<p>You are given an <strong>undirected weighted</strong> <strong>connected</strong> graph containing <code>n</code> nodes labeled from <code>0</code> to <code>n - 1</code>, and an integer array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>, w<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> with weight <code>w<sub>i</sub></code>.</p>

<p>Some edges have a weight of <code>-1</code> (<code>w<sub>i</sub> = -1</code>), while others have a <strong>positive</strong> weight (<code>w<sub>i</sub> &gt; 0</code>).</p>

<p>Your task is to modify <strong>all edges</strong> with a weight of <code>-1</code> by assigning them <strong>positive integer values </strong>in the range <code>[1, 2 * 10<sup>9</sup>]</code> so that the <strong>shortest distance</strong> between the nodes <code>source</code> and <code>destination</code> becomes equal to an integer <code>target</code>. If there are <strong>multiple</strong> <strong>modifications</strong> that make the shortest distance between <code>source</code> and <code>destination</code> equal to <code>target</code>, any of them will be considered correct.</p>

<p>Return <em>an array containing all edges (even unmodified ones) in any order if it is possible to make the shortest distance from </em><code>source</code><em> to </em><code>destination</code><em> equal to </em><code>target</code><em>, or an <strong>empty array</strong> if it&#39;s impossible.</em></p>

<p><strong>Note:</strong> You are not allowed to modify the weights of edges with initial positive weights.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><strong class="example"><img alt="" src="https://assets.leetcode.com/uploads/2023/04/18/graph.png" style="width: 300px; height: 300px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 5, edges = [[4,1,-1],[2,0,-1],[0,3,-1],[4,3,-1]], source = 0, destination = 1, target = 5
<strong>Output:</strong> [[4,1,1],[2,0,1],[0,3,3],[4,3,1]]
<strong>Explanation:</strong> The graph above shows a possible modification to the edges, making the distance from 0 to 1 equal to 5.
</pre>

<p><strong class="example">Example 2:</strong></p>

<p><strong class="example"><img alt="" src="https://assets.leetcode.com/uploads/2023/04/18/graph-2.png" style="width: 300px; height: 300px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 3, edges = [[0,1,-1],[0,2,5]], source = 0, destination = 2, target = 6
<strong>Output:</strong> []
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 3:</strong></p>

<p><strong class="example"><img alt="" src="https://assets.leetcode.com/uploads/2023/04/19/graph-3.png" style="width: 300px; height: 300px;" /></strong></p>

<pre>
<strong>Input:</strong> n = 4, edges = [[1,0,4],[1,2,3],[2,3,5],[0,3,-1]], source = 0, destination = 2, target = 6
<strong>Output:</strong> [[1,0,4],[1,2,3],[2,3,5],[0,3,1]]
<strong>Explanation:</strong> The graph above shows a modified graph having the shortest distance from 0 to 2 as 6.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 100</code></li>
	<li><code><font face="monospace">1 &lt;= edges.length &lt;= n * (n - 1) / 2</font></code></li>
	<li><code>edges[i].length == 3</code></li>
	<li><code>0 &lt;= a<sub>i</sub>, b<sub>i&nbsp;</sub>&lt;&nbsp;n</code></li>
	<li><code><font face="monospace">w<sub>i</sub>&nbsp;= -1&nbsp;</font></code>or <code><font face="monospace">1 &lt;= w<sub>i&nbsp;</sub>&lt;= 10<sup><span style="font-size: 10.8333px;">7</span></sup></font></code></li>
	<li><code>a<sub>i&nbsp;</sub>!=&nbsp;b<sub>i</sub></code></li>
	<li><code>0 &lt;= source, destination &lt; n</code></li>
	<li><code>source != destination</code></li>
	<li><code><font face="monospace">1 &lt;= target &lt;= 10<sup>9</sup></font></code></li>
	<li>The graph is connected, and there are no self-loops or repeated edges</li>
</ul>

from typing import List


class Solution:
    INF = int(2e9)

    def modifiedGraphEdges(
        self,
        n: int,
        edges: List[List[int]],
        source: int,
        destination: int,
        target: int,
    ) -> List[List[int]]:
        # Step 1: Compute the initial shortest distance from source to destination
        current_shortest_distance = self.run_dijkstra(
            edges, n, source, destination
        )

        # If the current shortest distance is less than the target, return an empty result
        if current_shortest_distance < target:
            return []
        matches_target = current_shortest_distance == target

        # Step 2: Iterate through each edge to adjust its weight if necessary
        for edge in edges:
            # Skip edges that already have a positive weight
            if edge[2] > 0:
                continue

            # Set edge weight to a large value if current distance matches target, else set to 1
            edge[2] = self.INF if matches_target else 1

            # Step 3: If current shortest distance does not match target
            if not matches_target:
                # Compute the new shortest distance with the updated edge weight
                new_distance = self.run_dijkstra(edges, n, source, destination)
                # If the new distance is within the target range, update edge weight to match target
                if new_distance <= target:
                    matches_target = True
                    edge[2] += target - new_distance

        # Return modified edges if the target distance is achieved, otherwise return an empty result
        return edges if matches_target else []

    def run_dijkstra(
        self, edges: List[List[int]], n: int, source: int, destination: int
    ) -> int:
        # Step 1: Initialize adjacency matrix and distance arrays
        adj_matrix = [[self.INF] * n for _ in range(n)]
        min_distance = [self.INF] * n
        visited = [False] * n

        # Set the distance to the source node as 0
        min_distance[source] = 0

        # Step 2: Fill the adjacency matrix with edge weights
        for nodeA, nodeB, weight in edges:
            if weight != -1:
                adj_matrix[nodeA][nodeB] = weight
                adj_matrix[nodeB][nodeA] = weight

        # Step 3: Perform Dijkstra's algorithm
        for _ in range(n):
            # Find the nearest unvisited node
            nearest_unvisited_node = -1
            for i in range(n):
                if not visited[i] and (
                    nearest_unvisited_node == -1
                    or min_distance[i] < min_distance[nearest_unvisited_node]
                ):
                    nearest_unvisited_node = i

            # Mark the nearest node as visited
            visited[nearest_unvisited_node] = True

            # Update the minimum distance for each adjacent node
            for v in range(n):
                min_distance[v] = min(
                    min_distance[v],
                    min_distance[nearest_unvisited_node]
                    + adj_matrix[nearest_unvisited_node][v],
                )
        # Return the shortest distance to the destination node
        return min_distance[destination]
19600