in lookup:
                            continue
                        if next_stop == T:
                            return result
                        next_q.append(next_stop)
                        to_route[next_stop].remove(i)
                        lookup.add(next_stop)
            q = next_q
            result += 1

        return -1　　

C++:

int numBusesToDestination(vector<vector<int>>& routes, int S, int T) {
        unordered_map<int, unordered_set<int>> to_route;
        for (int i = 0; i < routes.size(); ++i) for (auto& j : routes[i]) to_route[j].insert(i);
        queue<pair<int, int>> bfs; bfs.push(make_pair(S, 0));
        unordered_set<int> seen = {S};
        while (!bfs.empty()) {
            int stop = bfs.front().first, bus = bfs.front().second;
            bfs.pop();
            if (stop == T) return bus;
            for (auto& route_i : to_route[stop]) {
                for (auto& next_stop : routes[route_i])
                    if (seen.find(next_stop) == seen.end()) {
                        seen.insert(next_stop);
                        bfs.push(make_pair(next_stop, bus + 1));
                    }
                routes[route_i].clear();
            }
        }
        return -1;
    }

　　

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