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g2601_2700.s2699_modify_graph_edge_weights.readme.md Maven / Gradle / Ivy

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] = [ai, bi, wi] indicates that there is an edge between nodes ai and bi with weight wi.

Some edges have a weight of `-1` (wi = -1), while others have a **positive** weight (wi > 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:**

**![](https://assets.leetcode.com/uploads/2023/04/18/graph.png)**

**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:**

**![](https://assets.leetcode.com/uploads/2023/04/18/graph-2.png)**

**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:**

**![](https://assets.leetcode.com/uploads/2023/04/19/graph-3.png)**

**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 <= ai, bi < n
*   wi = -1 or 1 <= wi <= 107
*   ai != bi
*   `0 <= source, destination < n`
*   `source != destination`
*   1 <= target <= 109
*   The graph is connected, and there are no self-loops or repeated edges