題目鏈接：http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_A

Single Source Shortest Path

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|?1 t|E|?1 d|E|?1

|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,…, |V|?1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

c0
c1
:
c|V|?1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, … |V|?1 in order. If there is no path from the source to a vertex, print INF.

Constraints

1 ≤ |V| ≤ 100000
0 ≤ di ≤ 10000
0 ≤ |E| ≤ 500000
There are no parallel edges
There are no self-loops

Sample Input 1

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5

Sample Output 1

0
1
3
4

Sample Input 2

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5

Sample Output 2

3
0
2
INF

這題數據范圍比較大，最多有100000個頂點，用鄰接矩陣表示的話，空間肯定會超限。
我用Dijiksra的鄰接表來解了。

套一個模板就出來了：

#include <iostream> #include <algorithm> #include <map> #include <vector> using namespace std; typedef long long ll; #define INF 2147483647struct edge{int to,cost; }; int V,E; vector <edge> G[100010];multimap <int,int> l;ll d[500010];void dijkstra(int s){fill(d,d+V,INF);d[s] = 0;l.insert(make_pair(0,s));while(l.size() > 0){int p = l.begin()->first;int v = l.begin()->second;l.erase(l.begin());if(d[v] < p) continue;for(int i = 0;i < G[v].size(); i++){edge e = G[v][i];if(d[e.to] > d[v] + e.cost){d[e.to] = d[v] + e.cost;l.insert(make_pair(d[e.to], e.to));}}} }int main(){int r;cin >> V >> E >> r;for(int i = 0;i < E; i++){edge e;int from;cin >> from >> e.to >> e.cost;G[from].push_back(e);}dijkstra(r);for(int i = 0;i < V; i++){if(d[i] != INF) cout << d[i] << endl;else cout << "INF" <<endl;}return 0; }

總結

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