index.js

/**
 * Valid graph tree
 *
 * @author David Lacedonia <davidlacedonia@gmail.com>
 *
 * @param {number} n
 * @param {number[][]} edges
 *
 * @return {boolean}
 */
function validGraphTree(n, edges) {
    const adjacencyList = createAdjacencyList(n, edges);
    let seen = { 0: true };
    let stack = [0];

    while (stack.length) {
        const node = stack.pop();
        for (let neighbour of adjacencyList[node] || []) {
            if (seen[neighbour]) {
                return false;
            }

            stack.push(neighbour);
            seen[neighbour] = true;

            // remove actual node from neighbour, to prevent revisiting on undirected graphs
            adjacencyList[neighbour] = adjacencyList[neighbour].filter(
                (i) => i !== node
            );
        }
    }

    return Object.keys(seen).length === n;
}

/**
 * Adjacenct list
 *
 * List of sub-lists
 * where each sub-list is the list of the immediate neighbours for the i'th node
 */
const createAdjacencyList = (n, edges) => {
    let list = [];

    for (let edge of edges) {
        const [x, y] = edge;
        list[x] = [...(list[x] || []), y];
        list[y] = [...(list[y] || []), x];
    }

    return list;
};

export default validGraphTree;