Sync LeetCode submission Runtime - 207 ms (43.45%), Memory - 192.5 MB (46.83%)

Author: koralkulacoglu

LeetCode/2321-minimum-weighted-subgraph-with-the-required-paths/README.md

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+<p>You are given an integer <code>n</code> denoting the number of nodes of a <strong>weighted directed</strong> graph. The nodes are numbered from <code>0</code> to <code>n - 1</code>.</p>
+
+<p>You are also given a 2D integer array <code>edges</code> where <code>edges[i] = [from<sub>i</sub>, to<sub>i</sub>, weight<sub>i</sub>]</code> denotes that there exists a <strong>directed</strong> edge from <code>from<sub>i</sub></code> to <code>to<sub>i</sub></code> with weight <code>weight<sub>i</sub></code>.</p>
+
+<p>Lastly, you are given three <strong>distinct</strong> integers <code>src1</code>, <code>src2</code>, and <code>dest</code> denoting three distinct nodes of the graph.</p>
+
+<p>Return <em>the <strong>minimum weight</strong> of a subgraph of the graph such that it is <strong>possible</strong> to reach</em> <code>dest</code> <em>from both</em> <code>src1</code> <em>and</em> <code>src2</code> <em>via a set of edges of this subgraph</em>. In case such a subgraph does not exist, return <code>-1</code>.</p>
+
+<p>A <strong>subgraph</strong> is a graph whose vertices and edges are subsets of the original graph. The <strong>weight</strong> of a subgraph is the sum of weights of its constituent edges.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2022/02/17/example1drawio.png" style="width: 263px; height: 250px;" />
+<pre>
+<strong>Input:</strong> n = 6, edges = [[0,2,2],[0,5,6],[1,0,3],[1,4,5],[2,1,1],[2,3,3],[2,3,4],[3,4,2],[4,5,1]], src1 = 0, src2 = 1, dest = 5
+<strong>Output:</strong> 9
+<strong>Explanation:</strong>
+The above figure represents the input graph.
+The blue edges represent one of the subgraphs that yield the optimal answer.
+Note that the subgraph [[1,0,3],[0,5,6]] also yields the optimal answer. It is not possible to get a subgraph with less weight satisfying all the constraints.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+<img alt="" src="https://assets.leetcode.com/uploads/2022/02/17/example2-1drawio.png" style="width: 350px; height: 51px;" />
+<pre>
+<strong>Input:</strong> n = 3, edges = [[0,1,1],[2,1,1]], src1 = 0, src2 = 1, dest = 2
+<strong>Output:</strong> -1
+<strong>Explanation:</strong>
+The above figure represents the input graph.
+It can be seen that there does not exist any path from node 1 to node 2, hence there are no subgraphs satisfying all the constraints.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>3 &lt;= n &lt;= 10<sup>5</sup></code></li>
+	<li><code>0 &lt;= edges.length &lt;= 10<sup>5</sup></code></li>
+	<li><code>edges[i].length == 3</code></li>
+	<li><code>0 &lt;= from<sub>i</sub>, to<sub>i</sub>, src1, src2, dest &lt;= n - 1</code></li>
+	<li><code>from<sub>i</sub> != to<sub>i</sub></code></li>
+	<li><code>src1</code>, <code>src2</code>, and <code>dest</code> are pairwise distinct.</li>
+	<li><code>1 &lt;= weight[i] &lt;= 10<sup>5</sup></code></li>
+</ul>

LeetCode/2321-minimum-weighted-subgraph-with-the-required-paths/solution.cpp

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+// shortest path from src1 and src2 to a 'meeting point' and SP from dest to any 'meeting point'
+
+class Solution {
+public:
+    long long minimumWeight(int n, vector<vector<int>>& edges, int src1, int src2, int dest) {
+        vector<vector<pair<int, int>>> graph(n);
+        for (auto& e : edges) graph[e[0]].push_back({e[1], e[2]});
+
+        auto bfs = [&](int start) {
+            vector<long long> costs(n, 1e18);
+            priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<pair<long long, int>>> pq;
+            pq.push({0, start});
+            costs[start] = 0;
+            while (!pq.empty()) {
+                auto [cost, node] = pq.top();
+                pq.pop();
+    
+                if (cost > costs[node]) continue;
+
+                for (auto& neigh : graph[node]) {
+                    int newNode = neigh.first;
+                    long long newCost = cost + neigh.second;
+
+                    if (newCost < costs[newNode]) {
+                        costs[newNode] = newCost;
+                        pq.push({newCost, newNode});
+                    }
+                }
+            }
+            return costs;
+        };
+
+        vector<long long> src1Costs = bfs(src1);
+        vector<long long> src2Costs = bfs(src2);
+
+        vector<vector<pair<int, int>>> graphR(n);
+        for (int i=0; i<n; i++) {
+            for (auto& e : graph[i]) {
+                graphR[e.first].push_back({i, e.second});
+            }
+        }
+        graph = graphR;
+
+        vector<long long> destCosts = bfs(dest);
+
+        long long ans = 1e18;
+        for (int i=0; i<n; i++) ans = min(ans, src1Costs[i] + src2Costs[i] + destCosts[i]);
+
+        return ans < 1e18 ? ans : -1;
+    }
+};