<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 ll long long
#define REP(i,n)        FOR(i,0,n)
#define SORT(v)         sort((v).begin(),(v).end())
#define FOR(i,a,b)      for(ll i=(a);i<(b);i++)

class Solution {
public:
    ll djkstra(ll from, ll to, vector<vector<pair<ll, ll>>>& g) {
        ll n = g.size();
        priority_queue<pair<ll, ll >> pq; pq.push({0, from});
        vector<ll> vis(n, INT_MAX); vis[from] = 0;
        while (pq.size() > 0) {
            auto p = pq.top(); pq.pop();
            ll val = -p.first;
            if (vis[p.second] < val) continue;
            if (p.second == to) return val;
            for (auto a : g[p.second]) {
                if (vis[a.first] <= val + a.second) continue;
                vis[a.first] = val + a.second;
                pq.push({-val-a.second, a.first});
            }
        }
        return vis[to];
    }

    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
        vector<vector<pair<ll, ll>>> g(n);
        vector<vector<bool>> special(n);
        map<pair<int, int>, int> m;
        REP(i, edges.size()) {
            auto& e = edges[i];
            g[e[0]].push_back({e[1], max(e[2], 1)});
            g[e[1]].push_back({e[0], max(e[2], 1)});
            special[e[0]].push_back(e[2] == -1);
            special[e[1]].push_back(e[2] == -1);
            m[{e[0], e[1]}] = i;
            m[{e[1], e[0]}] = i;
        }
        if (djkstra(source, destination, g) > target) return {};

        REP(i, n) REP(j, g[i].size()) if (special[i][j]) {
            g[i][j].second = 2e9;
            edges[m[{i, g[i][j].first}]][2] = 2e9;
        }
        if (djkstra(source, destination, g) < target) return {};

        REP(i, n) REP(j, g[i].size()) if (special[i][j]) {
            ll to = g[i][j].first;
            g[i][j].second = 1;             
            REP(k, g[to].size()) if (g[to][k].first == i) { g[to][k].second = 1; break; }
            edges[m[{i, to}]][2] = 1;
            
            ll d = djkstra(source, destination, g);
            if (d > target) continue;
            g[i][j].second += (target-d);
            edges[m[{i, to}]][2] = g[i][j].second;

            return edges;
        }

        return edges;
    }
};
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