LeetCode-in-Java

2699. Modify Graph Edge Weights

Hard

You are given an undirected weighted connected graph containing n nodes labeled from 0 to n - 1, and an integer array edges where edges[i] = [a_i, b_i, w_i] indicates that there is an edge between nodes a_i and b_i with weight w_i.

Some edges have a weight of -1 (w_i = -1), while others have a positive weight (w_i > 0).

Your task is to modify all edges with a weight of -1 by assigning them positive integer values in the range [1, 2 * 10⁹] so that the shortest distance between the nodes source and destination becomes equal to an integer target. If there are multiple modifications that make the shortest distance between source and destination equal to target, any of them will be considered correct.

Return an array containing all edges (even unmodified ones) in any order if it is possible to make the shortest distance from source to destination equal to target, or an empty array if it’s impossible.

Note: You are not allowed to modify the weights of edges with initial positive weights.

Example 1:

Input: n = 5, edges = [[4,1,-1],[2,0,-1],[0,3,-1],[4,3,-1]], source = 0, destination = 1, target = 5

Output: [[4,1,1],[2,0,1],[0,3,3],[4,3,1]]

Explanation: The graph above shows a possible modification to the edges, making the distance from 0 to 1 equal to 5.

Example 2:

Input: n = 3, edges = [[0,1,-1],[0,2,5]], source = 0, destination = 2, target = 6

Output: []

Explanation: The graph above contains the initial edges. It is not possible to make the distance from 0 to 2 equal to 6 by modifying the edge with weight -1. So, an empty array is returned.

Example 3:

Input: n = 4, edges = [[1,0,4],[1,2,3],[2,3,5],[0,3,-1]], source = 0, destination = 2, target = 6

Output: [[1,0,4],[1,2,3],[2,3,5],[0,3,1]]

Explanation: The graph above shows a modified graph having the shortest distance from 0 to 2 as 6.

Constraints:

1 <= n <= 100
1 <= edges.length <= n * (n - 1) / 2
edges[i].length == 3
0 <= a_i, b_i< n
w_i = -1 or 1 <= w_i<= 10⁷
a_i!= b_i
0 <= source, destination < n
source != destination
1 <= target <= 10⁹
The graph is connected, and there are no self-loops or repeated edges

Solution

import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;
import java.util.PriorityQueue;

@SuppressWarnings({"unchecked", "java:S135"})
public class Solution {
    public int[][] modifiedGraphEdges(
            int n, int[][] edges, int source, int destination, int target) {
        List<int[]>[] graph = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            graph[i] = new ArrayList<>();
        }
        for (int i = 0; i < edges.length; i++) {
            int[] e = edges[i];
            graph[e[0]].add(new int[] {e[1], i});
            graph[e[1]].add(new int[] {e[0], i});
        }
        PriorityQueue<int[]> pq = new PriorityQueue<>(Comparator.comparingInt(v -> v[1]));
        pq.add(new int[] {destination, 0});
        Integer[] distances = new Integer[n];
        processQueue(edges, source, pq, distances, graph);
        if (distances[source] > target) {
            return new int[][] {};
        }
        pq = new PriorityQueue<>(Comparator.comparingInt(v -> v[1]));
        if (distances[source] != target) {
            pq.add(new int[] {source, 0});
        }
        boolean[] visited = new boolean[n];
        while (!pq.isEmpty()) {
            int[] c = pq.poll();
            if (visited[c[0]]) {
                continue;
            }
            visited[c[0]] = true;
            if (c[0] == destination) {
                return new int[][] {};
            }
            for (int[] e : graph[c[0]]) {
                if (visited[e[0]] || distances[e[0]] == null) {
                    continue;
                }
                int dif = target - c[1] - distances[e[0]];
                if (Math.abs(edges[e[1]][2]) >= dif) {
                    continue;
                }
                if (edges[e[1]][2] == -1) {
                    edges[e[1]][2] = dif;
                    continue;
                }
                pq.add(new int[] {e[0], c[1] + edges[e[1]][2]});
            }
        }
        for (int[] e : edges) {
            if (e[2] == -1) {
                e[2] = 1;
            }
        }
        return edges;
    }

    private void processQueue(
            int[][] edges,
            int source,
            PriorityQueue<int[]> pq,
            Integer[] distances,
            List<int[]>[] graph) {
        while (!pq.isEmpty()) {
            int[] c = pq.poll();
            if (distances[c[0]] != null) {
                continue;
            }
            distances[c[0]] = c[1];
            if (c[0] == source) {
                continue;
            }
            for (int[] e : graph[c[0]]) {
                if (distances[e[0]] != null) {
                    continue;
                }
                pq.add(new int[] {e[0], c[1] + Math.abs(edges[e[1]][2])});
            }
        }
    }
}

This site is open source. Improve this page.