<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>

using ll = long long;
using T = tuple<int, ll,  int, vector<int>>;
class Solution {
public:
    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
        vector<unordered_map<int, ll>> adj(n);

        for (auto v : edges) {
            auto a = v[0];
            auto b = v[1];
            auto w = v[2];
            adj[a][b] = w;
            adj[b][a] = w;
        }

        vector<unordered_map<int, ll>> newadj(n);

        // first check
        // bool bad = false;
        // priority_queue<pair<int, int>, vector<pair<int,int>>, greater<pair<int,int>>> q1;
        // vector<bool>v1(n, false);
        // q1.push({0, source});
        // while(!q1.empty()) {
        //     auto [a,b] = q1.top();
        //     q1.pop();
        //     if (v1[b]) {
        //         continue;
        //     }
        //     v1[b] = true;

        //     if (b == destination) {
        //         if (a < target) {
        //             bad = true;
        //             break;
        //         }
        //     }
        //     for (auto [e,w] : adj[b]) {
        //         if (w != -1)
        //             q1.push({a+w, e});
        //     }
        // }
        // if (bad) {
        //     // cout << "bad" << endl;
        //     return {};
        // }


        int bestun = n;
        ll bestdist = (ll)2e9;
        // first un, then dist
        priority_queue<
            T,
            vector<T>,
            greater<T> 
        > queue;
        queue.push({0, 0, source, {}});
        unordered_map<int, pair<int, int>> visited;

        bool possible = false;
        while (!queue.empty()) {
            auto [ un, dist, node, last] = queue.top();
            queue.pop();

            if (visited.count(node)>0) {
                auto [bestdist, bestun] = visited[node];
                if (!(un >= bestun && dist < bestdist || un < bestun)) {
                    continue;
                }
            }
            
            // printf("dist=%d, node=%d, un=%d\n", dist, node, un);
            visited[node] = {dist, un};

            if (node == destination) {
                if (un < bestun || (un == bestun && dist < bestdist)) {
                    if (un == 0 && dist == target) {
                        bestun = un;
                        bestdist = target;
                        newadj.clear();
                        newadj.resize(n);
                        possible=true;
                        break;
                    } else if (target - dist >= 0) {
                        bestun = un;
                        bestdist = dist;

                        ll delta = target - dist;
                        auto copy = last;
                        copy.push_back(node);
                        newadj.clear();
                        newadj.resize(n);
                        possible=false;
                        for (int i = 0; i < (int)copy.size()-1; ++i) {
                            if (adj[copy[i]][copy[i+1]] == -1) {
                                if (possible) {
                                    newadj[copy[i]][copy[i+1]] = 1;
                                    newadj[copy[i+1]][copy[i]] = 1;
                                } else {
                                    newadj[copy[i]][copy[i+1]] = 1+delta;
                                    newadj[copy[i+1]][copy[i]] = 1+delta;
                                    possible=true;
                                }   
                            }
                        }
                        break;
                    }

                    if (dist < target && un == 0) {
                        possible = false;
                        break;
                    }
                }
            }

            for (auto [ne, w] : adj[node]) {
                vector<int> newlast = last;
                newlast.push_back(node);
                // if (find(newlast.begin(), newlast.end(), ne) != newlast.end()) {
                //     continue;
                // }
                if (w == -1) {
                    
                    queue.push({un+1,dist+1,  ne, newlast});
                } else {
                    queue.push({un, dist+w, ne, newlast});
                }
            }
        }

        // cout << "here" << endl;
        if (!possible) {
            return {};
        }

        vector<vector<int>> output;
        for (auto v : edges) {
            auto a = v[0];
            auto b = v[1];
            auto w = v[2];
            if (adj[a][b] == -1) {
                if (newadj[a].count(b) == 0) {
                    output.push_back({a,b,(int)2e9});
                } else {
                    output.push_back({a,b,(int)newadj[a][b]});
                }
            } else {
                output.push_back({a,b,(int) adj[a][b]});
            }
        }

        return output;
    }
};
454112