<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 {
vector<int> findPath(vector<vector<int>> &mat, int curr, int d, vector<int> &ans , bool negEdge )
{
    auto comp = [](vector<int> a, vector<int> b ){return a[0]>b[0];};
    priority_queue<vector<int>,vector<vector<int>>,decltype(comp)> q;
    q.push({0,curr});
    int n= mat.size();
    vector<int> visited(n,1e9),parent(n,-1);
    visited[curr]= 0;
    while(q.size())
    {
        auto curr = q.top();
        q.pop();
        int cost = curr[0];
        int node = curr[1];
        for(int i = 0 ;i < n ; i++)
        {
            if(mat[node][i]==-1 && negEdge)
                continue;
                
            if( mat[node][i]!=0 && visited[i]>cost+abs(mat[node][i]))
            {
                visited[i] = cost + abs(mat[node][i]);
                parent[i] = node;
                q.push({visited[i],i});
            }
        }
    }
   
    int pr = d;
    while(pr != -1)
    {
        ans.push_back(pr);
        pr = parent[pr];
    }
    return visited;
}
vector<vector<int>> findAllPath(vector<vector<int>> mat)
{
    int n = mat.size();
    vector<vector<int>> ans(n,vector<int>(n,INT_MAX));
    for(int i = 0 ; i< n ;i++)
    {
        for(int j = 0 ; j< n ; j++)
        {
            if(mat[i][j]!=0 )
            {
                ans[i][j] = abs(mat[i][j]);
            }
        } 
    }
    for(int k = 0 ; k< n ; k++)
    {
        for(int i = 0 ; i< n ;i ++)
        {
            for(int j = 0 ; j < n ;j++)
            {
                if(ans[i][k]==INT_MAX || ans[k][j]==INT_MAX)
                {
                    continue;
                }    
                if(ans[i][k]+ans[k][j]<ans[i][j])
                    ans[i][j] = ans[i][k]+ans[k][j];
            }
        }
    }
    return ans;
}

int pathCost(vector<vector<int>> &mat , vector<int> &ans)
{
    if(ans.size()<=1)
        return 1e9;
    int cost = 0 ;
   for(int i = 0 ; i < ans.size()-1 && ans.size()>=2; i++)
        {
            int &val = mat[ans[i]][ans[i+1]];
            cost+=abs(val);
        }
        return cost;
}

void printMatrix(vector<vector<int>> &mat)
{
            for(auto row : mat)
        {
            for(auto val : row)
                cout<<val<<" ";
            cout<<endl;
        }
        
}
public:
    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
        vector<vector<int>> mat(n,vector<int>(n,0)) ;
        
        for(auto edge : edges)
        {
            int from = edge[0];
            int to = edge[1];
            int weight = edge[2];
            mat[from][to] = weight;
            mat[to][from] = weight;
        }
        vector<int> ans;
        auto costArr = findPath(mat, source , destination ,  ans , 1 );
        int pathCostOld  = pathCost(mat,ans);
        cout<<pathCostOld<<endl;
        if(pathCostOld<target)
            return {};
        ans = {};

        costArr = findPath(mat, source , destination ,  ans , 0 );
        int newCost = pathCost(mat,ans);


        int pathCostTarget = 0 ;
        int lastCost = 0;
        bool change = 1;
        vector<int> oldPath ; 
        while(change)
        {
            change = 0;
            vector<int> tempAns;
            costArr = findPath(mat, source , destination ,  tempAns , 0 );
    
            pathCostTarget = pathCost(mat,tempAns);

            ans = tempAns;

            for(int i = 0 ; i < ans.size()-1 && ans.size()>=2; i++)
            {
                int &val = mat[ans[i]][ans[i+1]];

                if(val==-1 )
                {
                    change = 1;
                    val  = target - pathCostTarget +1;    
                }
                mat[ans[i+1]][ans[i]] = val;
                if(change && val!=1)
                    break;
            }

        }

        for(auto &edge : edges)
        {
            int &from = edge[0];
            int &to = edge[1];
            int &weight = edge[2];
            if(mat[from][to]!=weight)
            {
                weight = mat[from][to];

            }
            if(weight==-1)
                weight = 1e9;
        }
        ans= {};
        costArr = findPath(mat, source , destination ,  ans , 0 );
    
        pathCostTarget = pathCost(mat,ans);

        if(pathCostTarget!=target)
            return {};
        return edges;
    }
};
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