## Graph Valid Tree

Question

Given n nodes labeled from `0` to `n - 1` and a list of undirected edges (each edge is a pair of nodes), write a function to check whether these edges make up a valid tree.

For example:

Given `n = 5` and `edges = [[0, 1], [0, 2], [0, 3], [1, 4]]`, return true.

Given `n = 5` and `edges = [[0, 1], [1, 2], [2, 3], [1, 3], [1, 4]]`, return false.

Hint:

Given n = 5 and edges = [[0, 1], [1, 2], [3, 4]], what should your return? Is this case a valid tree? According to the definition of tree on Wikipedia: “a tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any connected graph without simple cycles is a tree.” Note: you can assume that no duplicate edges will appear in edges. Since all edges are undirected, [0, 1] is the same as [1, 0] and thus will not appear together inedges.

Solution

1. Treating input as graph, making sure no cycles and one connected component.
2. check for cycle and connectness in Graph can be done by DFS, BFS and Union-find

DFS from here

``````class Solution {
public:
bool validTree(int n, vector<pair<int, int>>& edges) {
vector<vector<int>> matrix(n);
for (auto e : edges) {
matrix[e.first].push_back(e.second);
matrix[e.second].push_back(e.first);
}

int path[n];
fill(path, path + n, 0);
path = 1;
if (hasCycle(matrix, n, 0, -1, path)) return false; // has cycle
if (accumulate(path, path + n, 0) < n) return false; // not fully connected
return true;
}

bool hasCycle(vector<vector<int>> &matrix, int n, int src, int pre, int path[]) {
for (auto i:matrix[src]) {
if (i != pre) {
if (path[i]) return true;
path[i] = 1;
if (hasCycle(matrix, n, i, src, path)) return ture;
}
}
return false;
}

}
``````