Navigation Nightmare POJ - 1984 （带权并查集）

Posted 2021-02-21 fantadevourer

Navigation Nightmare

题目链接：virtual judge　　poj   

Farmer John‘s pastoral neighborhood has N farms (2 <= N <= 40,000), usually numbered/labeled 1..N. A series of M (1 <= M < 40,000) vertical and horizontal roads each of varying lengths (1 <= length <= 1000) connect the farms. A map of these farms might look something like the illustration below in which farms are labeled F1..F7 for clarity and lengths between connected farms are shown as (n):

           F1 --- (13) ---- F6 --- (9) ----- F3

            |                                 |

           (3)                                |

            |                                (7)

           F4 --- (20) -------- F2            |

            |                                 |

           (2)                               F5

            | 

           F7 

Being an ASCII diagram, it is not precisely to scale, of course.

Each farm can connect directly to at most four other farms via roads that lead exactly north, south, east, and/or west. Moreover, farms are only located at the endpoints of roads, and some farm can be found at every endpoint of every road. No two roads cross, and precisely one path
(sequence of roads) links every pair of farms.

FJ lost his paper copy of the farm map and he wants to reconstruct it from backup information on his computer. This data contains lines like the following, one for every road:

There is a road of length 10 running north from Farm #23 to Farm #17
There is a road of length 7 running east from Farm #1 to Farm #17
...

As FJ is retrieving this data, he is occasionally interrupted by questions such as the following that he receives from his navigationally-challenged neighbor, farmer Bob:

What is the Manhattan distance between farms #1 and #23?

FJ answers Bob, when he can (sometimes he doesn‘t yet have enough data yet). In the example above, the answer would be 17, since Bob wants to know the "Manhattan" distance between the pair of farms.
The Manhattan distance between two points (x1,y1) and (x2,y2) is just |x1-x2| + |y1-y2| (which is the distance a taxicab in a large city must travel over city streets in a perfect grid to connect two x,y points).

When Bob asks about a particular pair of farms, FJ might not yet have enough information to deduce the distance between them; in this case, FJ apologizes profusely and replies with "-1".

Input

* Line 1: Two space-separated integers: N and M



* Lines 2..M+1: Each line contains four space-separated entities, F1,

        F2, L, and D that describe a road. F1 and F2 are numbers of

        two farms connected by a road, L is its length, and D is a

        character that is either ‘N‘, ‘E‘, ‘S‘, or ‘W‘ giving the

        direction of the road from F1 to F2.



* Line M+2: A single integer, K (1 <= K <= 10,000), the number of FB‘s

        queries



* Lines M+3..M+K+2: Each line corresponds to a query from Farmer Bob

        and contains three space-separated integers: F1, F2, and I. F1

        and F2 are numbers of the two farms in the query and I is the

        index (1 <= I <= M) in the data after which Bob asks the

        query. Data index 1 is on line 2 of the input data, and so on.

Output

* Lines 1..K: One integer per line, the response to each of Bob‘s

        queries.  Each line should contain either a distance

        measurement or -1, if it is impossible to determine the

        appropriate distance.

Sample Input

7 6
1 6 13 E
6 3 9 E
3 5 7 S
4 1 3 N
2 4 20 W
4 7 2 S
3
1 6 1
1 4 3
2 6 6

Sample Output

13
-1
10

Hint

At time 1, FJ knows the distance between 1 and 6 is 13.
At time 3, the distance between 1 and 4 is still unknown.
At the end, location 6 is 3 units west and 7 north of 2, so the distance is 10.

 

题意：有n个农场，m条路。一一给出每条道路连接的两个村庄以及距离以及方向（前到后的方向），有k次提问，问两个村庄的曼哈顿距离。提问有一个索引i，表示是在第i次连接后问的。

思路：很普通的带权并查集，只是需要维护的数据有两个，一个是x方向的距离，一个是y方向的距离。然后是需要离线化操作（学到的新词）。

代码：

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <algorithm>
 4 using namespace std;
 5 const int N = 4e4+5;
 6 struct link{
 7     int x, y, dis;
 8     char dir;
 9 }l[N];
10 int f[N], rela[N][2], n, m, k;     //[0]代表横向,[1]代表竖向
11 
12 void init();
13 int find(int x);
14 void merge(int x, int y, int dis, char dir);
15 bool check(int x, int y);
16 
17 int main()
18 {
19     scanf("%d %d", &n, &m);
20     init();
21     for (int i=1;i<=m;i++)
22         scanf("%d %d %d %c", &l[i].x, &l[i].y, &l[i].dis, &l[i].dir);
23     scanf("%d", &k);
24     int cnt = 1;
25     for (int i=1;i<=k;i++)
26     {
27         int a, b, num;
28         scanf("%d%d%d", &a, &b, &num);
29             while (cnt <= num)
30         {
31             merge(l[cnt].x, l[cnt].y, l[cnt].dis, l[cnt].dir);
32             cnt++;
33         }
34         if (check(a, b))
35             printf("%d
", abs(rela[a][0] - rela[b][0]) + abs(rela[a][1] - rela[b][1]));
36         else
37             printf("-1
");
38     }
39     return 0;
40 }
41 
42 void init()
43 {
44     for (int i=1;i<=n;i++)
45         f[i] = i, rela[i][0] = rela[i][1] = 0;
46 }
47 int find(int x)
48 {
49     if (f[x] == x) return x;
50     int temp = f[x];
51     f[x] = find(f[x]);
52     rela[x][0] = rela[temp][0] + rela[x][0];
53     rela[x][1] = rela[temp][1] + rela[x][1];
54     return f[x];
55 }
56 void merge(int x, int y, int dis, char dir)
57 {
58     int fx = find(x), fy = find(y);
59     if (fx != fy)
60     {
61         int dx = 0, dy = 0;
62         f[fy] = fx;
63         if (dir == ‘E‘)
64             dy -= dis;
65         else if (dir == ‘W‘)
66             dy += dis;
67         else if (dir == ‘N‘)
68             dx -= dis;
69         else if (dir == ‘S‘)
70             dx += dis;
71         dx -= rela[y][1], dy -= rela[y][0];
72         dx += rela[x][1], dy += rela[x][0];
73         rela[fy][0] = dy, rela[fy][1] = dx;
74     }
75 }
76 bool check(int x, int y)
77 {
78     return find(x) == find(y);
79 }

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