hdu1428

每走一步需要保证 （走完之后所到区域）距离实验室的最短距离 < （当前区域）距离实验室的最短距离

问，从宿舍到实验室有多少条路可以走

单源最短路 + 记忆化搜索

 1 #include <cstdio>

 2 #include <cstring>

 3 #include <climits>

 4 #include <queue>

 5 

 6 #define MAXN 50

 7 

 8 struct QueueNode

 9 {

10     int x, y;

11 };

12 

13 int n, G[MAXN+5][MAXN+5], dist[MAXN+5][MAXN+5];

14 long long dp[MAXN+5][MAXN+5];

15 int dir[4][4] = { {1, 0}, {0, 1}, {-1, 0}, {0, -1} };

16 bool vis[MAXN+5][MAXN+5];

17 // for every moment , there are not two same elements in the queue is OK 

18 void spfa()

19 {

20     std::queue<QueueNode> q;

21 

22     QueueNode head;

23     dist[n][n] = G[n][n];

24     head.x = head.y = n;

25     q.push(head);

26 

27     while(q.empty()==false){

28 

29         QueueNode u = q.front();

30         // if u is out the queue

31         // vis[u] is false

32         vis[u.x][u.y] = false;

33         q.pop();

34 

35         QueueNode v;

36 

37         for(int i = 0; i < 4; ++i){

38             v.x = u.x + dir[i][0];

39             v.y = u.y + dir[i][1];

40             if( v.x>=1 && v.x<=n && v.y>=1 && v.y<=n ){

41                 if(dist[v.x][v.y] > dist[u.x][u.y] + G[v.x][v.y]){

42 

43                     dist[v.x][v.y] = dist[u.x][u.y] + G[v.x][v.y];

44 

45                     if(vis[v.x][v.y] == false){

46                         // if u is out of the queu

47                         // vis[u] is true

48                         vis[v.x][v.y] = true;

49                         q.push(v);

50                     }

51                 }

52             }

53         }

54 

55     }

56 }

57 

58 long long dfs(int x, int y)

59 {

60     if(dp[x][y] > 0)

61         return dp[x][y];

62 

63     for(int i = 0; i < 4; ++i){

64         int _x = x + dir[i][0];

65         int _y = y + dir[i][1];

66         if(_x>=1 && _x<=n && _y>=1 && _y<=n){

67             if(dist[_x][_y] < dist[x][y]){

68                 dp[x][y] += dfs(_x, _y); 

69             }

70         }

71     }

72     return dp[x][y];

73 }

74 

75 int main(int argc, char const *argv[])

76 {

77     // freopen("_in", "r", stdin);

78     while(~scanf("%d", &n)){

79         for(int i = 1; i <= n; ++i){

80             for(int j = 1; j <= n; ++j){

81                 scanf("%d", &G[i][j]);

82                 dist[i][j] = INT_MAX;

83                 vis[i][j] = false;

84             }

85         }

86         spfa();

87 

88         memset(dp, 0, sizeof(dp));

89         dp[n][n] = 1;

90 

91         printf("%lld\n", dfs(1, 1));        

92     }

93     return 0;

94 }