<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>

typedef pair<int,int> B;
class Solution {
public:
    const int INF = 2e9;

    vector<vector<int>> modifiedGraphEdges(int nodeCount,vector<vector<int>>& edges,
                                           int source, int destination,
                                           int target) {
        // Step 1: Compute the initial shortest distance from source to
        // destination
        long long currentShortestDistance =
            runDijkstra(edges, nodeCount, source, destination);

        // If the current shortest distance is less than the target, return an
        // empty result
        if (currentShortestDistance < target)
            return {};

        bool matchesTarget = (currentShortestDistance == target);

        // Step 2: Iterate through each edge to adjust its weight if necessary
        for (vector<int>& edge : 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] = matchesTarget ? INF : 1;

            // Step 3: If current shortest distance does not match target
            if (!matchesTarget) {
                // Compute the new shortest distance with the updated edge
                // weight
                long long newDistance =
                    runDijkstra(edges, nodeCount, source, destination);
                // If the new distance is within the target range, update edge
                // weight to match target
                if (newDistance <= target) {
                    matchesTarget = true;
                    edge[2] += target - newDistance;
                }
            }
        }

        // Return modified edges if the target distance is achieved, otherwise
        // return an empty result
        return matchesTarget ? edges : vector<vector<int>>{};
    }

    // Dijkstra's algorithm to find the shortest path distance
    long long runDijkstra(const vector<vector<int>>& edges, int nodeCount,
                          int s, int d) {
        // Step 1: Initialize adjacency matrix and distance arrays
        vector<vector<long long>> g(nodeCount,
                                            vector<long long>(nodeCount, INF));
        vector<long long> dist(nodeCount, INF);
        vector<bool> visit(nodeCount, false);

        // Set the distance to the source node as 0
     //   minDistance[sourceNode] = 0;
     dist[s] = 0;

        // Step 2: Fill the adjacency matrix with edge weights
        for (const vector<int>& edge : edges) {
            if (edge[2] != -1) {
                g[edge[0]][edge[1]] = edge[2];
                g[edge[1]][edge[0]] = edge[2];
            }
        }

        priority_queue<B, vector<B>, greater<B>> q;
         q.push({0,s});

       while(!q.empty()){
           int dis = q.top().first;
           int node = q.top().second;
           q.pop();

           if(visit[node]) continue;
           visit[node] = true;

           for(int i = 0; i<g[node].size() ; i++){
              if (g[node][i] != INF && dist[i] > dist[node] + g[node][i]) {
                    dist[i] = dist[node] + g[node][i];
                    q.push({dist[i], i});
                }
           }
       }  

        // Return the shortest distance to the destination node
        return dist[d];
    }
};
586502