子集枚举好题UVA1354

Posted 2020-09-11 wolf940509

题目

分析:枚举子集以及关于该子集的补集，然后用子集去暴力构造一颗二叉树，注意左边的最远距离不一定来自于左子树，右边的最远距离也不一定来自于右子树

 1 #include "iostream"
 2 #include "cstdio"
 3 #include "cstring"
 4 #include "string"
 5 #include "vector"
 6 using namespace std;
 7 const int maxn=15;
 8 int T,s,vis[1<<maxn]; 
 9 double r,w[maxn],sum[1<<maxn];
10 struct Tree{
11     double L,R;
12     Tree():L(0),R(0){};
13 };
14 vector<Tree> tree[1<<maxn];
15 
16 void dfs(int subset){
17     if(vis[subset])  return;
18     vis[subset]=1;
19     int flag=0;
20     for(int left=(subset-1)&subset;left;left=(left-1)&subset){
21         flag=1;
22         int right=left^subset;
23         double d1=sum[right]/sum[subset];
24         double d2=sum[left]/sum[subset];
25         dfs(left); dfs(right);
26         for(int i=0;i<tree[left].size();i++){
27             for(int j=0;j<tree[right].size();j++){
28                 Tree t;
29                 t.L=max(tree[left][i].L+d1,tree[right][j].L-d2);
30                 t.R=max(tree[left][i].R-d1,tree[right][j].R+d2);
31                 if(t.L+t.R<r)  tree[subset].push_back(t);
32             }
33         }
34     }
35     if(!flag)  tree[subset].push_back(Tree());
36 }
37 int main()
38 {
39     scanf("%d",&T);
40     while(T--){
41         scanf("%lf%d",&r,&s);
42         for(int i=0;i<s;i++)
43             cin>>w[i];
44         for(int i=0;i<1<<s;i++){
45             tree[i].clear();
46             sum[i]=0;
47             for(int j=0;j<s;j++){
48                 if(i&(1<<j)){
49                     sum[i]+=w[j];
50                 }
51             }
52         }
53         int root=(1<<s)-1;
54         memset(vis,0,sizeof(vis));
55         dfs(root);
56         double ans=-1;
57         for(int i=0;i<tree[root].size();i++)
58             ans=max(ans,tree[root][i].L+tree[root][i].R);
59         if(ans==-1)
60             printf("-1\n");
61         else
62             printf("%.10lf\n",ans);
63     }
64 }

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