<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:

    int shp(vector<vector<int>> &m, int s, int d) {
        set<int> visited;
        auto cmp = [](pair<int, int> &a, pair<int, int> &b) {
            return b.second < a.second;
        };
        priority_queue<pair<int, int>, vector<pair<int, int>>, decltype(cmp)> q(cmp);
        q.push({s, 0});
        while (!q.empty()) {
            auto [key, value] = q.top(); q.pop();
            if (visited.contains(key))
                continue;
            if (key == d)
                return value;
            for (int i = 0 ; i < m.size() ; i++) {
                if (m[key][i] <= 0)
                    continue;
                q.push({i, abs(m[i][key]) + value});
            }
            visited.insert(key);
        }
        return INT_MAX / 2;
    }

    vector<vector<int>> modifiedGraphEdges(int n, vector<vector<int>>& edges, int source, int destination, int target) {
        vector<vector<int>> m(n, vector<int>(n, 0));
        for (auto e : edges) {
            int w = e[2];
            /*if (w == -1)
                w = 1;*/
            m[e[0]][e[1]] = w;
            m[e[1]][e[0]] = w;
        }
        vector<int> prev(n, -1);
        set<int> visited;
        auto cmp = [](pair<pair<int, int>, int> &a, pair<pair<int, int>, int> &b) {
            return b.second < a.second;
        };
        priority_queue<pair<pair<int, int>, int>, vector<pair<pair<int, int>, int>>, decltype(cmp)> q(cmp);
        q.push({{source, -1}, 0});
        while (!q.empty()) {
            auto [key, value] = q.top(); q.pop();
            if (visited.contains(key.first))
                continue;
            prev[key.first] = key.second;
            if (key.first == destination)
                break;
            for (int i = 0 ; i < n ; i++) {
                if (!m[key.first][i])
                    continue;
                q.push({{i, key.first}, abs(m[i][key.first]) + value});
            }
            visited.insert(key.first);
        }

        if (shp(m,source, destination) < target)
            return {};
        
        if (shp(m, source, destination) == target) {

        } else {
            int cur = destination;
            int count = 0;
            int sum = 0;
            set<pair<int, int>> changable;
            while (cur != source) {
                if (prev[cur] == -1)
                    return {};
                sum += abs(m[cur][prev[cur]]);
                if (m[cur][prev[cur]] < 0) {
                    count++;
                    m[cur][prev[cur]] = 1;
                    m[prev[cur]][cur] = 1;
                    changable.insert({prev[cur], cur});
                    changable.insert({cur, prev[cur]});
                }
                cur = prev[cur];
            }
            if (sum > target)
                return {};
            if (sum < target && !count)
                return {};

            cur = destination;
            while (cur != source) {
                if (changable.contains({cur, prev[cur]})) {
                    int shpRes = shp(m, source, prev[cur]) + shp(m, cur, destination);
                    if (shpRes < target) {
                        m[cur][prev[cur]] = target - shpRes;
                        m[prev[cur]][cur] = target - shpRes;
                    }
                }
                cur = prev[cur];
            }
            /*if (sum < target)
                return {};*/
        }
        vector<vector<int>> res;
        for (int i = 0 ; i < n ; i++) {
            for (int j = i + 1; j < n ; j++) {
                if (!m[i][j])
                    continue;
                if (m[i][j] < 0) {
                    res.push_back({i, j, target + 1});
                } else {
                    res.push_back({i, j, m[i][j]});
                }
            }
        }
        cout << shp(m, source, destination) << endl;
        return res;
    }
};
307012