HDU/杭电2013多校第三场解题报告

今天悲剧了,各种被虐啊,还是太年轻了哭

Crime

这道题目给的时间好长,第一次就想到了暴力,结果华丽丽的TLE了。

后来找了一下,发现前24个是1, 2, 6, 12, 72, 72, 864, 1728, 13824, 22032, 555264, 476928, 17625600, 29599488, 321115392, 805146624, 46097049600, 36481536000, 2754120268800, 3661604352000, 83905105305600, 192859121664000, 20092043520000000, 15074060547686400。这样我们就需要找到递推的式子。可是怎么也推不出。请路过的大神指教。。。

JZPTREE

这道题目是我看的,题目挺好懂的,就是数据量太大。不知道怎么写,最后想尽办法也只能压缩到十二亿。果断不行,怎么优化呢?

Jinkeloid

深坑....

The Unsolvable Problem

这道题目是过的最多的了题目了。就是that a + b = n and [a, b] is as large as possible. [a, b] denote the least common multiplier of a, b.这样的话就直接求就行了。是偶数的话变成前后值,否则前后判:

#include <iostream>
#include <cstdio>
#include <string>
#include <string.h>
#include <map>
#include <vector>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <queue>
#include <set>
#include <stack>
using namespace std;

int main()
{
    int t;
    __int64 n;
    cin>>t;
    while(t--)
    {
        cin>>n;
        if(n==2)
        {
            cout<<1<<endl;
            continue;
        }
        if(n%2==1)
        {
            cout<<(n/2)*(n/2+1)<<endl;
        }
        else
        {
            if((n/2)%2==0)
            {
                cout<<(n/2-1)*(n/2+1)<<endl;
            }
            else
            {
                cout<<(n/2-2)*(n/2+2)<<endl;
            }
        }
    }
    return 0;
}

Pieces

这是经次于上一道出的最多的题了。就是把一个字符串变空。用的方法就是每次去一个回文串,直到取空。唯一的要求就是最后操作的次数要最小。这道题目需要考虑每次操作之后对后续的影响,不能直接求最长的回文串,可能后面就会因为这次操作而增加了操作次数;

Burning

一道几何题目,特判,精度...

Sad Love Story

这道题目T到死了。先用最近点对的方法求了,TTT。后来有交KD-tree的,结果也T了,这不科学啊,20S额。这:

#include <iostream>
#include <cstdio>
#include <string>
#include <string.h>
#include <map>
#include <vector>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <cmath>
#include <queue>
#include <set>
#include <stack>
using namespace std;
// 分治算法求最近点对

struct point
{
    __int64 x , y;
} p[500005],pp[500005];

__int64 a[500005];    //保存筛选的坐标点的索引

__int64 cmpx(const point &a , const point &b)
{
    return a.x < b.x;
}
__int64 cmpy(__int64 a , __int64 b)    //这里用的是下标索引
{
    return p[a].y < p[b].y;
}
inline __int64 dis(point &a , point &b)
{
    return  (a.x-b.x)*(a.x-b.x) + (a.y-b.y)*(a.y-b.y);
}
inline __int64 min(__int64 a , __int64 b)
{
    return a < b ? a : b;
}
__int64 closest(__int64 low , __int64 high)
{
    if(low + 1 == high)
        return dis(p[low] , p[high]);
    if(low + 2 == high)
        return min(dis(p[low] , p[high]) , min( dis(p[low] , p[low+1]) , dis(p[low+1] , p[high]) ));
    __int64 mid = (low + high)>>1;//求中点
    __int64 ans = min( closest(low , mid) , closest(mid + 1 , high) );    //分治法进行递归求解
    __int64 i , j , cnt = 0;
    for(i = low ; i <= high ; ++i)   //把x坐标在p[mid].x-ans~p[mid].x+ans范围内的点取出来
    {
        if(p[i].x >= p[mid].x - ans && p[i].x <= p[mid].x + ans)
            a[cnt++] = i;       //保存的是下标索引
    }
    sort(a,a + cnt,cmpy);   //按y坐标进行升序排序
    for(i = 0 ; i < cnt ; ++i)
    {
        for(j = i+1 ; j < cnt ; ++j)
        {
            if(p[a[j]].y - p[a[i]].y >= ans)   //注意下标索引
                break;
            ans = min(ans , dis(p[a[i]] , p[a[j]]));
        }
    }
    return ans;
}
int main()
{
    __int64 t;
    scanf("%I64d", &t);
    __int64 n, ax, bx,cx,ay,by,cy;
    __int64 ans = 0;
    while(t--)
    {
        ans = 0;
        scanf("%I64d", &n);
        scanf("%I64d%I64d%I64d%I64d%I64d%I64d", &ax,&bx,&cx,&ay,&by,&cy);
        for(int i = 0; i < n; ++i)
        {
            if(i==0)
            {
                pp[i].x = (0*ax+bx)%cx;
                pp[i].y = (0*ay+by)%cy;
            }
            else
            {
                pp[i].x = (pp[i-1].x*ax+bx)%cx;
                pp[i].y = (pp[i-1].y*ay+by)%cy;
                int tp = i;
                for(int kp = 0; kp <= i; ++kp)
                {
                    p[kp].x = pp[kp].x;
                    p[kp].y = pp[kp].y;
                }
                sort(p , p+tp+1 , cmpx);
                ans += closest(0 , tp);
            }
        }
        printf("%I64d
", ans);
    }
    return 0;
}

KD-tree

#include <iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
#define D 2
#define N 500010
const int inf=1000000001;
const long long Inf=1ll*inf*inf;
struct kdnode
{
    int x[D];
    int split;
    int l,r,p;
} kdtree[N],q[N];
bool operator==(const kdnode &a,const kdnode &b)
{
    for(int i=0; i<D; i++)
    {
        if(a.x[i]!=b.x[i])return false;
    }
    return true;
}
double avg[D],var[D];
int n;
void calAvg(int l,int r)
{
    for(int i=0; i<D; i++)avg[i]=0;
    for(int i=l; i<=r; i++)
        for(int j=0; j<D; j++)
            avg[j]+=1.0*kdtree[i].x[j]/(r-l+1);
}
void calVar(int l,int r)
{
    for(int i=0; i<D; i++)var[i]=0;
    for(int i=l; i<=r; i++)
        for(int j=0; j<D; j++)
            var[j]+=1.0*(kdtree[i].x[j]-avg[j])/n*(kdtree[i].x[j]-avg[j]);
}
int splitD;
double maxVar;
bool cmp(kdnode a,kdnode b)
{
    return a.x[splitD]<b.x[splitD];
}
int construct(int p,int l,int r)
{
    if(r<l)return -1;
    int root=(l+r)/2;
    calAvg(l,r);
    calVar(l,r);
    maxVar=-1.0;
    for(int i=0; i<D; i++)
        if(var[i]>maxVar)
            maxVar=var[i],splitD=i;
    sort(kdtree+l,kdtree+r+1,cmp);
    kdtree[root].split=splitD;
    kdtree[root].l=construct(root,l,root-1);
    kdtree[root].r=construct(root,root+1,r);
    kdtree[root].p=p;
    return root;
}
int Find(int root,kdnode x)
{
    if(root==-1)return -1;
    if(x==kdtree[root])
    {
        return root;
    }
    int d=kdtree[root].split;
    if(x.x[d]>kdtree[root].x[d])
    {
        return Find(kdtree[root].r,x);
    }
    else if(x.x[d]<kdtree[root].x[d])
    {
        return Find(kdtree[root].l,x);
    }
    else
    {
        int l=Find(kdtree[root].l,x);
        int r=Find(kdtree[root].r,x);
        return (l==-1?r:l);
    }
}
int FindMin(int root,int d)
{
    int ret=root;
    if(kdtree[root].l!=-1)
    {
        int v=FindMin(kdtree[root].l,d);
        if(kdtree[ret].x[d]>kdtree[v].x[d])
            ret=v;
    }
    if(kdtree[root].r!=-1)
    {
        int v=FindMin(kdtree[root].r,d);
        if(kdtree[ret].x[d]>kdtree[v].x[d])
            ret=v;
    }
    return ret;
}
int FindMax(int root,int d)
{
    int ret=root;
    if(kdtree[root].l!=-1)
    {
        int v=FindMax(kdtree[root].l,d);
        if(kdtree[ret].x[d]<kdtree[v].x[d])
            ret=v;
    }
    if(kdtree[root].r!=-1)
    {
        int v=FindMax(kdtree[root].r,d);
        if(kdtree[ret].x[d]<kdtree[v].x[d])
            ret=v;
    }
    return ret;
}
void DeleteNode(int v)
{
    int p=kdtree[v].p;
    kdtree[v].p=-1;
    if(kdtree[p].l==v)
        kdtree[p].l=-1;
    else
        kdtree[p].r=-1;
}
void Remove(int root,kdnode x)
{
    int pos=Find(root,x);
    if(kdtree[pos].l==-1&&kdtree[pos].r==-1)
    {
        DeleteNode(pos);
    }
    else if(kdtree[pos].l==-1)
    {
        int alt=FindMin(kdtree[pos].r,kdtree[pos].split);
        for(int i=0; i<D; i++)kdtree[pos].x[i]=kdtree[alt].x[i];
        Remove(alt,kdtree[alt]);
    }
    else
    {
        int alt=FindMax(kdtree[pos].l,kdtree[pos].split);
        for(int i=0; i<D; i++)kdtree[pos].x[i]=kdtree[alt].x[i];
        Remove(alt,kdtree[alt]);
    }
}
void Insert(int root,int x)
{
    int d=kdtree[root].split;
    if(kdtree[root].x[d]<kdtree[x].x[d])
    {
        if(kdtree[root].r==-1)
        {
            kdtree[root].r=x;
            kdtree[x].p=root;
        }
        else Insert(kdtree[root].r,x);
    }
    else
    {
        if(kdtree[root].l==-1)
        {
            kdtree[root].l=x;
            kdtree[x].p=root;
        }
        else Insert(kdtree[root].l,x);
    }
}
void Add(int root,kdnode x)
{
    int pos=n;
    kdtree[n++]=x;
    Insert(root,pos);
}

long long dist(kdnode a,kdnode b)
{
    long long ret=0;
    for(int i=0; i<D; i++)
    {
        ret+=1ll*(a.x[i]-b.x[i])*(a.x[i]-b.x[i]);
    }
    return ret;
}
long long query(int root,kdnode x)
{
    if(root==-1)return Inf;
    int d=kdtree[root].split;
    long long ret;
    if(x.x[d]<kdtree[root].x[d])
    {
        ret=query(kdtree[root].l,x);
        double dd=1.0*x.x[d]+sqrt(1.0*ret);
        if(dd>=1.0*kdtree[root].x[d])
        {
            ret=min(ret,query(kdtree[root].r,x));
        }
    }
    else if(x.x[d]>kdtree[root].x[d])
    {
        ret=query(kdtree[root].r,x);
        double dd=1.0*x.x[d]-sqrt(1.0*ret);
        if(dd<=1.0*kdtree[root].x[d])
        {
            ret=min(ret,query(kdtree[root].l,x));
        }
    }
    else
    {
        ret=query(kdtree[root].l,x);
        ret=min(ret,query(kdtree[root].r,x));
    }
    ret=min(ret,dist(kdtree[root],x));
    return ret;
}

int main()
{
   // freopen("in","w",stdout);
    int t;
    long long px,py;
    long long  ax,bx,cx,ay,by,cy;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        px=py=0;
        scanf("%I64d%I64d%I64d%I64d%I64d%I64d",&ax,&bx,&cx,&ay,&by,&cy);
        px=(ax*px+bx)%cx;
        py=(ay*py+by)%cy;
       // puts("fdsf");
        for(int i=0; i<1; i++)
        {
            kdtree[i].split=0;
            kdtree[i].p=kdtree[i].l=kdtree[i].r=-1;
            kdtree[i].x[0]=px;
            kdtree[i].x[1]=py;
            q[i]=kdtree[i];
          //  cout<<px<<" "<<py<<endl;
        }
        int root=construct(-1,0,0);

            px=(ax*px+bx)%cx;
            py=(ay*py+by)%cy;
            q[1].split=0;
            q[1].p=q[1].l=q[1].r=-1;
            q[1].x[0]=px;
            q[1].x[1]=py;
        //     cout<<px<<" "<<py<<endl;
            long long mindis=query(root,q[1]);
            long long ans=mindis;
              Add(root,q[1]);
           // cout<<mindis<<endl;
           // printf("%I64d
",mindis);
        int m=n;
        for(int i=3; i<m; i++)
        {
           // printf("%d %d
",i,n);
            px=(ax*px+bx)%cx;
            py=(ay*py+by)%cy;
            q[i].split=0;
            q[i].p=q[i].l=q[i].r=-1;
            q[i].x[0]=px;
            q[i].x[1]=py;
            mindis=min(mindis,query(root,q[i]));
            if(mindis==0LL)break;
            ans+=mindis;
            Add(root,q[i]);
        }
        printf("%I64d
",ans);
    }
    return 0;
}

不淡定了....



原文地址:https://www.cnblogs.com/riskyer/p/3225868.html