New Exercise

Exercise/Homework7/Q3Dij.cpp

@@ -0,0 +1,71 @@
+#include <iostream>
+#include <vector>
+#include <queue>
+
+using namespace std;
+const int INF = 1e9;
+vector<vector<pair<int, int>>> adj;
+vector<int> dist;
+vector<bool> vis;
+vector<vector<int>> path;
+priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
+bool lessthan(vector<int> a, vector<int> b) {
+    for(int i = 0; i < min(a.size(), b.size()); i++) {
+        if(a[i] < b[i]) return true;
+        if(a[i] > b[i]) return false;
+    }
+    return a.size() < b.size();
+}
+
+int main() {
+    int n, m;
+    cin >> n >> m;
+    adj.resize(n + 1);
+    dist.resize(n + 1, INF);
+    vis.resize(n + 1, false);
+    path.resize(n + 1);
+    for(int i = 0; i < m; i++) {
+        int a, b, c;
+        cin >> a >> b >> c;
+        adj[a].push_back(make_pair(b, c));
+    }
+
+    dist[0] = 0;
+    path[0].push_back(0);
+    pq.push(make_pair(0, 0));
+    while(!pq.empty()) {
+        int u = pq.top().second;
+        pq.pop();
+        if(vis[u]) continue;
+        vis[u] = true;
+        for(auto [v, w] : adj[u]) {
+            if(dist[v] > dist[u] + w) {
+                dist[v] = dist[u] + w;
+                path[v] = path[u];
+                path[v].push_back(v);
+                pq.push(make_pair(dist[v], v));
+            }
+            else if(dist[v] == dist[u] + w) {
+                vector<int> new_path = path[u];
+                new_path.push_back(v);
+                if(path[v].empty() || path[v].size() > new_path.size() || 
+                   (path[v].size() == new_path.size() && lessthan(new_path, path[v]))) {
+                    path[v] = new_path;
+                    pq.push(make_pair(dist[v], v));
+                }
+            }
+        }
+    }
+    
+    for(int i = 1; i < n; i++) {
+        if(dist[i] != INF && !path[i].empty()) {
+            for(int j = 0; j < path[i].size(); j++) {
+                if(j > 0) cout << "->";
+                cout << path[i][j];
+            }
+            cout << endl;
+        }
+    }
+    
+    return 0;
+}