add advance 1175

Author: tiny656

PAT (Advanced Level) Practice/1175_Professional Ability Test (30).cpp

@@ -0,0 +1,132 @@
+#include <iostream>
+#include <vector>
+#include <queue>
+using namespace std;
+
+// 1. use topology algorithm to check if graph is a DAG.
+// 2. construct a convergence start point to link all points which in degree is 0.
+// 3. call dijsktra algo to find all short distance from convergence start point.
+
+const int MAXN = 0x3fffffff;
+
+class Node {
+public:
+	int t, s, d;
+};
+
+vector<vector<Node>> G;
+vector<int> pre;
+vector<bool> hasInDegree;
+
+bool isDAG() {
+	vector<int> inDegree(G.size(), 0);
+	for (int i = 0; i < G.size(); i++) {
+		for (int j = 0; j < G[i].size(); j++) {
+			inDegree[G[i][j].t]++;
+		}
+	}
+
+	queue<int> q;
+	for (int i = 0; i < G.size(); i++) {
+		if (inDegree[i] == 0) q.push(i);
+	}
+
+	int cnt = 0;
+	while (!q.empty()) {
+		int u = q.front();
+		q.pop();
+		cnt++;
+		for (int i = 0; i < G[u].size(); i++) {
+			int v = G[u][i].t;
+			inDegree[v]--;
+			if (inDegree[v] == 0) q.push(v);
+		}
+	}
+
+	return cnt == G.size();
+}
+
+void dijkstra() {
+	int src = G.size() - 1; // G[n] is convergence start point
+	vector<int> dis(G.size(), MAXN), vou(G.size(), 0);
+	vector<bool> visited(G.size(), false);
+	pre.resize(G.size(), -1);
+	dis[src] = 0;
+
+	priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
+	pq.push({0, src});
+	while (!pq.empty()) {
+		auto e = pq.top(); pq.pop();
+		int s = e.first, u = e.second;
+		visited[u] = true;
+
+		if (dis[u] != MAXN && dis[u] < s) continue;
+
+		for (int i = 0; i < G[u].size(); i++) {
+			Node v = G[u][i];
+			if (visited[v.t]) continue;
+			if (dis[u] + v.s < dis[v.t]) {
+				dis[v.t] = dis[u] + v.s;
+				vou[v.t] = vou[u] + v.d;
+				pre[v.t] = u;
+				pq.push({dis[v.t], v.t});
+			} else if (dis[u] + v.s == dis[v.t] && vou[u] + v.d > vou[v.t]) {
+				vou[v.t] = vou[u] + v.d;
+				pre[v.t] = u;
+				pq.push({dis[v.t], v.t});
+			}
+		}
+	}
+}
+
+void print(int t) {
+	int src = G.size() - 1; // G[n] is convergence start point
+	if (t == src) return;
+	print(pre[t]);
+	if (hasInDegree[t]) cout << "->";
+	cout << t;
+}
+
+
+int main() {
+	ios::sync_with_stdio(false);
+	int n, m, t;
+	cin >> n >> m;
+	G.resize(n, vector<Node>());
+	hasInDegree.resize(n+1, false);
+	for (int i = 0; i < m; i++) {
+		Node node = Node();
+		cin >> t >> node.t >> node.s >> node.d;
+		hasInDegree[node.t] = true;
+		G[t].push_back(node);
+	}
+
+	vector<int> starts;
+	for (int i = 0; i < n; i++) {
+		if (!hasInDegree[i]) starts.push_back(i);
+	}
+
+	bool isValid = isDAG();
+	cout << (isValid ? "Okay." : "Impossible.") << endl;
+
+	// add a convergence point G[n] to link all starts
+	G.push_back(vector<Node>());
+	for (const int &t : starts) {
+		Node node = Node();
+		node.t = t;
+		node.s = node.d = 0;
+		G[n].push_back(node);
+	}
+	dijkstra();
+
+	int k;
+	cin >> k;
+	for (int i = 0; i < k; i++) {
+		cin >> t;
+		if (!hasInDegree[t]) cout << "You may take test " << t << " directly." << endl;
+		else if (!isValid) cout << "Error." << endl;
+		else { print(t); cout << endl;}
+	}
+
+	return 0;
+}