hdu 4647

Another Graph Game

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1274    Accepted Submission(s): 460

Problem Description

Alice and Bob are playing a game on an undirected graph with n (n is even) nodes and m edges. Every node i has its own weight W _v, and every edge e has its own weight W _e.

They take turns to do the following operations. During each operation, either Alice or Bob can take one of the nodes from the graph that haven't been taken before. Alice goes first.

The scoring rule is: One person can get the bonus attached to a node if he/she have choosen that node before. One person can get the bonus attached to a edge if he/she have choosen both node that induced by the edge before.

You can assume Alice and Bob are intelligent enough and do operations optimally, both Alice and Bob's target is maximize their score - opponent's.

What is the final result for Alice - Bob.

 

Input

Muilticases. The first line have two numbers n and m.(1 <= n <= 10 ⁵, 0<=m<=10 ⁵) The next line have n numbers from W ₁ to W _n which W _i is the weight of node i.(|W _i|<=10 ⁹)

The next m lines, each line have three numbers u, v, w,(1≤u,v≤n,|w|<=10 ⁹) the first 2 numbers is the two nodes on the edge, and the last one is the weight on the edge.

 

Output

One line the final result.

 

Sample Input

   
   
   
   

    
    
    
    4 0
9 8 6 5
   
   
   
   

 

Sample Output

   
   
   
   

    
    
    
    2
   
   
   
   
   
   
   
   

    
    
    
     
   
   
   
   
   
   
   
   

    
    
    
     
   
   
   
   
   
   
   
   

    
    
    
    刚开始一看以为是个博弈，直接就放弃了，下来一看，基本没啥联系，就是吓人的。
   
   
   
   
   
   
   
   

    
    
    
    下面是代码：
   
   
   
   
   
   
   
   

    
    
    
     
   
   
   
   
   
   
   
   

    
    
    
    
#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <stdlib.h>


using namespace std;

int n,m;
double a[100005];
int u,v;
double w;

int cmp(const double a,const double b){
       return a>b;
}

int main(){
   while(scanf("%d%d",&n,&m)!=EOF){
        for(int i=1;i<=n;i++){
            scanf("%lf",&a[i]);
        }
        for(int j=1;j<=m;j++){
            scanf("%d%d%lf",&u,&v,&w);
            a[u]+=w/2.0;//将边的权值分给两个结点
            a[v]+=w/2.0;
        }
        sort(a+1,a+1+n,cmp);//进行排序，因为都是最优的方案，所以每次都是选当前最大的
        double ans1,ans2;
        ans1=ans2=0;
        for(int i=1;i<=n;i++){
            if(i%2==1)
               ans1+=a[i];//奇数的是alice
            else
               ans2+=a[i];
        }
        printf("%.0lf\n",(ans1-ans2));
   }
   return 0;
}