hdu 4819 2013 Asia Regional Changchun G (四叉树|| 二维线段树单点更新 模板题)

Posted by 111qqz on Thursday, November 9, 2017

TOC

http://acm.hdu.edu.cn/showproblem.php?pid=4819

题意:

给你一个n*n的矩阵, 每个点是一个数字, Q个操作,每次选择一个子矩阵, 把中心元素替换成子矩阵中最大值和最小值之和的二分之一。

思路:

显然是一个二维线段树…..

然而菜鸡如我,并没有写过二维线段树啊?

那怎么办呢

一首《凉凉》送给自己

然而我们还有四叉树2333

2A,写错一个地方。第一次写四叉树,orz

#include <bits/stdc++.h>
#define ms(a,x) memset(a,x,sizeof(a))
#define lowbit(x) (x&(-x))
using namespace std;
typedef long long LL;
const double eps = 1e-8;
const double PI = acos(-1.0);
const int N=805;
int n;
int a[N][N];
struct Tree
{
    int mn,mx;
    Tree()
    {
        mn = 1E9;
        mx = 0;
    }
    void init()
    {
        mn = 1E9;
        mx = 0;
    }
}tree[N*10000];
int _max( int a,int b,int c,int d)
{
    int ret = max(a,b);
    ret = max(ret,c);
    ret = max(ret,d);
    return ret;
}
int _min( int a,int b,int c,int d)
{
    int ret = min(a,b);
    ret = min(ret,c);
    ret = min(ret,d);
    return ret;
}
void PushUp( int rt)
{
//  cout<<"rt:"<<rt<<endl;
    tree[rt].mn = _min(tree[rt*4+1].mn,tree[rt*4+2].mn,tree[rt*4+3].mn,tree[rt*4+4].mn);
    tree[rt].mx = _max(tree[rt*4+1].mx,tree[rt*4+2].mx,tree[rt*4+3].mx,tree[rt*4+4].mx);
}


void insert( int idx,int lx,int rx,int ly,int ry,int X,int Y,int val)
{
//  cout<<"val:"<<val<<endl;
    if (lx==rx&&ly==ry)
    {
        tree[idx].mn = tree[idx].mx = val;
//      cout<<"fuck"<<" val:"<<val<<" mn:"<<tree[idx].mn <<" mx:"<<tree[idx];
        return;
    }
    int mx = (lx+rx) >> 1;
    int my = (ly+ry) >> 1;
    if (X<=mx&&Y<=my) insert(idx*4+1,lx,mx,ly,my,X,Y,val);
    if (X<=mx&&Y>=my+1) insert(idx*4+2,lx,mx,my+1,ry,X,Y,val);
    if (X>=mx+1&&Y<=my) insert(idx*4+3,mx+1,rx,ly,my,X,Y,val);
    if (X>=mx+1&&Y>=my+1) insert(idx*4+4,mx+1,rx,my+1,ry,X,Y,val);
//  puts("miao");
    PushUp(idx);
}
int queryMN( int idx,int lx,int rx,int ly,int ry,int Lx,int Rx,int Ly,int Ry)
{
    if (Lx<=lx && Rx>=rx && Ly<=ly && Ry>=ry) return tree[idx].mn;
    int mx = (lx+rx)>>1,my = (ly+ry)>>1,t=1E9;
    if (Lx<=mx && Ly<=my)  t = min(t,queryMN(idx*4+1,lx,mx,ly,my,Lx,Rx,Ly,Ry));
    if (Lx<=mx && Ry>my) t = min(t,queryMN(idx*4+2,lx,mx,my+1,ry,Lx,Rx,Ly,Ry));
    if (Rx>mx  && Ly<=my) t = min (t,queryMN(idx*4+3,mx+1,rx,ly,my,Lx,Rx,Ly,Ry)); 
    if (Rx>mx&&Ry>my) t = min (t,queryMN(idx*4+4,mx+1,rx,my+1,ry,Lx,Rx,Ly,Ry));
    return t;
}
int queryMX( int idx,int lx,int rx,int ly,int ry,int Lx,int Rx,int Ly,int Ry)
{
    if (Lx<=lx && Rx>=rx && Ly<=ly && Ry>=ry) return tree[idx].mx;
    int mx = (lx+rx)>>1,my = (ly+ry)>>1,t=0;
    if (Lx<=mx && Ly<=my)  t = max(t,queryMX(idx*4+1,lx,mx,ly,my,Lx,Rx,Ly,Ry));
    if (Lx<=mx && Ry>my) t = max(t,queryMX(idx*4+2,lx,mx,my+1,ry,Lx,Rx,Ly,Ry));
    if (Rx>mx  && Ly<=my) t = max (t,queryMX(idx*4+3,mx+1,rx,ly,my,Lx,Rx,Ly,Ry)); 
    if (Rx>mx&&Ry>my) t = max(t,queryMX(idx*4+4,mx+1,rx,my+1,ry,Lx,Rx,Ly,Ry));
    return t;
}
void init()
{
    for ( int i = 0 ; i < 8E6 ; i++) tree[i].init();
}
int main(){
#ifdef YourCodeHasBug
//  freopen("in2","r",stdin);
#endif
    int T;
    cin>>T;
    int cas = 0 ;
    while (T--)
    {
        init();
        scanf("%d",&n);
        for ( int i = 1 ; i <= n ; i++)
            for ( int j = 1 ; j <= n ; j++)
            {
                scanf("%d",&a[i][j]);
//              cout<<"a[i][j]:"<<a[i][j]<<endl;
                insert(0,1,n,1,n,i,j,a[i][j]);
            }
//      for ( int i = 0 ; i <= 20 ; i++) printf("tree_mn:%d mx:%d\n",tree[i].mn,tree[i].mx);
        int m;
        scanf("%d",&m);
            printf("Case #%d:\n",++cas);
        while (m--)
        {
            int x,y,L;
            scanf("%d %d %d",&x,&y,&L);
            int Lx = max(x-L/2,1);
            int Rx = min(n,x+L/2);
            int Ly = max(y-L/2,1);
            int Ry = min(n,y+L/2);
//          printf("x:[%d,%d] y:[%d,%d]\n",Lx,Rx,Ly,Ry);
            int mn = queryMN(0,1,n,1,n,Lx,Rx,Ly,Ry);
            int mx = queryMX(0,1,n,1,n,Lx,Rx,Ly,Ry);
            int newval = floor((mn+mx)/2);
            //printf("mn:%d mx:%d %d\n",mn,mx,newval);
            printf("%d\n",newval);
            insert(0,1,n,1,n,x,y,newval);
        }
    }
#ifdef YourCodeHasBug
    fclose(stdin);
#endif
    return 0;
}

然后又写了一个二维线段树的版本,借鉴了kuangbin的写法,改成了自己习惯的代码风格。

果然常数差好多。。。(据说是因为四叉树退化得厉害QAQ


第三个是四叉树的做法,第二个是kuangbin 的 树套树版本的二维线段树

第一个是我改写kuangbin代码之后的代码。

可以看出,四叉树虽然好写好理解一点,但是时间上不太优秀啊….

/* ***********************************************
Author :111qqz
Created Time :2017年11月10日 星期五 17时18分40秒
File Name :4819_2D.cpp
 ************************************************ */

#include <bits/stdc++.h>
#define PB push_back
#define fst first
#define sec second
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define ms(a,x) memset(a,x,sizeof(a))
typedef long long LL;
#define pi pair < int ,int >
#define MP make_pair

using namespace std;
const double eps = 1E-8;
const int dx4[4]={1,0,0,-1};
const int dy4[4]={0,-1,1,0};
const int inf = 0x3f3f3f3f;
const int N=803;
struct Treey
{
    int l,r;
    int Max,Min;
};
int n;
int rtx[N],rty[N] ; //rtx[i]表示横坐标为i的点属于哪棵线段树
struct  Treex
{
    int l,r;
    Treey treey[N<<2];
    void build ( int _l,int _r,int rt)
    {
    treey[rt].l = _l;
    treey[rt].r = _r;
    treey[rt].Max = -inf;
    treey[rt].Min = inf;
    if (_l==_r)
    {
        rty[_l] = rt;
        return;
    }
    int m = (_l + _r) / 2;
    build (_l,m,rt<<1);
    build(m+1,_r,rt<<1|1);
    }
    int QMin( int L,int R,int rt)
    {
    if (treey[rt].l >= L && treey[rt].r <= R) return treey[rt].Min;
    int m = (treey[rt].l + treey[rt].r) / 2;
    int ret = 1E9;
    if (L<=m) ret = QMin(L,R,rt<<1);
    if (R>=m+1) ret = min(ret,QMin(L,R,rt<<1|1));
    return ret;
    }
    int QMax( int L,int R,int rt)
    {
    if (treey[rt].l >= L && treey[rt].r <= R) return treey[rt].Max;
    int m = (treey[rt].l + treey[rt].r) / 2;
    int ret = 0 ;
    if (L<=m) ret = QMax (L,R,rt<<1);
    if (R>=m+1) ret = max(ret,QMax(L,R,rt<<1|1));
    return ret;
    }
}treex[N<<2];

void build (int l,int r,int rt)
{
    treex[rt].l = l;
    treex[rt].r = r;
    treex[rt].build(1,n,1);
    if (l==r)
    {
    rtx[l] = rt;
    return;
    }
    int m = (l+r)>>1;
    build (lson);
    build (rson);
}
void update ( int x,int y,int val) //单点更新,更新a[x,y]到val
{
    int rx = rtx[x];
    int ry = rty[y];
    treex[rx].treey[ry].Min = treex[rx].treey[ry].Max = val;
    for ( int i = rx ; i ; i >>=1)
    for ( int j = ry ; j ; j >>=1)
    {
        if (i==rx && j==ry) continue; //上面更新过了
        if (j==ry)
        {
        treex[i].treey[j].Min = min(treex[i<<1].treey[j].Min,treex[i<<1|1].treey[j].Min);
        treex[i].treey[j].Max = max(treex[i<<1].treey[j].Max,treex[i<<1|1].treey[j].Max);
        }
        else
        {
            treex[i].treey[j].Min = min(treex[i].treey[j<<1].Min,treex[i].treey[j<<1|1].Min);
        treex[i].treey[j].Max = max(treex[i].treey[j<<1].Max,treex[i].treey[j<<1|1].Max);
        }
    }
}
int QMin( int L1,int R1,int L2,int R2,int rt)
{
    if (treex[rt].l >= L1 && treex[rt].r <= R1) return treex[rt].QMin(L2,R2,1);
    int m = (treex[rt].l + treex[rt].r)/2;
    int ret = 1E9;
    if (L1<=m) ret = QMin(L1,R1,L2,R2,rt<<1);
    if (R1>=m+1) ret = min(ret,QMin(L1,R1,L2,R2,rt<<1|1));
    return ret;
}
int QMax ( int L1,int R1,int L2,int R2,int rt)
{
 //   printf("rt:%d l:%d r:%d  L1:%d R1:%d \n",rt,treex[rt].l,treex[rt].r,L1,R1);
    if (treex[rt].l >= L1 && treex[rt].r <=R1) return treex[rt].QMax(L2,R2,1);
    int m = (treex[rt].l + treex[rt].r) / 2;
    int ret = 0 ;
    if (L1<=m) ret = QMax(L1,R1,L2,R2,rt<<1);
    if (R1>=m+1) ret = max(ret, QMax(L1,R1,L2,R2,rt<<1|1));
    return ret;
}

int main() 
{
#ifndef  ONLINE_JUDGE 
    freopen("./in.txt","r",stdin);
#endif
    int T,cas=0;
    cin>>T;
    while (T--)
    {
    printf("Case #%d:\n",++cas);
    scanf("%d",&n);
    build (1,n,1);
    for ( int i = 1 ; i  <= n ; i++)
        for ( int j = 1; j <= n ; j++)
        {
        int x;
        scanf("%d",&x);
        update(i,j,x);
        }
    int q;
    scanf("%d",&q);
    while (q--)
    {
        int x,y,L;
        scanf("%d %d %d",&x,&y,&L);
        int L1 = max(x-L/2,1);
        int R1 = min(x+L/2,n);
        int L2 = max(y-L/2,1);
        int R2 = min(y+L/2,n);
//      printf("[%d,%d] [%d,%d]\n",L1,R1,L2,R2);
        int Mx = QMax(L1,R1,L2,R2,1);
        int Mn = QMin(L1,R1,L2,R2,1);
        int val = floor((Mx+Mn)/2);
        printf("%d\n",val);
        update(x,y,val);
    }
    }   
#ifndef ONLINE_JUDGE  
    fclose(stdin);
#endif
    return 0;
}

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