HDU 6070 二分+线段树

Dirt Ratio

Time Limit: 18000/9000 MS (Java/Others)    Memory Limit: 524288/524288 K (Java/Others)
Total Submission(s): 335    Accepted Submission(s): 105
Special Judge

Problem Description

In ACM/ICPC contest, the ''Dirt Ratio'' of a team is calculated in the following way. First let's ignore all the problems the team didn't pass, assume the team passed Xproblems during the contest, and submitted Y times for these problems, then the ''Dirt Ratio'' is measured as XY. If the ''Dirt Ratio'' of a team is too low, the team tends to cause more penalty, which is not a good performance.

Picture from MyICPC

Little Q is a coach, he is now staring at the submission list of a team. You can assume all the problems occurred in the list was solved by the team during the contest. Little Q calculated the team's low ''Dirt Ratio'', felt very angry. He wants to have a talk with them. To make the problem more serious, he wants to choose a continuous subsequence of the list, and then calculate the ''Dirt Ratio'' just based on that subsequence.

Please write a program to find such subsequence having the lowest ''Dirt Ratio''.

 

Input

The first line of the input contains an integer T(1≤T≤15), denoting the number of test cases.

In each test case, there is an integer n(1≤n≤60000) in the first line, denoting the length of the submission list.

In the next line, there are n positive integers a1,a2,...,an(1≤ai≤n), denoting the problem ID of each submission.

 

Output

For each test case, print a single line containing a floating number, denoting the lowest ''Dirt Ratio''. The answer must be printed with an absolute error not greater than 10−4.

 

Sample Input

1

5

1 2 1 2 3

 

Sample Output

0.5000000000

Hint

For every problem, you can assume its final submission is accepted.

 

Source

2017 Multi-University Training Contest - Team 4

 

题意：给你一个长度为n的区间 X=区间不同数的个数 Y=区间长度  求子区间X/Y的最小值

题解：二分答案mid   check  X/Y<=mid

X/Y=X/(r-L+1)<=mid

=> X+L*mid<=(r+1)*mid

建树初始每个点的maxn为L*mid

从左向右遍历右边界 遍历到r  更新(last[r]+1,r) 值增加1  last[r]表示a[r]相同值的上一个位置

r之前的每个结点L存的是L到r不同数的个数X+L*mid (这些便是不等式的左边）取最小值 与 (r+1)*mid 比较

 #pragma comment(linker, "/STACK:102400000,102400000")
 #include <bits/stdc++.h>
 #include <cstdlib>
 #include <cstdio>
 #include <iostream>
 #include <cstdlib>
 #include <cstring>
 #include <algorithm>
 #include <cmath>
 #include <cctype>
 #include <map>
 #include <set>
 #include <queue>
 #include <bitset>
 #include <string>
 #include <complex>
 #define LL long long
 #define mod 1000000007
 using namespace std;
 int t;
 int n;
 int a[];
 int last[];
 map<int,int> mp;
 struct node
 {
     int l,r;
     double maxn;
     int add;
 } tree[];
 void buildtree(int root ,int left,int right,double zz)
 {
     tree[root].l=left;
     tree[root].r=right;
     tree[root].add=;
     if(left==right)
     {
         tree[root].maxn=left*zz;
         return ;
     }
     int mid=(left+right)>>;
     buildtree(root<<,left,mid,zz);
     buildtree(root<<|,mid+,right,zz);
     tree[root].maxn=min(tree[root<<].maxn,tree[root<<|].maxn);
 }
 void pushdown(int root)
 {
     if(tree[root].add==) return ;
     tree[root<<].add+=tree[root].add;
     tree[root<<|].add+=tree[root].add;
     tree[root<<].maxn+=tree[root].add;
     tree[root<<|].maxn+=tree[root].add;
     tree[root].add=;
 }
 void update(int root,int left,int right,int c)
 {
     if(tree[root].l==left&&tree[root].r==right)
     {
         tree[root].add+=c;
         tree[root].maxn+=c;
         return ;
     }
     pushdown(root);
     int mid=(tree[root].l+tree[root].r)>>;
     if(right<=mid)
     {
         update(root<<,left,right,c);
     }
     else
     {
         if(left>mid)
             update(root<<|,left,right,c);
         else
         {
             update(root<<,left,mid,c);
             update(root<<|,mid+,right,c);

         }
     }
     tree[root].maxn=min(tree[root<<].maxn,tree[root<<|].maxn);
 }
 double query(int root,int left,int right)
 {
     if(left>right)
         return ;
     if(tree[root].l==left&&tree[root].r==right)
     {
         return  tree[root].maxn;
     }
     pushdown(root);
     int mid=(tree[root].l+tree[root].r)>>;
     if(right<=mid)
         return query(root<<,left,right);
     else
     {
         if(left>mid)
             return query(root<<|,left,right);
         else
             return  min(query(root<<,left,mid),query(root<<|,mid+,right));
     }
 }
 bool check (double x)
 {
     buildtree(,,n,x);
     for(int i=; i<=n; i++)
     {
         update(,last[i]+,i,);
         double zha=(double)query(,,i);
         if(zha<=(i+)*x)
             return true;
     }
     return false;
 }
 int main()
 {
     scanf("%d",&t);
     for(int kk=;kk<=t;kk++){
     scanf("%d",&n);
     mp.clear();
     for(int i=; i<=n; i++){
         scanf("%d",&a[i]);
         last[i]=mp[a[i]];
         mp[a[i]]=i;
     }
     double l=,r=1.0,mid,ans;
     while(abs(l-r)>=0.00001)
     {
         mid=(l+r)/;
         if(check(mid)){
             ans=mid;
             r=mid;
         }
         else
           l=mid;
     }
     printf("%f\n",ans);
  }
     return ;
 }