<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:
    int64_t dijkstra(vector<unordered_set<int>> const & adj,
                     vector<vector<int>> weight, int src, int dest) {
        const int N = weight.size();
        vector<bool> visit(N);
        vector<int64_t> minDist(N, INT32_MAX);
        using pr = pair<int,int64_t>; // id, cost
        auto cmp = [] (const pr &lhs, const pr &rhs) {
            return lhs.second > rhs.second;
        };
        priority_queue<pr, vector<pr>, decltype(cmp)> pq;
        pq.emplace(src, 0LL);
        while (!pq.empty()) {
            auto [cur, cost] = pq.top(); pq.pop();
            if (cost > minDist[cur]) continue;
            if (visit[cur]) continue;
            visit[cur] = true;
            minDist[cur] = cost;
            if (cur == dest) {
                return cost;
            }
            for (auto next: adj[cur]) {
                if (visit[next] or weight[cur][next] == -1) continue;
                pq.emplace(next, cost+weight[cur][next]);
            }
        }
        return INT32_MAX; // can't reach
    }
    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
        // V => 100, E => V^2
        // weight can be unassigned
        // make shortest path from source to dst == target
        // if there is a valid shortest path < target, then it's impossible
        constexpr int64_t MAX = 2000000000LL;
        cin.tie(0); ios_base::sync_with_stdio(0);
        vector weight(n, vector<int>(n));
        vector<unordered_set<int>> adj(n);
        for (auto edge:edges) {
            adj[edge[0]].insert(edge[1]);
            adj[edge[1]].insert(edge[0]);
            weight[edge[0]][edge[1]] = edge[2];
            weight[edge[1]][edge[0]] = edge[2];
        }
        auto minDist = dijkstra(adj, weight, source, destination);
        if (minDist < target) return vector<vector<int>>();
        bool match = minDist == target;
        for (int i=0;i<edges.size();i++) {
            if (edges[i][2] != -1) continue;
            int src = edges[i][0], dst = edges[i][1];
            // if matched assign large val else assign min
            if (match) {
                weight[src][dst] = weight[dst][src] = edges[i][2] = MAX;
            } else {
                weight[src][dst] = weight[dst][src] = edges[i][2] = 1;
                minDist = dijkstra(adj, weight, source, destination);
                if (minDist <= target) {
                    match = true;
                    // make up the difference
                    weight[src][dst] = weight[dst][src] = edges[i][2] = 1 + target - minDist;
                }
            }
        }
        return match ? edges : vector<vector<int>>();
    }
};
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