E. Thematic Contests【dp】
E. Thematic Contests
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
Polycarp has prepared nn competitive programming problems. The topic of the ii-th problem is aiai, and some problems' topics may coincide.
Polycarp has to host several thematic contests. All problems in each contest should have the same topic, and all contests should have pairwise distinct topics. He may not use all the problems. It is possible that there are no contests for some topics.
Polycarp wants to host competitions on consecutive days, one contest per day. Polycarp wants to host a set of contests in such a way that:
- number of problems in each contest is exactly twice as much as in the previous contest (one day ago), the first contest can contain arbitrary number of problems;
- the total number of problems in all the contests should be maximized.
Your task is to calculate the maximum number of problems in the set of thematic contests. Note, that you should not maximize the number of contests.
Input
The first line of the input contains one integer n (1≤n≤2⋅105) — the number of problems Polycarp has prepared.
The second line of the input contains nn integers a1,a2,…,an (1≤ai≤109) where aiai is the topic of the ii-th problem.
Output
Print one integer — the maximum number of problems in the set of thematic contests.
Examples
input
18
2 1 2 10 2 10 10 2 2 1 10 10 10 10 1 1 10 10
output
14
input
10
6 6 6 3 6 1000000000 3 3 6 6
output
9
input
3
1337 1337 1337
output
3
Note
In the first example the optimal sequence of contests is: 22 problems of the topic 11, 44 problems of the topic 22, 88 problems of the topic 1010.
In the second example the optimal sequence of contests is: 33 problems of the topic 33, 66 problems of the topic 66.
In the third example you can take all the problems with the topic 13371337 (the number of such problems is 33 so the answer is 33) and host a single contest.
題意：
Ñ個問題，每個問題對應一個主題，每一天的問題的主題要保證全部一樣，每一天的問題數量是前一天的兩倍，要求任何兩天的
主題是一樣的，求最大的問題數目。
分析：
先按數目排序，dp [i]代表滿足最後一天的問題數量是i，所能滿足條件的最大問題數量。
例如DP [I] = DP [I / 2] + I; DP [i]於可能是4 + 8 + 16 + I組成的，
類似多重揹包
程式碼：
#include<bits/stdc++.h>
#define ll long long
#define mod 1000000007
using namespace std;
int a[210005],dp[210005],b[2100005],n;
int main()
{
int i,j,maxn,num;
maxn=1;
scanf("%d",&n);
for(i=0;i<n;i++)scanf("%d",&a[i]);
sort(a,a+n);
int str=0;
num=0;
for(i=1;i<n;i++)
{
if(a[i]!=a[i-1])
{
b[num++]=i-str;
str=i;
}
}
b[num++]=i-str;
sort(b,b+num);
for(i=0;i<num;i++)
{
for(j=b[i];j;j--)
{
if(j%2==0)
dp[j]=max(dp[j],dp[j/2]+j);
else
dp[j]=j;
maxn=max(maxn,dp[j]);
}
}
printf("%d\n",maxn);
}