《数据结构与算法分析：C语言描述》复习——第九章“图论”——无权值的最短路径问题

2014.07.04 18:24

简介：

　　给定一个有向图，你可以认为每条边长度都是1（所以叫无权值）。下面的算法可以求出从特定的起点到终点的最短路径长度。

描述：

　　从起点出发，根据当前顶点出发的边进行广度优先搜索，直至找到终点即可。如果搜索结束了仍然没有找到终点，那么起点无法到达终点。

实现：

 1 // A simple illustration for unweighted shortest path. Graph represented by adjacency matrix.

 2 #include <iostream>

 3 #include <queue>

 4 #include <vector>

 5 using namespace std;

 6 

 7 void unweightedShortestPath(const vector<vector<bool> > &graph, 

 8     vector<int> &dist, vector<bool> &reachable)

 9 {

10     // The minimal distances from 0th vertex to others.

11     int n;

12     int i, j;

13     

14     n = (int)graph.size();

15     dist.resize(n);

16     reachable.resize(n);

17 

18     if (n < 1) {

19         return;

20     }

21     

22     for (i = 0; i < n; ++i) {

23         reachable[i] = false;

24     }

25     

26     queue<int> q;

27     

28     dist[0] = 0;

29     reachable[0] = true;

30     

31     q.push(0);

32     while (!q.empty()) {

33         i = q.front();

34         q.pop();

35         for (j = 0; j < n; ++j) {

36             if (!graph[i][j] || reachable[j]) {

37                 continue;

38             }

39             dist[j] = dist[i] + 1;

40             reachable[j] = true;

41             q.push(j);

42         }

43     }

44 }

45 

46 int main()

47 {

48     vector<vector<bool> > graph;

49     vector<int> dist;

50     vector<bool> reachable;

51     int n;

52     int nk;

53     int i, j;

54     int tmp;

55     

56     while (cin >> n && n > 0) {

57         graph.resize(n);

58         for (i = 0; i < n; ++i) {

59             graph[i].resize(n, false);

60         }

61         

62         for (i = 0; i < n; ++i) {

63             cin >> nk;

64             for (j = 0; j < nk; ++j) {

65                 cin >> tmp;

66                 graph[i][tmp] = true;

67             }

68         }

69         

70         unweightedShortestPath(graph, dist, reachable);

71         

72         for (i = 0; i < n; ++i) {

73             cout << i << ": ";

74             if (reachable[i]) {

75                 cout << dist[i] << endl;

76             } else {

77                 cout << "Unreachable" << endl;

78             }

79         }

80         

81         for (i = 0; i < n; ++i) {

82             graph[i].clear();

83         }

84         graph.clear();

85     }

86     

87     return 0;

88 }