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Zjnu Stadium

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 3726 Accepted Submission(s): 1415

Problem Description In 12th Zhejiang College Students Games 2007, there was a new stadium built in Zhejiang Normal University. It was a modern stadium which could hold thousands of people. The audience Seats made a circle. The total number of columns were 300 numbered 1--300, counted clockwise, we assume the number of rows were infinite.
These days, Busoniya want to hold a large-scale theatrical performance in this stadium. There will be N people go there numbered 1--N. Busoniya has Reserved several seats. To make it funny, he makes M requests for these seats: A B X, which means people numbered B must seat clockwise X distance from people numbered A. For example: A is in column 4th and X is 2, then B must in column 6th (6=4+2).
Now your task is to judge weather the request is correct or not. The rule of your judgement is easy: when a new request has conflicts against the foregoing ones then we define it as incorrect, otherwise it is correct. Please find out all the incorrect requests and count them as R.

Input There are many test cases:
For every case:
The first line has two integer N(1<=N<=50,000), M(0<=M<=100,000),separated by a space.
Then M lines follow, each line has 3 integer A(1<=A<=N), B(1<=B<=N), X(0<=X<300) (A!=B), separated by a space.

Output For every case:
Output R, represents the number of incorrect request.

Sample Input 10 10 1 2 150 3 4 200 1 5 270 2 6 200 6 5 80 4 7 150 8 9 100 4 8 50 1 7 100 9 2 100

Sample Output 2 Hint Hint: （PS： the 5th and 10th requests are incorrect）

Source 2009 Multi-University Training Contest 14 - Host by ZJNU 題目連接：http://acm.hdu.edu.cn/showproblem.php?pid=3047 題意：n個點，m個關系。每個關系有3個整數a，b，x表示為a到b的距離為x。問m個關系中有幾個不合理的。 思路：並查集，在壓縮路徑的時候順便處理一下距離dist[x]+=dist[pa[x]]。關系合並時距離關系為：dist[fb]=dist[a]+x-dist[b]（fb為b的祖先；dist[a],diat[b]分別表示a，b到祖先的距離）。 代碼：

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<map>
#include<queue>
#include<stack>
#include<vector>
#include<set>
using namespace std;
#define PI acos(-1.0)
typedef long long ll;
typedef pair<int,int> P;
const int maxn=1e5+100,maxm=1e5+100,inf=0x3f3f3f3f,mod=1e9+7;
const ll INF=1e13+7;
int pa[maxn];
int dist[maxn];
void init(int n)
{
    for(int i=1; i<=n; i++)
        pa[i]=i,dist[i]=0;
}
int findset(int x)
{
    if(pa[x]==x) return x;
    int fax=pa[x];
    pa[x]=findset(pa[x]);
    dist[x]+=dist[fax];
    return pa[x];
}
void unit(int x,int y,int w)
{
    int fx=findset(x),fy=findset(y);
    pa[fx]=fy;
    dist[fx]=dist[y]+w-dist[x];
}
bool same(int x,int y,int w)
{
    if(findset(x)!=findset(y)) return false;
    else if(dist[findset(x)]==dist[y]+w-dist[x]) return false;
    else return true;
}
int main()
{
    int n,m;
    while(scanf("%d%d",&n,&m)!=EOF)
    {
        int ans=0;
        init(n);
        for(int i=1; i<=m; i++)
        {
            int a,b,x;
            scanf("%d%d%d",&a,&b,&x);
            if(same(a,b,x)) ans++;
            else unit(a,b,x);
        }
        cout<<ans<<endl;
    }
    return 0;
}

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HDU 3407.Zjnu Stadium 加權並查集