AOJ GRL_1_B: Shortest Path
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题目链接:
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
这题求单源最短路径+负圈,用Bellman-Ford算法。
注意:这里求的负圈附带了条件,就是源点r能触及到的负圈。
Bellman-Ford算法+求负圈链接
代码:
#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]; //存储边 int d[1010]; // d[i] 表示点i离源点的最短距离 int V,E; //点和边的数量 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;}
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