<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>

import heapq

class Solution:
    def modifiedGraphEdges(self, n: int, edges: List[List[int]], src: int, des: int, target: int) -> List[List[int]]:
        alist = {i:{} for i in range(n)}
        for edge in edges:
            w = edge[2] if edge[2]!=-1 else 2*10**9
            alist[edge[0]][edge[1]] = w
            alist[edge[1]][edge[0]] = w
        heap = []
        heapq.heappush(heap, (0, src))
        dis = [float("inf")]*n
        dis[src] = 0
        visited = [False]*n
        while len(heap):
            d, u = heapq.heappop(heap)
            if visited[u]:
                continue
            visited[u] = True
            for i in alist[u]:
                if not visited[i]:
                    dis[i] = min(dis[i], d+alist[u][i])
                    heapq.heappush(heap, (dis[i], i))
        if dis[des]<target:
            return []
        if dis[des]==target:
            return [(i, j, alist[i][j]) for i, j, w in edges]
        seti = set()
        for i in alist:
            for j in alist[i]:
                if alist[i][j]==2*10**9:
                    seti.add((i, j))
                    alist[i][j] = 1
        def func(target, seti):
            heap = []
            heapq.heappush(heap, (0, src))
            parent = [-1]*n
            parent[src] = src
            dis = [float("inf")]*n
            dis[src] = 0
            visited = [False]*n
            while len(heap):
                d, u = heapq.heappop(heap)
                if visited[u]:
                    continue
                visited[u] = True
                for i in alist[u]:
                    if not visited[i]:
                        if d+alist[u][i]<dis[i]:
                            dis[i] = d+alist[u][i]
                            parent[i] = u
                        heapq.heappush(heap, (dis[i], i))
            if dis[des]>target:
                return dis[des]
            path = [des]
            p = des
            while parent[p]!=p:
                p = parent[p]
                path.append(p)
            path = path[::-1]
            for i in range(1, len(path)):
                target -= alist[path[i]][path[i-1]]
            flag = True
            for i in range(1, len(path)):
                if (path[i-1], path[i]) in seti:
                    if flag:
                        alist[path[i-1]][path[i]] += target
                        alist[path[i]][path[i-1]] += target
                        flag = False
                    seti.remove((path[i-1], path[i]))
                    seti.remove((path[i], path[i-1]))
            for i in alist:
                for j in alist[i]:
                    if (i, j) in seti:
                        alist[i][j] = 2*10**9
            return dis[des]
        d = func(target, set(seti))
        if d>target:
            return []
        while d!=target:
            d = func(target, set(seti))
        return [(i, j, alist[i][j]) for i, j, w in edges]
        
20853