<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>

#define vvi vector<vector<int>>

class cmp{
public:
    bool operator()(vector<int> p1, vector<int> p2){
        if(p1[0]<=p2[0]){
            return false;
        }
        else{
            return true;
        }
    }
};


class Solution {
public:
    
    int bfs(int n, int src, int dest, int target, vvi& adj, vvi& wt, set<pair<int, int>>& not_fixed){
        priority_queue<vector<int>, vvi, cmp> pq1;
        pq1.push({0, src, src});
        vector<int> par(n, -1);
        int got_dis=-1;
        while(!pq1.empty()){
            int dis=pq1.top()[0], node=pq1.top()[1], p=pq1.top()[2];
            pq1.pop();
            
            if(par[node]!=-1){
                continue;
            }
            par[node]=p;
            if(node==dest){
                got_dis=dis;
                break;
            }
            
            for(auto ele: adj[node]){
                if(par[ele]==-1){
                    pq1.push({dis+wt[node][ele], ele, node});
                }
            }
        }
        
        // check if got_dis == target
        if(got_dis>target){
            return -1;
        }
        else if(got_dis==target){
            return 0; 
        }
        else{
            // now we get the path which has the shortest distance
            int curr=dest;
            set<pair<int, int>> mod_edges;
            while(curr!=src){
                int nxt=par[curr];
                if(not_fixed.find({curr, nxt})!=not_fixed.end() or
                   not_fixed.find({nxt, curr})!=not_fixed.end()){
                    mod_edges.insert({curr, nxt});
                }
                curr=nxt;
            }
            
            if(mod_edges.size()==0){
                return -1;
            }
            else{
                // set all edges not in mod_edges = target
                for(auto ele: not_fixed){
                    if(mod_edges.find({ele.first, ele.second})==mod_edges.end() and
                       mod_edges.find({ele.second, ele.first})==mod_edges.end()){
                        wt[ele.first][ele.second]=target+10;
                        wt[ele.second][ele.first]=target+10;
                    }
                }
                // set one of the modified edges in the path to required val
                pair<int, int> p1=*(mod_edges.begin());
                int n1=p1.first, n2=p1.second;
                mod_edges.erase(mod_edges.begin());
                int leftover=target-got_dis;
                wt[n1][n2]+=leftover;
                wt[n2][n1]+=leftover;
                
                // not_fixed now gets changed to mod_edges
                not_fixed=mod_edges;
                
                return 1;
            }
        }
        
        
        
    }
    // break if this func returns 0 or -1
    
    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
        vvi wt(n, vector<int>(n, -1)), adj(n);
        set<pair<int, int>> not_fixed;
        for(auto ed: edges){
            adj[ed[0]].push_back(ed[1]);
            adj[ed[1]].push_back(ed[0]);
            wt[ed[0]][ed[1]]=max(ed[2], 1);
            wt[ed[1]][ed[0]]=max(ed[2], 1);
            
            if(ed[2]==-1){
                not_fixed.insert({ed[0], ed[1]});
            }
        }
        
        int flag=0;
        
        while(true){
            int res=bfs(n, source, destination, target, adj, wt, not_fixed);
            if(res==1){
                continue;
            }
            else if(res==0){
                break;
            }
            else{
                flag=1;
                break;
            }
        }
        
        
        vector<vector<int>> res_vec;
        if(flag!=1){
            for(auto ed: edges){
                res_vec.push_back({ed[0], ed[1], wt[ed[0]][ed[1]]});
            }
        }
        return res_vec;
        
    }
};
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