How do you solve Find Closest Node to Given Two Nodes on LeetCode?

Find Closest Node to Given Two Nodes (LeetCode #2359) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Using BFS allows us to efficiently find distances in a directed graph.

What is the time complexity of Find Closest Node to Given Two Nodes?

The optimal solution for Find Closest Node to Given Two Nodes runs in O(n) time and uses O(n) space. This complexity arises because we perform BFS twice, each taking linear time relative to the number of nodes.

What is the brute force solution for Find Closest Node to Given Two Nodes?

The brute force approach for Find Closest Node to Given Two Nodes is Brute Force, with O(n²) time complexity and O(1) space complexity. We can explore all possible nodes reachable from both node1 and node2. By calculating the distances to each reachable node, we can find the one that minimizes the maximum distance from both nodes. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find Closest Node to Given Two Nodes?

Find Closest Node to Given Two Nodes uses the following concepts: Depth-First Search, Graph Theory. The recommended patterns to study are: BFS, Graph Traversal, Distance Calculation.

What are the interview tips for Find Closest Node to Given Two Nodes?

Always clarify the problem statement and constraints before jumping to code. Think about edge cases, such as disconnected graphs or cycles. Explain your thought process clearly while coding.

What are common mistakes when solving Find Closest Node to Given Two Nodes?

Not handling cycles correctly, leading to infinite loops. Forgetting to check if nodes are reachable before accessing their distances.

#2359

Find Closest Node to Given Two Nodes

Medium

Depth-First SearchGraph TheoryBFSGraph TraversalDistance Calculation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

We can use Breadth-First Search (BFS) to efficiently find the shortest distance from both nodes to all reachable nodes. This way, we avoid redundant calculations and can directly find the minimum maximum distance.

⚙️

Algorithm

4 steps

1Step 1: Use BFS to find the shortest distance from node1 to all reachable nodes and store them in a distance array.
2Step 2: Use BFS again to find the shortest distance from node2 to all reachable nodes and store them in another distance array.
3Step 3: Iterate through both distance arrays to find the common nodes and calculate the maximum distance for each common node.
4Step 4: Track the node with the smallest maximum distance, and if there are ties, choose the smallest index.

solution.py31 lines

1# Full working Python code
2
3def find_closest_node(edges, node1, node2):
4    from collections import deque
5
6    def bfs(start):
7        distances = [-1] * len(edges)
8        queue = deque([start])
9        distances[start] = 0
10        while queue:
11            current = queue.popleft()
12            next_node = edges[current]
13            if next_node != -1 and distances[next_node] == -1:
14                distances[next_node] = distances[current] + 1
15                queue.append(next_node)
16        return distances
17
18    dist1 = bfs(node1)
19    dist2 = bfs(node2)
20
21    min_max_distance = float('inf')
22    result_node = -1
23
24    for node in range(len(edges)):
25        if dist1[node] != -1 and dist2[node] != -1:
26            max_distance = max(dist1[node], dist2[node])
27            if max_distance < min_max_distance or (max_distance == min_max_distance and node < result_node):
28                min_max_distance = max_distance
29                result_node = node
30
31    return result_node

ℹ

Complexity note: This complexity arises because we perform BFS twice, each taking linear time relative to the number of nodes.

1Using BFS allows us to efficiently find distances in a directed graph.
2Minimizing the maximum distance helps in finding the optimal node.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.