<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:
    #define INF 0x3f3f3f3f
    vector<int> dij(int s, vector<vector<int> > g)
    {
        int n = g.size() - 1;
        vector<int> dis(g.size() + 2, INF);
        vector<int> vis(g.size() + 2, 0);
        dis[s] = 0;
        vis[s] = 0;
        for (int i = 0; i < n; i++)
        {
            int p = n + 1;
            for (int i = 0; i < n; i++)
                if (vis[i] == 0 && dis[i] < dis[p])
                    p = i;
            if (p == n + 1)
                break;
            //cout << p << ' ' << dis[p] << endl;
            for (int j = 0; j < n; j++)
                dis[j] = min(dis[j], dis[p] + g[p][j]);
            vis[p] = 1;
        }
        return dis;
    }
    
    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
        vector<vector<int> > g(n + 1, vector<int> (n + 1, INF));
        for (auto &p : edges)
        {
            int x = p[0];
            int y = p[1];
            int w = p[2];
            if (w == -1)
                continue;
            g[x][y] = g[y][x] = w;
        }
        int s = source;
        int t = destination;
        auto dis1 = dij(s, g);
        auto dis2 = dij(t, g);
        if (dis1[t] < target)
            return vector<vector<int>>();
        if (dis1[t] == target)
        {
            for (auto &p : edges)
            {
                int x = p[0];
                int y = p[1];
                int w = p[2];
                if (w == -1)
                    p[2] = 2000'000'000;
            }
            return edges;
        }
        int l = 1, r = INF;
        auto ans = edges;
        while (l < r)
        {
            int mid = (l + r) / 2;
            ans = edges;
            for (auto &p : ans)
            {
                int x = p[0];
                int y = p[1];
                int w = p[2];
                if (w == -1)
                    g[x][y] = g[y][x] = mid;
                else
                    g[x][y] = g[y][x] = w;
            }
            if (dij(s, g)[t] <= target)
                l = mid + 1;
            else
                r = mid;
        }
        int ww = r;
        int m = edges.size();
        l = 0;
        r = m;
        cout << ww << endl;
        int fk = 0;
        while (1)
        {
            fk ++;
            if (fk > 20)
            {
                return vector<vector<int>>();
            }
            int mid = (l + r) / 2;
            ans = edges;
            int cnt = 0;
            for (auto &p : ans)
            {
                int x = p[0];
                int y = p[1];
                int w = p[2];
                if (w == -1)
                {
                    w = ww;
                    p[2] = ww;
                    if (cnt < mid)
                    {
                        w --;
                    }
                    g[x][y] = g[y][x] = w;
                    if (cnt < mid)
                    {
                        p[2] --;
                    }
                        
                }
                g[x][y] = g[y][x] = w;
                cnt ++;
            }
            auto dis = dij(s, g)[t];
            if (dis == target)
                return ans;
            else if (dis > target)
                l = mid + 1;
            else
                r = mid - 1;
        }
        
        return vector<vector<int>>();
        
    }
};
417337