LeetCode 2492: Minimum Score of a Path Between Two Cities Solution

Master LeetCode problem 2492 (Minimum Score of a Path Between Two Cities), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

2492. Minimum Score of a Path Between Two Cities

Medium

Depth-First Search Breadth-First Search Union Find Graph

Problem Explanation

Explanation:

To find the minimum score of a path between cities 1 and n, we can use Dijkstra's algorithm. We will start from city 1 and explore all possible paths to other cities while keeping track of the minimum distance encountered so far. Once we reach city n, we will have the minimum score of a path between cities 1 and n.

Create an adjacency list to represent the graph where each city is connected to its neighboring cities with corresponding distances.
Initialize a priority queue (min heap) to store the cities to explore based on the minimum distance encountered so far.
Initialize an array to store the minimum distances from city 1 to each city.
Start with city 1, add it to the priority queue with distance 0.
While the priority queue is not empty, pop the city with the minimum distance.
For each neighboring city of the popped city, update the minimum distance if a shorter path is found and add the neighboring city to the priority queue.
Continue this process until we reach city n.
The minimum score of the path between cities 1 and n will be the minimum distance encountered at city n.

Time Complexity: O(ElogV), where E is the number of roads and V is the number of cities. Space Complexity: O(V + E), where V is the number of cities and E is the number of roads.

Solution Code

import java.util.*;

class Solution {
    public int minimumScore(int n, int[][] roads) {
        Map<Integer, List<int[]>> graph = new HashMap<>();
        for (int[] road : roads) {
            graph.computeIfAbsent(road[0], k -> new ArrayList<>()).add(new int[]{road[1], road[2]});
            graph.computeIfAbsent(road[1], k -> new ArrayList<>()).add(new int[]{road[0], road[2]});
        }

        PriorityQueue<int[]> pq = new PriorityQueue<>((a, b) -> a[1] - b[1]);
        int[] dist = new int[n + 1];
        Arrays.fill(dist, Integer.MAX_VALUE);

        pq.offer(new int[]{1, 0});
        dist[1] = 0;

        while (!pq.isEmpty()) {
            int[] curr = pq.poll();
            int city = curr[0];
            int distance = curr[1];

            if (city == n) {
                return distance;
            }

            if (distance > dist[city]) {
                continue;
            }

            if (graph.containsKey(city)) {
                for (int[] neighbor : graph.get(city)) {
                    int nextCity = neighbor[0];
                    int nextDist = Math.min(distance, neighbor[1]);
                    if (nextDist < dist[nextCity]) {
                        dist[nextCity] = nextDist;
                        pq.offer(new int[]{nextCity, nextDist});
                    }
                }
            }
        }

        return -1;
    }
}

Try It Yourself

Loading code editor...

Frequently Asked Questions

How to solve LeetCode 2492 (Minimum Score of a Path Between Two Cities)?

This page provides optimized solutions for LeetCode problem 2492 (Minimum Score of a Path Between Two Cities) in Java, C++, and Python, along with a detailed explanation and an interactive code editor to test your code.

What is the time complexity of LeetCode 2492 (Minimum Score of a Path Between Two Cities)?

The time complexity for LeetCode 2492 (Minimum Score of a Path Between Two Cities) varies by solution. Check the detailed explanation section for specific complexities in Java, C++, and Python implementations.

Can I run code for LeetCode 2492 on DevExCode?

Yes, DevExCode provides an interactive code editor where you can write, test, and run your code for LeetCode 2492 in Java, C++, or Python.

Back to LeetCode Solutions