《Cracking the Coding Interview》——第4章：树和图——题目2

2014-03-19 03:32

题目：给定一个有向图，判断其中两点是否联通。

解法：DFS搜索解决，如果是无向图的话，就可以用并查集高效解决问题了。

代码：

  1 // 4.2 Write a program to check if there exists a path between two nodes in a directed graph.

  2 #include <algorithm>

  3 #include <cstdio>

  4 #include <unordered_map>

  5 #include <unordered_set>

  6 #include <vector>

  7 using namespace std;

  8 

  9 struct  GraphNode {

 10     int label;

 11     unordered_set<GraphNode *> neighbors;

 12     

 13     GraphNode(int _label = 0): label(_label) {};

 14 };

 15 

 16 bool hasPath(GraphNode *n1, GraphNode *n2, unordered_set<GraphNode *> &checked, vector<GraphNode *> &path)

 17 {

 18     if (n1 == nullptr || n2 == nullptr) {

 19         return false;

 20     }

 21     

 22     checked.insert(n1);

 23     path.push_back(n1);

 24 

 25     if (n1 == n2) {

 26         return true;

 27     }

 28 

 29     unordered_set<GraphNode *>::iterator it;

 30     for (it = n1->neighbors.begin(); it != n1->neighbors.end(); ++it) {

 31         if (checked.find(*it) == checked.end()) {

 32             if (hasPath(*it, n2, checked, path)) {

 33                 return true;

 34             }

 35         }

 36     }

 37     checked.erase(n1);

 38     path.pop_back();

 39     return false;

 40 }

 41 

 42 void constructGraph(int n, vector<GraphNode *> &nodes)

 43 {

 44     int i;

 45     int ne, x, y;

 46     int label;

 47     

 48     nodes.resize(n);

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

 50         scanf("%d", &label);

 51         nodes[i] = new GraphNode(label);

 52     }

 53     

 54     scanf("%d", &ne);

 55     for (i = 0; i < ne; ++i) {

 56         scanf("%d%d", &x, &y);

 57         nodes[x]->neighbors.insert(nodes[y]);

 58     }

 59 }

 60 

 61 void clearGraph(vector<GraphNode *> &nodes)

 62 {

 63     int n = (int)nodes.size();

 64     int i;

 65     

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

 67         nodes[i]->neighbors.clear();

 68         delete nodes[i];

 69         nodes[i] = nullptr;

 70     }

 71     nodes.clear();

 72 }

 73 

 74 int main()

 75 {

 76     int n;

 77     vector<GraphNode *> nodes;

 78     vector<GraphNode *> path;

 79     unordered_set<GraphNode *> checked;

 80     int idx1, idx2;

 81     

 82     while (scanf("%d", &n) == 1 && n > 0) {

 83         constructGraph(n, nodes);

 84         while (scanf("%d%d", &idx1, &idx2) == 2 && (idx1 >= 0 && idx2 >= 0)) {

 85             if (idx1 >= n || idx2 >= n) {

 86                 continue;

 87             }

 88 

 89             if (hasPath(nodes[idx1], nodes[idx2], checked, path)) {

 90                 printf("Yes\n");

 91                 printf("%d", path[0]->label);

 92                 for (int i = 1; i < (int)path.size(); ++i) {

 93                     printf("->%d", path[i]->label);

 94                 }

 95                 printf("\n");

 96             } else {

 97                 printf("No\n");

 98             }

 99             checked.clear();

100             path.clear();

101         }

102         clearGraph(nodes);

103     }

104     

105     return 0;

106 }