<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>

// class Solution {
// public:
//     int Dijkstra(int n, vector<vector<pair<int, int>>> &adj, int source, int destination){
//         vector<int> dist(n, INT_MAX);

//         dist[source]=0;

//         priority_queue<pair<int, int>, vector<pair<int, int>>, greater<>> pq;
//         pq.push({source, 0});

//         while(!pq.empty()){
//             pair<int, int> p = pq.top();pq.pop();

//             int node = p.first;int dis = p.second;

//             if(dis>dist[node])continue;

//             for(auto it: adj[node]){
//                 int nextneighbour = it.first;
//                 int nextdis = it.second;

//                 if(dis+nextdis<dist[nextneighbour]){
//                     dist[nextneighbour] = dis+nextdis;
//                     pq.push({nextneighbour, dist[nextneighbour]}); 
//                 }
//             }
//         }
//         return dist[destination];
//     }
//     vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
//         vector<vector<pair<int, int>>> adj(n);

//         for(auto it: edges){
//             if(it[2]==-1)continue;
//             adj[it[0]].push_back({it[1], it[2]});
//             adj[it[1]].push_back({it[0], it[2]});
//         }

//         int shortest_dist = Dijkstra(n, adj, source, destination);

//         if(shortest_dist<target)return {};

//         bool matched = (shortest_dist==target);

//         for(auto it: edges){
//             if(it[2]!=-1)continue;

//             it[2]= matched?2e9:1;

//             adj[it[0]].push_back({it[1], it[2]});
//             adj[it[1]].push_back({it[0], it[2]});

//             if(matched == false){
//                 int currShortest = Dijkstra(n, adj, source, destination);
//                 if(currShortest <= target){
//                     matched = true;
//                     it[2] += target - currShortest;
//                 }
//             }

           
//         }
//          if(matched) return edges;
//             return {};


//     }
// };


class Solution {
public:
    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout.tie(NULL);
        // Note:
        // The graph is undirected, weighted and then connected
        // Undirected in the sense there is no directions in which we proceed to go, weighthed in the sense each edge is having a corresponding weight and the connected in the sense there are n nodes and n - 1 edges.
        // -1 : There is no connection even.
        // There may be n paths from source to target and we need to assign any -1 node multiple -1 nodes any value from 1 to 2*10^9 to get the shortest distance from source to dest as target.
        // Ignore -1 edge wegiths
        // And then find the minimum distance between source and destination
        // < target : Then the answer itself is not possible
        // == target : Then every -1 be converted to INF
        // > target : Then we will consider every -1 edge and then find the minimum distance values. If mimumumDistance will be equal to target and then we will convert every -1 to INT_MAX
        vector<vector<pair<int, int>>> adjList(n);
        for(auto &edge : edges){
            if(edge[2] == -1) continue;
            adjList[edge[0]].push_back({edge[1], edge[2]});
            adjList[edge[1]].push_back({edge[0], edge[2]});
        }
        int shortestDist = Dijsktra(n, adjList, source, destination);
        if(shortestDist < target) return {};
        bool matched = (shortestDist == target);
        for(auto &edge : edges){
            if(edge[2] != -1) continue;
            edge[2] = matched ? 2e9 : 1;
            adjList[edge[0]].push_back({edge[1], edge[2]});
            adjList[edge[1]].push_back({edge[0], edge[2]});
            if(matched == false){
                int currShortest = Dijsktra(n, adjList, source, destination);
                if(currShortest <= target){
                    matched = true;
                    edge[2] += target - currShortest;
                }
            }
        }
        if(matched) return edges;
        return {};
    }
    int Dijsktra(int n, vector<vector<pair<int, int>>> &adjList, int source, int destination){
        vector<int> dist(n, INT_MAX);
        dist[source] = 0;
        priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
        pq.push({source, 0});
        while(!pq.empty()){
            auto top = pq.top();
            pq.pop();
            int currNode = top.first;
            int currDist = top.second;
            if(currDist > dist[currNode]) continue;
            for(auto &ele : adjList[currNode]){
                int neiNode  = ele.first;
                int neiDist  = ele.second;
                if(currDist + neiDist < dist[neiNode]){
                    dist[neiNode] = currDist + neiDist;
                    pq.push({neiNode, currDist + neiDist});
                }
            }
        }
        return dist[destination];
    }
};
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