<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:
    vector<int> al[128], w[128];
    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
        long long maxd = 2e9;
        for(int i=0; i<edges.size(); i++){
            al[edges[i][0]].push_back(edges[i][1]);
            w[edges[i][0]].push_back(edges[i][2] < 0 ? maxd : edges[i][2]);
            al[edges[i][1]].push_back(edges[i][0]);
            w[edges[i][1]].push_back(edges[i][2] < 0 ? maxd : edges[i][2]);
        }
        long long dis[128][128];
        int bt[128][128];
        for(int i=0; i<n; i++){ 
            for(int j=0; j<n; j++) dis[i][j] = 1e18;
        }
        // backtrack dijkstra
        dis[source][0] = 0;
        set<pair<long long, pair<int, int>>> pq;
        pq.insert({0, {source, 0}});
        while(pq.size()){
            int head = (pq.begin())->second.first;
            int nb = (pq.begin())->second.second;
            long long curdis = (pq.begin())->first;
            pq.erase(pq.begin());
            for(int i=0; i<al[head].size(); i++){
                int to = al[head][i];
                if(w[head][i] == maxd && nb < n){
                    if(curdis+1 < dis[to][nb+1]){
                        pq.erase({dis[to][nb+1], {to, nb+1}});
                        dis[to][nb+1] = curdis+1;
                        pq.insert({dis[to][nb+1], {to, nb+1}});
                        bt[to][nb+1] = head;
                    }
                }else if(w[head][i] < maxd){
                    if(curdis + w[head][i] < dis[to][nb]){
                        pq.erase({dis[to][nb], {to, nb}});
                        dis[to][nb] = curdis + w[head][i];
                        pq.insert({dis[to][nb], {to, nb}});
                        bt[to][nb] = head;
                    }
                }
            }
        }
        vector<vector<int>> ans;
        vector<int> edge; edge.push_back(0); edge.push_back(0); edge.push_back(0);
        if(dis[destination][0] < target) return ans;
        bool nemu = false;
        for(int i=0; i<n && !nemu; i++){
            if(dis[destination][i] <= target){
                long long dif = target - dis[destination][i];
                nemu = true;
                int curnode = destination, curnb = i;
                while(curnode != source){
                    int nxtnode = bt[curnode][curnb];
                    for(int j=0; j<al[curnode].size(); j++){
                        if(al[curnode][j] == nxtnode && w[curnode][j] == maxd){
                            w[curnode][j] = 1 + dif; curnb--;
                        }
                    }
                    for(int j=0; j<al[nxtnode].size(); j++){
                        if(al[nxtnode][j] == curnode && w[nxtnode][j] == maxd){
                            w[nxtnode][j] = 1 + dif; dif = 0;
                        }
                    }
                    curnode = nxtnode;
                }
            }
        }
        if(!nemu) return ans;
        for(int i=0; i<n; i++){
            edge[0] = i;
            for(int j=0; j<al[i].size(); j++){
                if(al[i][j] > i){
                    edge[1] = al[i][j]; edge[2] = w[i][j]; ans.push_back(edge);
                }
            }
        }
        return ans;
    }
};
409982