<p>You are given an array <code>routes</code> representing bus routes where <code>routes[i]</code> is a bus route that the <code>i<sup>th</sup></code> bus repeats forever.</p>

<ul>
	<li>For example, if <code>routes[0] = [1, 5, 7]</code>, this means that the <code>0<sup>th</sup></code> bus travels in the sequence <code>1 -&gt; 5 -&gt; 7 -&gt; 1 -&gt; 5 -&gt; 7 -&gt; 1 -&gt; ...</code> forever.</li>
</ul>

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

<p>Return <em>the least number of buses you must take to travel from </em><code>source</code><em> to </em><code>target</code>. Return <code>-1</code> if it is not possible.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> routes = [[1,2,7],[3,6,7]], source = 1, target = 6
<strong>Output:</strong> 2
<strong>Explanation:</strong> The best strategy is take the first bus to the bus stop 7, then take the second bus to the bus stop 6.
</pre>

<p><strong class="example">Example 2:</strong></p>

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

<p>&nbsp;</p>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= routes.length &lt;= 500</code>.</li>
	<li><code>1 &lt;= routes[i].length &lt;= 10<sup>5</sup></code></li>
	<li>All the values of <code>routes[i]</code> are <strong>unique</strong>.</li>
	<li><code>sum(routes[i].length) &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= routes[i][j] &lt; 10<sup>6</sup></code></li>
	<li><code>0 &lt;= source, target &lt; 10<sup>6</sup></code></li>
</ul>

#include <bits/stdc++.h>
using namespace std;

class Solution {
public:
int numBusesToDestination(vector<vector<int>>& routes, int source, int target) {
    if (source == target) return 0;

    unordered_map<int, vector<int>> terminal_has_bus;
    unordered_map<int, unordered_set<int>> graph_of_bus;
    unordered_map<int, int> distance;
    queue<int> q;
    
    // Build the map from terminal to buses
    for (int i = 0; i < routes.size(); ++i) {
        for (int stop : routes[i]) {
            terminal_has_bus[stop].push_back(i);
        }
    }
    
    // Build the graph of buses
    for (auto& [stop, buses] : terminal_has_bus) {
        for (int bus1 : buses) {
            for (int bus2 : buses) {
                if (bus1 != bus2) {
                    graph_of_bus[bus1].insert(bus2);
                }
            }
        }
    }
    
    // BFS initialization
    unordered_set<int> visited_stops;
    unordered_set<int> visited_buses;
    q.push(source);
    visited_stops.insert(source);
    
    int num_buses = 0;

    while (!q.empty()) {
        ++num_buses;
        int size = q.size();
        for (int i = 0; i < size; ++i) {
            int stop = q.front();
            q.pop();
            
            if (stop == target) return num_buses - 1;
            
            for (int bus : terminal_has_bus[stop]) {
                if (visited_buses.find(bus) != visited_buses.end()) continue;
                
                visited_buses.insert(bus);
                for (int next_stop : routes[bus]) {
                    if (visited_stops.find(next_stop) == visited_stops.end()) {
                        visited_stops.insert(next_stop);
                        q.push(next_stop);
                    }
                }
            }
        }
    }
    
    return -1;
}
};
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