LeetCode #2359 — MEDIUM

Find Closest Node to Given Two Nodes

Move from brute-force thinking to an efficient approach using core interview patterns strategy.

Solve on LeetCode
The Problem

Problem Statement

You are given a directed graph of n nodes numbered from 0 to n - 1, where each node has at most one outgoing edge.

The graph is represented with a given 0-indexed array edges of size n, indicating that there is a directed edge from node i to node edges[i]. If there is no outgoing edge from i, then edges[i] == -1.

You are also given two integers node1 and node2.

Return the index of the node that can be reached from both node1 and node2, such that the maximum between the distance from node1 to that node, and from node2 to that node is minimized. If there are multiple answers, return the node with the smallest index, and if no possible answer exists, return -1.

Note that edges may contain cycles.

Example 1:

Input: edges = [2,2,3,-1], node1 = 0, node2 = 1
Output: 2
Explanation: The distance from node 0 to node 2 is 1, and the distance from node 1 to node 2 is 1.
The maximum of those two distances is 1. It can be proven that we cannot get a node with a smaller maximum distance than 1, so we return node 2.

Example 2:

Input: edges = [1,2,-1], node1 = 0, node2 = 2
Output: 2
Explanation: The distance from node 0 to node 2 is 2, and the distance from node 2 to itself is 0.
The maximum of those two distances is 2. It can be proven that we cannot get a node with a smaller maximum distance than 2, so we return node 2.

Constraints:

  • n == edges.length
  • 2 <= n <= 105
  • -1 <= edges[i] < n
  • edges[i] != i
  • 0 <= node1, node2 < n

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You are given a directed graph of n nodes numbered from 0 to n - 1, where each node has at most one outgoing edge. The graph is represented with a given 0-indexed array edges of size n, indicating that there is a directed edge from node i to node edges[i]. If there is no outgoing edge from i, then edges[i] == -1. You are also given two integers node1 and node2. Return the index of the node that can be reached from both node1 and node2, such that the maximum between the distance from node1 to that node, and from node2 to that node is minimized. If there are multiple answers, return the node with the smallest index, and if no possible answer exists, return -1. Note that edges may contain cycles.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: General problem-solving

Example 1

[2,2,3,-1]
0
1

Example 2

[1,2,-1]
0
2
Step 02

Core Insight

What unlocks the optimal approach

  • How can you find the shortest distance from one node to all nodes in the graph?
  • Use BFS to find the shortest distance from both node1 and node2 to all nodes in the graph. Then iterate over all nodes, and find the node with the minimum max distance.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2359: Find Closest Node to Given Two Nodes
class Solution {
    private int n;
    private List<Integer>[] g;

    public int closestMeetingNode(int[] edges, int node1, int node2) {
        n = edges.length;
        g = new List[n];
        Arrays.setAll(g, k -> new ArrayList<>());
        for (int i = 0; i < n; ++i) {
            if (edges[i] != -1) {
                g[i].add(edges[i]);
            }
        }
        int[] d1 = f(node1);
        int[] d2 = f(node2);
        int d = 1 << 30;
        int ans = -1;
        for (int i = 0; i < n; ++i) {
            int t = Math.max(d1[i], d2[i]);
            if (t < d) {
                d = t;
                ans = i;
            }
        }
        return ans;
    }

    private int[] f(int i) {
        int[] dist = new int[n];
        Arrays.fill(dist, 1 << 30);
        dist[i] = 0;
        Deque<Integer> q = new ArrayDeque<>();
        q.offer(i);
        while (!q.isEmpty()) {
            i = q.poll();
            for (int j : g[i]) {
                if (dist[j] == 1 << 30) {
                    dist[j] = dist[i] + 1;
                    q.offer(j);
                }
            }
        }
        return dist;
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n)
Space
O(1)

Approach Breakdown

BRUTE FORCE
O(n²) time
O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED
O(n) time
O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.