Codeforces Round #384 (Div. 2) E. Vladik and cards 状压dp
E. Vladik and cards
题目链接
http://codeforces.com/contest/743/problem/E
题面
Vladik was bored on his way home and decided to play the following game. He took n cards and put them in a row in front of himself. Every card has a positive integer number not exceeding 8 written on it. He decided to find the longest subsequence of cards which satisfies the following conditions:
the number of occurrences of each number from 1 to 8 in the subsequence doesn't differ by more then 1 from the number of occurrences of any other number. Formally, if there are ck cards with number k on them in the subsequence, than for all pairs of integers the condition |ci - cj| ≤ 1 must hold.
if there is at least one card with number x on it in the subsequence, then all cards with number x in this subsequence must form a continuous segment in it (but not necessarily a continuous segment in the original sequence). For example, the subsequence [1, 1, 2, 2] satisfies this condition while the subsequence [1, 2, 2, 1] doesn't. Note that [1, 1, 2, 2] doesn't satisfy the first condition.
Please help Vladik to find the length of the longest subsequence that satisfies both conditions.
输入
The first line contains single integer n (1 ≤ n ≤ 1000) — the number of cards in Vladik's sequence.
The second line contains the sequence of n positive integers not exceeding 8 — the description of Vladik's sequence.
输出
Print single integer — the length of the longest subsequence of Vladik's sequence that satisfies both conditions.
样例输入
3
1 1 1
样例输出
1
题意
给你n个数字,你需要找到一个最长的子序列,满足以下要求:
1.对于每个i和j,要求abs(num[i]-num[j])<=1,num[i]表示这个数字i出现的次数
2.所有相同的数字应该挨在一起。
求最长的子序列长度
题解
枚举每个数字的长度num,那么显然每个数字要么是num,要么就是num+1
然后我们对于每个长度进行check就好了
dp[i][j]表示当前状态为i的时候,其中有i个数的长度为num+1,用一个next进行转移就好了
next[i][j][k]表示从i开始,j出现k次的位置是啥位置。
代码
#include<bits/stdc++.h>
using namespace std;
const int maxn = 1050;
int dp[maxn][9];
int nxt[maxn][9][maxn],a[maxn],n,cnt[9];
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;i++)
scanf("%d",&a[i]);
for(int i=1;i<=n;i++){
for(int j=1;j<=8;j++)cnt[j]=0;
for(int j=1;j<=8;j++)for(int k=1;k<=n;k++)
nxt[i][j][k]=1e9;
for(int j=i;j<=n;j++){
cnt[a[j]]++;
nxt[i][a[j]][cnt[a[j]]]=j;
}
}
int ans=0;
for(int num=0;num*8<=n;num++){
for(int i=0;i<256;i++)
for(int k=0;k<=8;k++)
dp[i][k]=1e9;
dp[0][0]=1;
for(int i=0;i<256;i++){
for(int j=0;j<=8;j++){
for(int k=1;k<=8;k++){
if((1<<(k-1))&i)continue;
if(dp[i][j]>n)continue;
dp[i^(1<<(k-1))][j]=min(dp[i^(1<<(k-1))][j],nxt[dp[i][j]][k][num]+1);
dp[i^(1<<(k-1))][j+1]=min(dp[i^(1<<(k-1))][j+1],nxt[dp[i][j]][k][num+1]+1);
}
}
}
for(int i=0;i<=8;i++)if(dp[255][i]<=n+1)ans=max(ans,8*num+i);
}
cout<<ans<<endl;
}
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