<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>

static const int iofast = [](){
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  return 0;
}();

int adj[100][100];
int d[100];

struct compare {
  bool operator()(int u, int v) {
    return d[u] > d[v];
  }
};

class Solution {
  int dijkstra(int n, int src, int dst) {
    for (int i = 0; i < n; i++) {
      d[i] = 1000000007;
    }
    d[src] = 0;
    priority_queue<int, vector<int>, compare> q = {};
    q.push(src);
    while (size(q)) {
      int u = q.top();
      q.pop();
      for (int v = 0; v < n; v++) {
        if (adj[u][v]) {
          if (d[u] + adj[u][v] < d[v]) {
            d[v] = d[u] + adj[u][v];
            q.push(v);
          }
        }
      }
    }
    return d[dst];
  }
public:
    vector<vector<int>> modifiedGraphEdges(
      int n,
      vector<vector<int>>& edges,
      int src,
      int dst,
      int target) {
    memset(adj, 0, sizeof(adj));
    for (int i = 0; i < size(edges); i++) {
      auto& edge = edges[i];
      if (edge[2] != -1) {
        adj[edge[0]][edge[1]] = edge[2];
        adj[edge[1]][edge[0]] = edge[2];
      }
    }
    if (dijkstra(n, src, dst) < target) {
      return {};
    }
    auto ans = edges;
    for (int i = 0; i < size(ans); i++) {
      auto& edge = ans[i];
      if (edge[2] == -1) {
        adj[edge[0]][edge[1]] = 1;
        adj[edge[1]][edge[0]] = 1;
        edge[2] = 1;
      }
    }
    if (dijkstra(n, src, dst) > target) {
      return {};
    }
    for (int i = 0; i < size(edges); i++) {
      if (edges[i][2] == -1) {
        if (dijkstra(n, src, dst) == target) {
          return ans;
        } 
        int u = edges[i][0];
        int v = edges[i][1];
        if (d[u] > d[v]) {
          swap(u, v);
        }
        int d1 = d[u];
        int d2 = d[dst]-d1-adj[u][v];
        ans[i][2] = max(1, target-d1-d2);
        adj[u][v] = ans[i][2];
        adj[v][u] = ans[i][2];
      }
    }
    return ans;
  }
};

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