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POJ 1984 Navigation Nightmare （数据结构-并查集）

2024-07-14 23:05:16   222人阅读

Navigation Nightmare
Time Limit: 2000MS Memory Limit: 30000K
Total Submissions: 4072 Accepted: 1615
Case Time Limit: 1000MS

Description

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. 

Source

USACO 2004 February


题目大意：

给定n个城市，m条边告诉你城市间的相对距离，接下来q组询问，问你在第几条边添加后两城市的距离。


解题思路：

用离线处理，再用并查集维护每个城市到父亲城市的距离。


解题思路：

#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;

const int maxn=41000;

struct edge{
    int u,v,dis;
    char ch;
}e[maxn];

struct node{
    int u,v,cnt,id,ans;
}a[maxn];

int n,m,q;
int father[maxn],offx[maxn],offy[maxn];

bool cmp1(node x,node y){
    return x.cnt<y.cnt;
}

bool cmp2(node x,node y){
    return x.id<y.id;
}

void input(){
    scanf("%d%d",&n,&m);
    for(int i=0;i<=n;i++){
        father[i]=i;
        offx[i]=offy[i]=0;
    }
    for(int i=0;i<m;i++){
        scanf("%d%d%d %c",&e[i].u,&e[i].v,&e[i].dis,&e[i].ch);
    }
    scanf("%d",&q);
    for(int i=0;i<q;i++){
        scanf("%d%d%d",&a[i].u,&a[i].v,&a[i].cnt);
        a[i].id=i;
    }
    sort(a,a+q,cmp1);
}

int find(int x){
    if(father[x]!=x){
        int tmp=father[x];
        father[x]=find(father[x]);
        offx[x]+=offx[tmp];
        offy[x]+=offy[tmp];
    }
    return father[x];
}

void combine(int x,int y,int dis,char ch){
    int fx=find(x);
    int fy=find(y);
    father[fy]=fx;
    int offx0=offx[x]-offx[y];
    int offy0=offy[x]-offy[y];
    //cout<<fy<<"->"<<fx;
    if(ch=='N')  offy0+=dis;
    else if(ch=='S') offy0-=dis;
    else if(ch=='E') offx0+=dis;
    else offx0-=dis;
    //cout<<":("<<offx[fy]<<","<<offy[fy]<<")"<<endl;
    offx[fy]=offx0;
    offy[fy]=offy0;
    //cout<<":("<<offx[fy]<<","<<offy[fy]<<")"<<endl;
}

void solve(){
    int k=0;
    for(int i=0;i<q;i++){
        for(;k<a[i].cnt;k++){
            if(find(e[k].u)!=find(e[k].v)){
                combine(e[k].u,e[k].v,e[k].dis,e[k].ch);
            }
        }
        if( find(a[i].u)!=find(a[i].v) ) a[i].ans=-1;
        else{
            int ans=abs(offx[a[i].u]-offx[a[i].v])+abs(offy[a[i].u]-offy[a[i].v]);
            a[i].ans=ans;
        }
    }
    sort(a,a+q,cmp2);
    for(int i=0;i<q;i++){
        printf("%d\n",a[i].ans);
    }
}

int main(){
    input();
    solve();
    return 0;
}






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