Codeforces Round #277 (Div. 2) E. LIS of Sequence DP
E. LIS of Sequence
Time Limit: 20 Sec
Memory Limit: 256 MB
题目连接
http://codeforces.com/contest/486/problem/E
Description
Nam created a sequence a consisting of n (1 ≤ n ≤ 105) elements a1, a2, ..., an (1 ≤ ai ≤ 105). A subsequence ai1, ai2, ..., aik where 1 ≤ i1 < i2 < ... < ik ≤ n is called increasing if ai1 < ai2 < ai3 < ... < aik. An increasing subsequence is called longest if it has maximum length among all increasing subsequences.
Nam realizes that a sequence may have several longest increasing subsequences. Hence, he divides all indexes i (1 ≤ i ≤ n), into three groups:
group of all i such that ai belongs to no longest increasing subsequences.
group of all i such that ai belongs to at least one but not every longest increasing subsequence.
group of all i such that ai belongs to every longest increasing subsequence.
Since the number of longest increasing subsequences of a may be very large, categorizing process is very difficult. Your task is to help him finish this job.
Input
The first line contains the single integer n (1 ≤ n ≤ 105) denoting the number of elements of sequence a.
The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 105).
Output
Print a string consisting of n characters. i-th character should be '1', '2' or '3' depending on which group among listed above index i belongs to.
Sample Input
4
1 3 2 5
Sample Output
3223
HINT
题意
给你n个数
然后问你这里面的每个数,是否是
1.不属于任何最长上升子序列中
2.属于多个最长上升子序列中
3.唯一属于一个最长上升子序列中
题解:
对于每一个数,维护两个dp
dp1表示1到i的最长上升子序列长度
dp2表示从n到i最长递减子序列长度
然后如果dp1[i]+dp2[i] - 1 == lis ,就说明属于lis里面,如果dp1[i]的值是唯一的,就说明唯一属于一个lis
否则就不属于咯
代码
#include<iostream>
#include<stdio.h>
#include<map>
#include<cstring>
#include<algorithm>
using namespace std;
#define maxn 100005
int b[maxn];
int a[maxn];
void add(int x,int val)
{
while(x<=)
{
b[x] = max(b[x],val);
x += x & (-x);
}
}
int get(int x)
{
int ans = ;
while(x)
{
ans = max(ans,b[x]);
x -= x & (-x);
}
return ans;
}
int dp1[maxn];
int dp2[maxn];
int ans[maxn];
map<int,int> H;
int main()
{
int n;scanf("%d",&n);
int LIS = ;
for(int i=;i<=n;i++)
{
scanf("%d",&a[i]);
dp1[i] = + get(a[i]-);
add(a[i],dp1[i]);
LIS = max(LIS,dp1[i]);
}
reverse(a+,a++n);
memset(b,,sizeof(b));
for(int i=;i<=n;i++)
{
a[i] = - a[i] + ;
dp2[i] = + get(a[i] - );
add(a[i],dp2[i]);
}
reverse(dp2+,dp2++n);
for(int i=;i<=n;i++)
{
if(dp1[i]+dp2[i]-!=LIS)ans[i]=;
else H[dp1[i]]++;
}
for(int i=;i<=n;i++)
{
if(ans[i]!=&&H[dp1[i]]==)
{
ans[i]=;
}
}
for(int i=;i<=n;i++)
if(ans[i]==)
cout<<"";
else if(ans[i]==)
cout<<"";
else if(ans[i]==)
cout<<"";
}
/*
10
2 2 2 17 8 9 10 17 10 5
*/
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