UVA 10534 Wavio Sequence(LIS)

题意：给定一个长度为n的整数序列，求一个最长子序列，使得该序列的长度为2*k+1，前k+1个数严格递增，后k+1个数严格递减。

分析：用O(nlogn)分别求出递增序列和递减序列，再O(n)求在某个位置符合条件的序列长度。

/*
Author:Zhaofa Fang
Lang:C++
*/
#include <cstdio>
#include <cstdlib>
#include <sstream>
#include <iostream>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <string>
#include <utility>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
using namespace std;

typedef long long ll;
#define DEBUG(x) cout<< #x << ':' << x << endl
#define REP(i,n) for(int i=0;i < (n);i++)
#define FOR(i,s,t) for(int i = (s);i <= (t);i++)
#define PII pair<int,int>
#define PB push_back
#define MP make_pair
#define FI first
#define SE second
#define lowbit(x) (x&(-x))
#define INF (1<<30)

const int maxn = 10011;
int a[maxn];
int g1[maxn],g2[maxn];
int d1[maxn],d2[maxn];
int mx1[maxn],mx2[maxn];
int main()
{
    //freopen("in","r",stdin);
    int n;
    while(~scanf("%d",&n))
    {
        for(int i=0;i<n;i++)scanf("%d",&a[i]);
        for(int i=1;i<=n;i++)g1[i] = g2[i] = INF;
        memset(mx1,0,sizeof(mx1));
        memset(mx2,0,sizeof(mx2));
        for(int i=0;i<n;i++)
        {
            int k = lower_bound(g1+1,g1+n+1,a[i]) - g1;
            g1[k] = a[i];
            d1[i] = k;
        }
        for(int i=n-1;i>=0;i--)
        {
            int k = lower_bound(g2+1,g2+n+1,a[i]) - g2;
            g2[k] = a[i];
            d2[i] = k;
        }
        mx1[0] = d1[0];
        for(int i=1;i<n;i++)mx1[i] = max(mx1[i-1],d1[i]);
        for(int i=n-1;i>=0;i--)mx2[i] = max(mx2[i+1],d2[i]);
        int ans = 0;
        for(int i=0;i<n;i++)
        {
            int tmp = min(mx1[i],mx2[i]);
            ans = max(ans,(tmp-1)*2+1);
            //DEBUG(i);
            //DEBUG(mx1[i]);DEBUG(mx2[i]);DEBUG(ans);
        }
        printf("%d\n",ans);
    }
    return 0;
}