<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 {
    bool cmp(vector<int>&a , vector<int> &b ){
        return a[2] > b[2] ; 
    }

    long long dijstra_algo(int n, vector<vector<int>>& edges, int source,
                           int destination , unordered_map<int, vector<pair<int, int>>>& adj) {

        
        set<pair<long long, long long>> st;
        vector<long long> dist(n, INT_MAX);
        dist[source] = 0;

        st.insert(make_pair(0, source));

        while (!st.empty()) {

            auto top = *(st.begin());

            long long node_dist = top.first;

            long long top_node = top.second;

            st.erase(st.begin());

            for (auto i : adj[top_node]) {

                if (node_dist + i.second < dist[i.first]) {


                    dist[i.first] = node_dist + i.second;

                    st.insert(make_pair(dist[i.first], i.first));
                }
            }
        }

        return dist[destination];
    }

public:
    const int large = 2e9;
    typedef long long ll;
    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges,
                                           int source, int destination,
                                           int target) {
        // sort(edges.begin() , edges.end() cmp ) ;
    unordered_map<int, vector<pair<int, int>>> adj;

        for (auto edge : edges) {
            if (edge[2] != -1) {

                int u = edge[0];
                int v = edge[1];
                int w = edge[2];

                adj[u].push_back({v, w});
                adj[v].push_back({u, w});
            }
        }
        ll curr_dist = dijstra_algo(n, edges, source, destination , adj );

        if (curr_dist < target) {
            return {};
        }

        bool matched = (curr_dist == target);

        // curr_dist > target.
        for (auto& edge : edges) {

            if (edge[2] == -1) {
                edge[2] = matched == true ? large : 1;

                adj[edge[0]].push_back({edge[1] , edge[2]});
                adj[edge[1]].push_back({edge[0] , edge[2]});
                if (!matched) {

                    ll new_dist = dijstra_algo(n, edges, source, destination , adj );


                    if (new_dist <= target) {

                        edge[2] += target - new_dist;
                        matched = true;
                    }
                }
            }
        }
        if (!matched) {
            return {};
        }
        return edges;
    }
};
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