# 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<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;
}
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++) {
}
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;
while (!q.isEmpty()) {
int n = q.pollFirst();
for (int p : transpose[n]) {
if (!vis[p]) {
vis[p] = true;
}
}
}
return vis;
}
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, edges, a, b):
graph = defaultdict(set)
for u, v in edges:

def explore(root):
queue = [root]
seen = {root}
for node in queue:
for nei in graph[node] - seen:
queue.append(nei)
return seen

return bool(explore(a) & explore(b))```
```

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