gym/101955/problem/E - The Kouga Ninja Scrolls 线段数 维护 切比雪夫距离 2018沈阳icpc

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思路:  

  这道题要把给定的每个坐标利用切比雪夫坐标表示,这样两个点的距离就是max(dx,dy),而不是一开始的dx + dy,有利于线段树的维护,又由于询问的是区间的最大差值,限制是两个点是属于不同门派的,所以我们可以维护每个区间的最大,次大值,最小次小值。

#include <algorithm>
#include  <iterator>
#include  <iostream>
#include   <cstring>
#include   <cstdlib>
#include   <iomanip>
#include    <bitset>
#include    <cctype>
#include    <cstdio>
#include    <string>
#include    <vector>
#include     <stack>
#include     <cmath>
#include     <queue>
#include      <list>
#include       <map>
#include       <set>
#include   <cassert>

using namespace std;
#define lson (l , mid , rt << 1)
#define rson (mid + 1 , r , rt << 1 | 1)
#define debug(x) cerr << #x << " = " << x << "\n";
#define pb push_back
#define pq priority_queue



typedef long long ll;
typedef unsigned long long ull;
//typedef __int128 bll;
typedef pair<ll ,ll > pll;
typedef pair<int ,int > pii;
typedef pair<int,pii> p3;
typedef pair<ll,int>pli;
//priority_queue<int> q;//这是一个大根堆q
//priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q
#define fi first
#define se second
//#define endl '\n'

#define OKC ios::sync_with_stdio(false);cin.tie(0)
#define FT(A,B,C) for(int A=B;A <= C;++A)  //用来压行
#define REP(i , j , k)  for(int i = j ; i <  k ; ++i)
#define max3(a,b,c) max(max(a,b), c);
#define min3(a,b,c) min(min(a,b), c);
//priority_queue<int ,vector<int>, greater<int> >que;

const ll mos = 0x7FFFFFFF;  //2147483647
const ll nmos = 0x80000000;  //-2147483648
const int inf = 0x3f3f3f3f;
const ll inff = 0x3f3f3f3f3f3f3f3f; //18
const int mod = 9999973;
const double esp = 1e-8;
const double PI=acos(-1.0);
const double PHI=0.61803399;    //黄金分割点
const double tPHI=0.38196601;


template<typename T>
inline T read(T&x){
    x=0;int f=0;char ch=getchar();
    while (ch<'0'||ch>'9') f|=(ch=='-'),ch=getchar();
    while (ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x=f?-x:x;
}
/*-----------------------showtime----------------------*/

                const int maxn = 5e5+9;
                int n,m;
                struct node{
                    ll x,y,c;
                }a[maxn];

                struct Tree{
                    ///p[0] x轴 1,2 第一第二大,3,4第一第二小
                    ///p[1] y轴
                    pli p[2][5];
                } t[maxn<<2];


                void pushup34(int rt,int id){
                    pli tmp[5];
                    tmp[1] = t[rt<<1].p[id][3];
                    tmp[2] = t[rt<<1].p[id][4];
                    tmp[3] = t[rt<<1|1].p[id][3];
                    tmp[4] = t[rt<<1|1].p[id][4];

                    t[rt].p[id][3] = {inff,0};
                    t[rt].p[id][4] = {inff,0};
                    for(int i=1; i<=4; i++){
                        if(t[rt].p[id][3].fi > tmp[i].fi && tmp[i].se){
                            t[rt].p[id][3] = tmp[i];
                        }
                    }

                    for(int i=1; i<=4; i++){
                        if(t[rt].p[id][4].fi > tmp[i].fi && tmp[i].se != t[rt].p[id][3].se){
                            t[rt].p[id][4] = tmp[i];
                        }
                    }

                }
                void pushup12(int rt,int id){
                    pli tmp[5];
                    tmp[1] = t[rt<<1].p[id][1];
                    tmp[2] = t[rt<<1].p[id][2];
                    tmp[3] = t[rt<<1|1].p[id][1];
                    tmp[4] = t[rt<<1|1].p[id][2];

                    t[rt].p[id][1] = {-inff,0};
                    t[rt].p[id][2] = {-inff,0};
                    for(int i=1; i<=4; i++){
                        if(t[rt].p[id][1].fi < tmp[i].fi && tmp[i].se){

                            t[rt].p[id][1] = tmp[i];
                        }
                    }

                    for(int i=1; i<=4; i++){
                        if(t[rt].p[id][2].fi < tmp[i].fi && tmp[i].se != t[rt].p[id][1].se){
                            t[rt].p[id][2] = tmp[i];
                        }
                    }
                }
                void build(int l,int r,int rt){
                    if(l == r){

                            t[rt].p[0][1].fi = a[l].x; t[rt].p[0][1].se = a[l].c;
                            t[rt].p[0][2] = {-inff,0};
                            t[rt].p[0][3].fi = a[l].x; t[rt].p[0][3].se = a[l].c;
                            t[rt].p[0][4] = {inff,0};

                            /*-----------------------*/
                            t[rt].p[1][1].fi = a[l].y; t[rt].p[1][1].se = a[l].c;
                            t[rt].p[1][2] = {-inff,0};
                            t[rt].p[1][3].fi = a[l].y; t[rt].p[1][3].se = a[l].c;
                            t[rt].p[1][4] = {inff,0};

                        return;
                    }
                    int mid = (l + r) >> 1;
                    build(l,mid,rt<<1);
                    build(mid+1,r,rt<<1|1);
                    pushup12(rt, 0);  pushup34(rt, 0);

                    pushup12(rt, 1);  pushup34(rt, 1);
                }

                void update(int k,int c,int dx,int dy,int l,int r,int rt){
                    if(l == r){
                        a[l].x += 1ll*dx;
                        a[l].y += 1ll*dy;
                        a[l].c = c;
                            t[rt].p[0][1].fi = a[l].x; t[rt].p[0][1].se = a[l].c;
                            t[rt].p[0][2] = {-inff,0};
                            t[rt].p[0][3].fi = a[l].x; t[rt].p[0][3].se = a[l].c;
                            t[rt].p[0][4] = {inff,0};


                        //-----------------------------------//
                            t[rt].p[1][1].fi = a[l].y; t[rt].p[1][1].se = a[l].c;
                            t[rt].p[1][2] = {-inff,0};
                            t[rt].p[1][3].fi = a[l].y; t[rt].p[1][3].se = a[l].c;
                            t[rt].p[1][4] = {inff,0};




                        return;
                    }
                    int mid = (l + r) >> 1;
                    if(k <= mid) update(k,c,dx,dy,l,mid,rt<<1);
                    else update(k,c,dx,dy,mid+1,r,rt<<1|1);
                    pushup12(rt, 0);  pushup34(rt, 0);

                    pushup12(rt, 1);  pushup34(rt, 1);
                }


                void query(int L,int R,int l,int r,int rt,pli &b1,pli &b2,pli &s1, pli &s2,int id){
                        if( L <= l && r <= R){

                            for(int i=1; i<=2; i++) {
                                if(b1.fi < t[rt].p[id][i].fi)
                                    {
                                        if(b1.se != t[rt].p[id][i].se)
                                           b2 = b1;
                                        b1 = t[rt].p[id][i];
                                    }
                            }
                            for(int i=1; i<=2; i++){
                                if(b2.fi < t[rt].p[id][i].fi && b1.se != t[rt].p[id][i].se){
                                    b2 = t[rt].p[id][i];
                                }
                            }

                            for(int i=3; i<=4; i++) {
                                if(s1.fi > t[rt].p[id][i].fi){
                                        if(s1.se != t[rt].p[id][i].se)
                                            s2 = s1;
                                        s1 = t[rt].p[id][i];
                                }
                            }
                            for(int i=3; i<=4; i++){
                                if(s2.fi > t[rt].p[id][i].fi && s1.se != t[rt].p[id][i].se){
                                    s2 = t[rt].p[id][i];
                                }
                            }
                            return ;
                        }


                        int mid = (l + r) >> 1;
                        if(mid >= L)  query(L, R, l, mid, rt<<1, b1,b2,s1,s2,id);
                        if(mid < R)   query(L, R, mid+1, r,rt<<1|1, b1,b2,s1,s2,id);

                }
int main(){
            int T;  scanf("%d", &T);
            for(int cas=1; cas<=T; cas++){
                printf("Case #%d:\n", cas);
                scanf("%d%d", &n, &m);
                for(int i=1; i<=n; i++){
                    int x,y,c;
                    scanf("%d%d%d", &x, &y, &c);
                    a[i].x = x + y, a[i].y = x - y;
                    a[i].c = c;
                }

                build(1,n,1);

                while(m --) {
                        int op;     scanf("%d", &op);
                        if(op == 1){
                            int k,x,y;
                            scanf("%d%d%d", &k, &x, &y);
                            update(k,a[k].c,x+y, x-y,1,n,1);
                        }
                        else if(op == 2){
                            int k,c;
                            scanf("%d%d", &k, &c);
                            update(k,c,0,0,1,n,1);
                        }
                        else {
                            int l,r;
                            scanf("%d%d", &l, &r);


                            pli q[5];
                            q[1] = q[2] = {-inff, 0};
                            q[3] = q[4] = {inff, 0};


                            query(l,r,1,n,1,q[1],q[2],q[3],q[4],0);
                            ll res = -inff;
                            for(int i=1; i<=4; i++){
                                for(int j=1; j<=4; j++){
                                    if(q[i].se != q[j].se && q[i].se && q[j].se){
                                        res = max(res, abs(q[i].fi - q[j].fi));
                                    }
                                }
                            }


                            pli e[5];
                            e[1] = e[2] = {-inff, 0};
                            e[3] = e[4] = {inff, 0};
                            query(l,r,1,n,1,e[1],e[2],e[3],e[4],1);

                            for(int i=1; i<=4; i++){
                                for(int j=1; j<=4; j++){
                                    if(e[i].se != e[j].se && e[i].se && e[j].se){
                                        res = max(res, abs(e[i].fi - e[j].fi));
                                    }
                                }
                            }

                            if(res <= -inff) res = 0;
                            printf("%lld\n", res);
                        }
                }
            }

            return 0;
}
View Code
posted @ 2019-01-25 11:27  ckxkexing  阅读(322)  评论(0编辑  收藏  举报