# 815. Bus Routes

## Description

You are given an array routes representing bus routes where routes[i] is a bus route that the ith bus repeats forever.

• For example, if routes[0] = [1, 5, 7], this means that the 0th bus travels in the sequence 1 -> 5 -> 7 -> 1 -> 5 -> 7 -> 1 -> ... forever.

You will start at the bus stop source (You are not on any bus initially), and you want to go to the bus stop target. You can travel between bus stops by buses only.

Return the least number of buses you must take to travel from source to target. Return -1 if it is not possible.

Example 1:

Input: routes = [[1,2,7],[3,6,7]], source = 1, target = 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.


Example 2:

Input: routes = [[7,12],[4,5,15],[6],[15,19],[9,12,13]], source = 15, target = 12
Output: -1


Constraints:

• 1 <= routes.length <= 500.
• 1 <= routes[i].length <= 105
• All the values of routes[i] are unique.
• sum(routes[i].length) <= 105
• 0 <= routes[i][j] < 106
• 0 <= source, target < 106

## Solutions

• class Solution {
public int numBusesToDestination(int[][] routes, int source, int target) {
if (source == target) {
return 0;
}
int n = routes.length;
Set<Integer>[] s = new Set[n];
List<Integer>[] g = new List[n];
Arrays.setAll(s, k -> new HashSet<>());
Arrays.setAll(g, k -> new ArrayList<>());
Map<Integer, List<Integer>> d = new HashMap<>();
for (int i = 0; i < n; ++i) {
for (int v : routes[i]) {
s[i].add(v);
d.computeIfAbsent(v, k -> new ArrayList<>()).add(i);
}
}
for (var ids : d.values()) {
int m = ids.size();
for (int i = 0; i < m; ++i) {
for (int j = i + 1; j < m; ++j) {
int a = ids.get(i), b = ids.get(j);
g[a].add(b);
g[b].add(a);
}
}
}
Deque<Integer> q = new ArrayDeque<>();
Set<Integer> vis = new HashSet<>();
int ans = 1;
for (int v : d.get(source)) {
q.offer(v);
vis.add(v);
}
while (!q.isEmpty()) {
for (int k = q.size(); k > 0; --k) {
int i = q.pollFirst();
if (s[i].contains(target)) {
return ans;
}
for (int j : g[i]) {
if (!vis.contains(j)) {
vis.add(j);
q.offer(j);
}
}
}
++ans;
}
return -1;
}
}

• class Solution {
public:
int numBusesToDestination(vector<vector<int>>& routes, int source, int target) {
if (source == target) {
return 0;
}
int n = routes.size();
vector<unordered_set<int>> s(n);
vector<vector<int>> g(n);
unordered_map<int, vector<int>> d;
for (int i = 0; i < n; ++i) {
for (int v : routes[i]) {
s[i].insert(v);
d[v].push_back(i);
}
}
for (auto& [_, ids] : d) {
int m = ids.size();
for (int i = 0; i < m; ++i) {
for (int j = i + 1; j < m; ++j) {
int a = ids[i], b = ids[j];
g[a].push_back(b);
g[b].push_back(a);
}
}
}
queue<int> q;
unordered_set<int> vis;
int ans = 1;
for (int v : d[source]) {
q.push(v);
vis.insert(v);
}
while (!q.empty()) {
for (int k = q.size(); k; --k) {
int i = q.front();
q.pop();
if (s[i].count(target)) {
return ans;
}
for (int j : g[i]) {
if (!vis.count(j)) {
vis.insert(j);
q.push(j);
}
}
}
++ans;
}
return -1;
}
};

• class Solution:
def numBusesToDestination(
self, routes: List[List[int]], source: int, target: int
) -> int:
if source == target:
return 0

s = [set(r) for r in routes]
d = defaultdict(list)
for i, r in enumerate(routes):
for v in r:
d[v].append(i)

g = defaultdict(list)
for ids in d.values():
m = len(ids)
for i in range(m):
for j in range(i + 1, m):
a, b = ids[i], ids[j]
g[a].append(b)
g[b].append(a)
q = deque(d[source])
ans = 1
vis = set(d[source])
while q:
for _ in range(len(q)):
i = q.popleft()
if target in s[i]:
return ans
for j in g[i]:
if j not in vis:
vis.add(j)
q.append(j)
ans += 1
return -1


• func numBusesToDestination(routes [][]int, source int, target int) int {
if source == target {
return 0
}
n := len(routes)
s := make([]map[int]bool, n)
g := make([][]int, n)
d := map[int][]int{}
for i, r := range routes {
for _, v := range r {
if s[i] == nil {
s[i] = make(map[int]bool)
}
s[i][v] = true
d[v] = append(d[v], i)
}
}
for _, ids := range d {
m := len(ids)
for i := 0; i < m; i++ {
for j := i + 1; j < m; j++ {
a, b := ids[i], ids[j]
g[a] = append(g[a], b)
g[b] = append(g[b], a)
}
}
}
q := d[source]
vis := map[int]bool{}
for _, v := range d[source] {
vis[v] = true
}
ans := 1
for len(q) > 0 {
for k := len(q); k > 0; k-- {
i := q[0]
q = q[1:]
if s[i][target] {
return ans
}
for _, j := range g[i] {
if !vis[j] {
vis[j] = true
q = append(q, j)
}
}
}
ans++
}
return -1
}

• public class Solution {
public int NumBusesToDestination(int[][] routes, int source, int target) {
if (source == target) {
return 0;
}

Dictionary<int, HashSet<int>> stopToRoutes = new Dictionary<int, HashSet<int>>();
List<HashSet<int>> routeToStops = new List<HashSet<int>>();

for (int i = 0; i < routes.Length; i++) {
routeToStops.Add(new HashSet<int>());
foreach (int stop in routes[i]) {
routeToStops[i].Add(stop);
if (!stopToRoutes.ContainsKey(stop)) {
stopToRoutes[stop] = new HashSet<int>();
}
stopToRoutes[stop].Add(i);
}
}

Queue<int> queue = new Queue<int>();
HashSet<int> visited = new HashSet<int>();
int ans = 0;

foreach (int routeId in stopToRoutes[source]) {
queue.Enqueue(routeId);
visited.Add(routeId);
}

while (queue.Count > 0) {
int count = queue.Count;
ans++;

for (int i = 0; i < count; i++) {
int routeId = queue.Dequeue();

foreach (int stop in routeToStops[routeId]) {
if (stop == target) {
return ans;
}

foreach (int nextRoute in stopToRoutes[stop]) {
if (!visited.Contains(nextRoute)) {
visited.Add(nextRoute);
queue.Enqueue(nextRoute);
}
}
}
}
}

return -1;
}
}