Poj 3378 -- crazy thairs (tree array + dp + high precision) Data Structure Optimization DP

Crazy thairs

Time limit:3000 Ms		Memory limit:65536 K
Total submissions:6598		Accepted:1636

Description

These days, sepageris crazed on one problem named Crazy Thair. GivenN(1 ≤N≤ 50000) numbers, which are no more than 109, crazy Thair is a group of 5 numbers {I,J,K,L,M} Satisfying:

1. 1 ≤I<J<K<L<M≤N
2.AI<AJ<AK<Al<AM

For example, in the sequence {2, 1, 3, 4, 5, 7, 6}, there are four crazy Thair groups: {1, 3, 4, 5, 6}, {2, 3, 4, 5, 6}, {1, 3, 4, 5, 7} and {2, 3, 4, 5, 7 }.

Cocould you help sepr to count how many crazy thairs in the sequence?

Input

Input contains several test cases. Each test case begins with a line containing a numberN, Followed by a line containingNNumbers.

Output

Output The amount of crazy thairs in each sequence.

Sample Input

51 2 3 4 572 1 3 4 5 7 671 2 3 4 5 6 7

Sample output

1421

------------------Split line--------------------

Question:

Given n numbers, satisfy

1. 1 ≤ I <j <k <L <m ≤ n
2. AI <AJ <AK <Al <AM

Total number of solutions

Ideas:

DP [I] [J] indicates the number of solutions for the sequence with the ending length of J as I, DP [I] [J] = DP [I-1] [K], where a [k] Must be smaller than a [J]

Therefore, if you want to know the number of 5 tuples, you need to know the number of 4 tuples and the number of 3 tuples ........ when the length is 1, the number of solutions is 1

It is no longer appropriate to count the number of elements smaller than a [I] using a tree array.

The data range of each element is 9 to the power of 10, and the number given by the question is 50000. discretization is required.

And the combination of C (, 5) must exceed _ int64, so use high precision

#include<iostream>#include<cstring>#include<cstdio>#include<algorithm>#define M 50000+10#define ll long long#define local1using namespace std;int n,ans[50],f[M];ll c[4][M];struct node{    int x,index;    bool operator< (const node &A)const    {        return x<A.x;    }}a[M];void update(int x,ll v,int k){    for(int i=x;i<=n;i+=i&-i){        c[k][i]+=v;    }}ll getsum(int x,int k){    ll sum=0;    for(int i=x;i>0;i-=i&-i){        sum+=c[k][i];    }    return sum;}void add(ll s){    int t1[50],t2[50],k=0;    memset(t1,0,sizeof(t1));memset(t2,0,sizeof(t2));    while(s>0){        t2[k++]=s%10;        s/=10;    }    for(int i=0;i<50;++i){        t1[i]+=t2[i]+ans[i];        if(t1[i]>=10){            t1[i+1]=t1[i]/10;            t1[i]%=10;        }        ans[i]=t1[i];    }}int main(){#ifdef local    freopen("in.txt","r",stdin);    freopen("ou.txt","w",stdout);#endif // local    while(scanf("%d",&n)!=EOF){        memset(c,0,sizeof(c));memset(ans,0,sizeof(ans));        for(int i=0;i<n;++i){            scanf("%d",&a[i].x);            a[i].index=i;        }        sort(a,a+n);        int key=1;f[a[0].index]=1;        for(int i=1;i<n;++i){            if(a[i].x>a[i-1].x) f[a[i].index]=++key;            else f[a[i].index]=key;        }        for(int i=0;i<n;++i){            update(f[i],1,0);            for(int j=1;j<=3;++j){                update(f[i],getsum(f[i]-1,j-1),j);            }            add(getsum(f[i]-1,3));        }        int k=49;        for(;k>=0;--k){            if(ans[k]) break;        }        for(int i=k;i>=0;--i){            printf("%d",ans[i]);        }        printf("\n");    }    return 0;}

Poj 3378 -- crazy thairs (tree array + dp + high precision) Data Structure Optimization DP