<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:

    long long dijkstra(std::vector<std::vector<std::tuple<int, int *>>> &graph,
                       int source,
                       int destination)
    {
        auto n = graph.size();
        typedef long long Cost;
        typedef int Node;
        typedef std::pair<Node, Cost> NodeCostPair;
        std::queue<NodeCostPair> q;
        q.push({ source, 0 });
        std::vector<Cost> distances(n, 2e9);
        Cost minCost = 2e9;
        while (!q.empty())
        {
            auto [node, cost] = q.front();
            q.pop();
            if (  cost >= distances[node]
               || cost > minCost)
            {
                continue;
            }
            distances[node] = cost;
            if (node == destination)
            {
                minCost = std::min(minCost, cost);
            }
            auto &neighborCostPairs = graph[node];
            for (auto &[neighbor, weight] : neighborCostPairs)
            {
                if (*weight > 0)
                {
                    q.push({ neighbor, cost + *weight });
                }
            }
        }
        return minCost;
    }

    std::vector<std::vector<int>> modifiedGraphEdges(int n,
                                                     std::vector<std::vector<int>> &edges,
                                                     int source,
                                                     int destination,
                                                     int target)
    {
        std::vector<std::vector<std::tuple<int, int *>>> graph(n);
        for (int i = 0; i < edges.size(); ++i)
        {
            auto &edge = edges[i];
            auto u = edge[0];
            auto v = edge[1];
            auto &w = edge[2];
            graph[u].push_back({ v, &edge[2] });
            graph[v].push_back({ u, &edge[2] });
        }

        auto minCost = dijkstra(graph, source, destination);
        if (minCost < target)
        {
            return { };
        }

        bool okay = minCost == target;
        for (auto &edge : edges)
        {
            auto u = edge[0];
            auto v = edge[1];
            auto &w = edge[2];
            if (w > 0)
            {
                continue;
            }

            if (okay)
            {
                w = 2e9;
                continue;
            } 
            w = 1;
            minCost = dijkstra(graph, source, destination);
            if (minCost <= target)
            {
                okay = true;
                w += target - minCost;
            }
        }
        return okay ? edges : std::vector<std::vector<int>>{ };
    }
};
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