HDU 4647 Another Graph Game

Posted 2021-02-09 bravewtz

Another Graph Game

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 660    Accepted Submission(s): 235

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 <= 10⁵, 0<=m<=10⁵) The next line have n numbers from W₁ to W_n which W_i is the weight of node i.(|W_i|<=10⁹)

The next m lines, each line have three numbers u, v, w,(1≤u,v≤n,|w|<=10⁹) 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

 

 

Source

2013 Multi-University Training Contest 5

题意： 有N个点，M条边。 点有权值， 边有权值。 Alice, Bob 分别选点。 如果一条边的两个顶点被同一个人选了， 那么能获得该权值。问 Alice - Bob？

分析：贪心，如没有边权，则对点权进行从大到小排序即可，加入边权之后，将边权拆分两半之后加到他所关联的两个点权中即可，这样，当两个人分别选择同边的两个点时，

相互抵消，一个人选了同边的两个点时，边权也都加进去了。。。

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<cstring>
 4 #include<algorithm>
 5 using namespace std;
 6 
 7 const int maxn = 1e5+10;
 8 double a[maxn];
 9 bool cmp(double x,double y){
10     return x>y;
11 }
12 
13 int main(){
14     int n,m;
15     while(~scanf("%d%d",&n,&m)){
16         for( int i=1; i<=n; i++ ){
17             scanf("%lf",&a[i]);
18         }
19         int u,v,w;
20         while(m--){
21             cin>>u>>v>>w;
22             a[u]+=1.0*w/2;
23             a[v]+=1.0*w/2;
24         }
25         double t1=0,t2=0;
26         sort(a+1,a+1+n,cmp);
27         for( int i=1; i<=n; i++ ){
28             if(i%2==1){/*等同于 i&1 */
29                 t1+=a[i];
30             }
31             else{
32                 t2+=a[i];
33             }
34         }
35         printf("%.01f
",t1-t2);
36     }
37     return 0;
38 }