題目鏈接：

　　http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_B

Single Source Shortest Path (Negative Edges)

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
If the graph contains a negative cycle (a cycle whose sum of edge costs is a negative value) which is reachable from the source r, print

NEGATIVE CYCLE
in a line.

Otherwise, print

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| ≤ 1000
0 ≤ |E| ≤ 2000
-10000 ≤ di ≤ 10000
There are no parallel edges
There are no self-loops
Sample Input 1
4 5 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2
Sample Output 1
0
2
-3
-1

Sample Input 2
4 6 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2
3 1 0
Sample Output 2
NEGATIVE CYCLE

Sample Input 3
4 5 1
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2
Sample Output 3
INF
0
-5
-3

這題求單源最短路徑+負圈，用Bellman-Ford算法。

注意：這里求的負圈附帶了條件，就是源點r能觸及到的負圈。

Bellman-Ford算法+求負圈鏈接

代碼：

#include <iostream> #include <algorithm> #include <map> #include <vector> using namespace std; typedef long long ll; #define INF 2147483647struct edge{int from,to,cost; };edge es[2010]; //存儲邊 int d[1010]; // d[i] 表示點i離源點的最短距離 int V,E; //點和邊的數(shù)量 bool shortest_path(int s){fill(d,d+V,INF);d[s] = 0;int v = 0;while(true){bool update = false;for(int i = 0;i < E; i++){edge e = es[i];if(d[e.from] != INF && d[e.to] > d[e.from] + e.cost){d[e.to] = d[e.from] + e.cost;update = true;if(v == V-1) return true;}}if(!update) break;v++;}return false; }int main(){int r;cin >> V >> E >> r;for(int i = 0;i < E; i++) cin >> es[i].from >> es[i].to >>es[i].cost;if(!shortest_path(r)){for(int i = 0;i < V; i++){if(d[i] == INF) cout <<"INF" <<endl;else cout << d[i] << endl;}}else{cout <<"NEGATIVE CYCLE" <<endl;}return 0; }

總結

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