**Common Reachable Node - Facebook Top Interview Questions**

### Problem Statement :

You are given a two-dimensional list of integers edges representing a directed graph and integers a and b. Each element in edges contains [u, v] meaning there's an edge from u to v. Return whether there's some node c such that we can go from c to a and c to b. Constraints 1 ≤ n ≤ 100,000 where n is the length of edges Example 1 Input edges = [ [0, 4], [4, 3], [1, 2], [0, 1], [0, 2], [1, 1] ] a = 2 b = 3 Output True Explanation We can reach 2 and 3 from 0 Example 2 Input edges = [ [0, 1], [1, 2], [1, 3], [1, 1], [4, 5] ] a = 2 b = 4 Output False Explanation 2 and 4 are on different connected components. Example 3 Input edges = [ [0, 0] ] a = 0 b = 0 Output True

### Solution :

` ````
Solution in C++ :
vector<int> adj[100001];
vector<bool> vis(100001, false);
unordered_map<int, int> mp;
bool flag;
void dfs(int curr) {
vis[curr] = true;
mp[curr]++;
if (mp[curr] > 1) {
flag = true;
return;
}
for (int node : adj[curr])
if (!vis[node]) dfs(node);
}
bool solve(vector<vector<int>>& edges, int a, int b) {
int n = edges.size() + 1;
if (a == b) return true;
for (int i = 0; i < n; i++) adj[i].clear();
for (int i = 0; i < n - 1; i++) {
adj[edges[i][1]].push_back(edges[i][0]);
}
mp.clear();
flag = false;
for (int i = 0; i < n; i++) vis[i] = false;
dfs(a);
for (int i = 0; i < n; i++) vis[i] = false;
dfs(b);
return flag;
}
```

` ````
Solution in Java :
import java.util.*;
class Solution {
static ArrayList<Integer>[] transpose;
static int N;
public boolean solve(int[][] edges, int a, int b) {
N = 0;
for (int[] e : edges) N = Math.max(N, Math.max(e[0], e[1]));
N++;
// build the transpose of the graph
transpose = new ArrayList[N];
for (int i = 0; i < N; i++) transpose[i] = new ArrayList<Integer>();
for (int[] e : edges) transpose[e[1]].add(e[0]);
// find ancestors of A and B
boolean[] visA = bfs(a);
boolean[] visB = bfs(b);
// cehck if there is any overlap
for (int i = 0; i < N; i++) {
if (visA[i] && visB[i]) {
// node i is a common ancestor!
return true;
}
}
return false;
}
public boolean[] bfs(int root) {
ArrayDeque<Integer> q = new ArrayDeque<Integer>();
boolean[] vis = new boolean[N];
vis[root] = true;
q.add(root);
while (!q.isEmpty()) {
int n = q.pollFirst();
for (int p : transpose[n]) {
if (!vis[p]) {
vis[p] = true;
q.add(p);
}
}
}
return vis;
}
}
```

` ````
Solution in Python :
class Solution:
def solve(self, edges, a, b):
graph = defaultdict(set)
for u, v in edges:
graph[v].add(u)
def explore(root):
queue = [root]
seen = {root}
for node in queue:
for nei in graph[node] - seen:
seen.add(nei)
queue.append(nei)
return seen
return bool(explore(a) & explore(b))
```

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