HDU-6592

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题意

给一个序列 $a[]$ ，找出最长的单峰序列，输出该序列的下标，输出字典序最大和最小的情况

题解

易证，当取第一个峰的时候字典序最小，当取最后一个峰的时候字典序最大。

代码

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#include <bits/stdc++.h>
using namespace std;
#define forl(i, l, r) for (int i = l; i <= r; i++)
#define forr(i, r, l) for (int i = r; i >= l; i--)
#define for1(i, n) for (int i = 1; i <= n; i++)
#define fro1(i, n) for (int i = 1; i <= n; i++)
#define for0(i, n) for (int i = 0; i < n; i++)
#define fro0(i, n) for (int i = 0; i < n; i++)
#define meminf(a) memset(a, inf, sizeof(a))
#define mem_1(a) memset(a, -1, sizeof(a))
#define mem0(a) memset(a, 0, sizeof(a))
#define memcp(a,b) memcpy(a,b,sizeof(b))
#define oper(type) bool operator <(const type y)const
#define mp make_pair
#define pu_b push_back
#define pu_f push_front
#define po_b pop_back
#define po_f pop_front
#define fi first
#define se second
#define whiel while
#define retrun return
typedef pair<long long, long long> pll;
typedef vector<long long> vll;
typedef pair<int, int> pii;
typedef unsigned long long ull;
typedef vector<int> vii;
typedef double db;
typedef long long ll;
typedef int itn;
int in(int &a,int &b,int &c,int &d){return scanf("%d%d%d%d",&a,&b,&c,&d);}
int in(int &a,int &b,int &c){return scanf("%d%d%d",&a,&b,&c);}
int in(int &a,int &b){return scanf("%d%d",&a,&b);}
int in(ll &a){return scanf("%lld",&a);}
int in(int &a){return scanf("%d",&a);}
int in(char *s){return scanf("%s",s);}
int in(char &s){return scanf("%c",&s);}
int in(db &a){return scanf("%lf",&a);}
void out(int a){printf("%d ",a);}
void outln(int a){printf("%d\n",a);}
void out(ll a){printf("%lld ",a);}
void outln(ll a){printf("%lld\n",a);}
const db pi = acos((db)-1);
const ll inf =0x3f3f3f3f;
const db eps = 1e-8;
const int N = 3.1e5;
const int M = 2.1e5;
const ll mod = 1e9+7;
int sign(db a) { return a < -eps ? -1 : a > eps;}
int db_cmp(db a, db b){ return sign(a-b); }

int a[N],f[N],g[N],pre[N],ans[N];
int main() {
#ifdef PerpEternal
    // freopen("/Users/perpeternal/Documents/Sketch/data/in.dat", "r", stdin);
    // freopen("/Users/perpeternal/Documents/Sketch/data/out.dat", "w", stdout);
#endif
    //ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    int n;
    while(~in(n)){
        for1(i,n)in(a[i]);
        int len=0;
        for1(i,n){
            int posi=upper_bound(pre+1,pre+1+len,a[i])-pre;
            // out(posi);
            if(posi==len+1){
                if(a[i]>pre[len]){
                    pre[++len]=a[i];
                    f[i]=len;
                }else f[i]=len;
            }else{
                if(a[i]>pre[posi-1]){
                    pre[posi]=a[i];
                    f[i]=posi;
                }else{
                    f[i]=posi-1;
                }
            }
        }
        // puts(""/);
        len=0;
        for1(i,n){
            int j=n-i+1;
            int posi=upper_bound(pre+1,pre+1+len,a[j])-pre;
            if(posi==len+1){
                if(a[j]>pre[len]){
                    pre[++len]=a[j];
                    g[j]=len;
                }else g[j]=len;
            }else{
                if(a[j]>pre[posi-1]){
                    pre[posi]=a[j];
                    g[j]=posi;
                }else{
                    g[j]=posi-1;
                }
            }
        }
        int maxx=0,Fi=0,La=0;
        for1(i,n)maxx=max(maxx,f[i]+g[i]-1);
        for1(i,n){
            if(f[i]+g[i]-1==maxx){
                if(!Fi)Fi=i;
                La=i;
            }
        }

        int tail=f[Fi];
        ans[tail]=Fi;
        for(int i=Fi-1;i>0;i--){
            if(f[i]+1>=tail&&f[i]<f[Fi]){
                if(a[ans[f[i]+1]]>a[i]){
                    tail=f[i];
                    ans[f[i]]=i;
                }
            }
        }
        // assert(tail==1);
        tail=f[Fi];
        // cout<<tail<<endl;
        for(int i=Fi+1;i<=n;i++){
            if(a[i]<a[ans[tail]]&&g[i]+1==g[ans[tail]]){
                ans[++tail]=i;
            }
        }
        for1(i,maxx){
            printf("%d%c",ans[i]," \n"[i==maxx]);
        }


        tail=maxx-g[La]+1;
        ans[tail]=La;
        for(int i=La+1;i<=n;i++){
            if(g[i]+tail>=maxx&&g[i]<g[La]){
                if(a[ans[maxx-g[i]]]>a[i]){
                    tail=maxx-g[i]+1;
                    ans[tail]=i;
                }
            }
        }
        // assert(tail==maxx);
        tail=maxx-g[La]+1;
        for(int i=La-1;i>0;i--){
            if(a[i]<a[ans[tail]]&&f[i]+1==f[ans[tail]]){
                ans[--tail]=i;
            }
        }
        for1(i,maxx){
            printf("%d%c",ans[i]," \n"[i==maxx]);
        }
    }
    return 0;
}