POJ 3378 Crazy Thairs（树状数组优化）

题目链接：http://poj.org/problem?id=3378

题意：给出一个数列，求有多少长度为5的上升子列？

思路：首先离散化，c[i][j]表示以数字i结束的长度为j的子列有多少个。

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <cmath>
#include <vector>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <map>


#define max(x,y) ((x)>(y)?(x):(y))
#define min(x,y) ((x)<(y)?(x):(y))
#define abs(x) ((x)>=0?(x):-(x))
#define i64 long long
#define u32 unsigned int
#define u64 unsigned long long
#define clr(x,y) memset(x,y,sizeof(x))
#define CLR(x) x.clear()
#define ph(x) push(x)
#define pb(x) push_back(x)
#define Len(x) x.length()
#define SZ(x) x.size()
#define PI acos(-1.0)
#define sqr(x) ((x)*(x))
#define MP(x,y) make_pair(x,y)
#define EPS 1e-9

#define FOR0(i,x) for(i=0;i<x;i++)
#define FOR1(i,x) for(i=1;i<=x;i++)
#define FOR(i,a,b) for(i=a;i<=b;i++)
#define FORL0(i,a) for(i=a;i>=0;i--)
#define FORL1(i,a) for(i=a;i>=1;i--)
#define FORL(i,a,b)for(i=a;i>=b;i--)
using namespace std;


void RD(int &x){scanf("%d",&x);}
void RD(u32 &x){scanf("%u",&x);}
void RD(double &x){scanf("%lf",&x);}
void RD(int &x,int &y){scanf("%d%d",&x,&y);}
void RD(u32 &x,u32 &y){scanf("%u%u",&x,&y);}
void RD(double &x,double &y){scanf("%lf%lf",&x,&y);}
void RD(int &x,int &y,int &z){scanf("%d%d%d",&x,&y,&z);}
void RD(int &x,int &y,int &z,int &t){scanf("%d%d%d%d",&x,&y,&z,&t);}
void RD(u32 &x,u32 &y,u32 &z){scanf("%u%u%u",&x,&y,&z);}
void RD(double &x,double &y,double &z){scanf("%lf%lf%lf",&x,&y,&z);}
void RD(char &x){x=getchar();}
void RD(char *s){scanf("%s",s);}
void RD(string &s){cin>>s;}


void PR(int x) {printf("%d\n",x);}
void PR(int x,int y) {printf("%d %d\n",x,y);}
void PR(i64 x) {printf("%lld\n",x);}
void PR(u32 x) {printf("%u\n",x);}
void PR(double x) {printf("%.5lf\n",x);}
void PR(char x) {printf("%c\n",x);}
void PR(char *x) {printf("%s\n",x);}
void PR(string x) {cout<<x<<endl;}


const i64 MOD=10000000;
class BigNum
{
public:
    int a[10];

    BigNum operator+(BigNum temp)
    {
        BigNum ans;
        int i,j,k,p;
        if(a[0]>temp.a[0]) p=a[0];
        else p=temp.a[0];
        for(i=a[0],j=temp.a[0],k=p;j>=1&&i>=1;i--,j--,k--)
        {
            ans.a[k]=a[i]+temp.a[j];
        }
        if(j==0)
        {
            while(i>=1) ans.a[i]=a[i--];
        }
        else
        {
            while(j>=1) ans.a[j]=temp.a[j--];
        }
        ans.a[0]=0;
        for(i=p;i>=1;i--)
        {
            ans.a[i-1]+=ans.a[i]/MOD;
            ans.a[i]%=MOD;
        }
        if(ans.a[0])
        {
            for(i=p+1;i>=1;i--) ans.a[i]=ans.a[i-1];
            ans.a[0]=p+1;
        }
        else ans.a[0]=p;
        return ans;
    }

    BigNum()
    {
        a[0]=1;
        a[1]=0;
    }

    BigNum(int x)
    {
        if(x>=MOD) a[0]=2,a[1]=x/MOD,a[2]=x%MOD;
        else a[0]=1,a[1]=x;
    }

    void print()
    {
        int i=1;
        while(i<=a[0]&&a[i]==0) i++;
        if(i>a[0])
        {
            puts("0");
            return;
        }
        printf("%d",a[i++]);
        while(i<=a[0]) printf("%07d",a[i++]);
    }
};


const int N=50005;
int a[N],b[N];
BigNum c[N][6];
int n,M;


int find(int low,int high,int x)
{
    int mid;
    while(low<=high)
    {
        mid=(low+high)>>1;
        if(b[mid]==x) return mid;
        if(b[mid]>x) high=mid-1;
        else low=mid+1;
    }
}


BigNum get(int x,int t)
{
    BigNum ans=BigNum(0);
    while(x>0)
    {
        ans=ans+c[x][t];
        x-=x&-x;
    }
    return ans;
}


void update(int x,int t,BigNum temp)
{
    while(x<M)
    {
        c[x][t]=c[x][t]+temp;
        x+=x&-x;
    }
}

int main()
{
    while(scanf("%d",&n)!=-1)
    {
        int i,j;
        FOR0(i,n) RD(a[i]),b[i]=a[i];
        sort(b,b+n);
        int x=unique(b,b+n)-b;
        FOR0(i,n) a[i]=find(0,x-1,a[i])+1;
        FOR1(i,M) FOR0(j,6) c[i][j]=BigNum(0);
        M=x+2;
        BigNum temp,ans=BigNum(0);
        FOR0(i,n)
        {
            FORL1(j,4)
            {
                temp=get(a[i]-1,j);
                update(a[i],j+1,temp);
            }
            update(a[i],1,BigNum(1));
        }
        temp=get(M-1,5);
        temp.print();
        puts("");
    }
    return 0;
}