2018ICPC 沈阳 E

https://cn.vjudge.net/problem/2057332/origin

题目的询问为L - R之间的两人曼哈顿距离最长

将曼哈顿距离转切比雪夫距离，线段树维护区间内的最(次)大x和最(次)小x，并且最大次大，最小次小的种族不同

y轴同理，建两颗线段树即可，询问的时候查询区间最大小值的差就好了

#include <map>
#include <set>
#include <ctime>
#include <cmath>
#include <queue>
#include <stack>
#include <vector>
#include <string>
#include <bitset>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <sstream>
#include <iostream>
#include <algorithm>
#include <functional>
using namespace std;
#define For(i, x, y) for(int i=x;i<=y;i++)  
#define _For(i, x, y) for(int i=x;i>=y;i--)
#define Mem(f, x) memset(f,x,sizeof(f))  
#define Sca(x) scanf("%d", &x)
#define Sca2(x,y) scanf("%d%d",&x,&y)
#define Sca3(x,y,z) scanf("%d%d%d",&x,&y,&z)
#define Scl(x) scanf("%lld",&x)  
#define Pri(x) printf("%d
", x)
#define Prl(x) printf("%lld
",x)  
#define CLR(u) for(int i=0;i<=N;i++)u[i].clear();
#define LL long long
#define ULL unsigned long long  
#define mp make_pair
#define PII pair<int,int>
#define PIL pair<int,long long>
#define PLI pair<long long,int>
#define PLL pair<long long,long long>
#define pb push_back
#define fi first
#define se second 
typedef vector<int> VI;
int read(){int x = 0,f = 1;char c = getchar();while (c<'0' || c>'9'){if (c == '-') f = -1;c = getchar();}
while (c >= '0'&&c <= '9'){x = x * 10 + c - '0';c = getchar();}return x*f;}
const double PI = acos(-1.0);
const double eps = 1e-9;
const int maxn = 1e5 + 10;
const LL INF = 1e18;
const int mod = 1e9 + 7; 
int N,M,K;
struct Node{
    LL x,y;
    LL c;
}node[maxn];
struct Tree{
    int l,r;
    PLI Max,Mmax,Min,Mmin;
}tree[2][maxn << 2];
void Pushup(Tree &t,Tree a,Tree b){  
    if(a.Max.fi < b.Max.fi) swap(a,b);
    if(b.Max.fi > a.Mmax.fi && b.Max.se != a.Max.se) a.Mmax = b.Max;
    if(b.Mmax.fi > a.Mmax.fi && b.Mmax.se != a.Max.se) a.Mmax = b.Mmax;
    t.Max = a.Max; t.Mmax = a.Mmax;
    
    if(a.Min.fi > b.Min.fi) swap(a,b);
    if(b.Min.fi < a.Mmin.fi && b.Min.se != a.Min.se) a.Mmin = b.Min;
    if(b.Mmin.fi < a.Mmin.fi && b.Mmin.se != a.Min.se) a.Mmin = b.Mmin; 
    t.Min = a.Min; t.Mmin = a.Mmin;
}
void Build(Tree * tree,int t,int l,int r,bool flag){
    tree[t].l = l; tree[t].r = r;
    tree[t].Max = tree[t].Mmax = mp(-INF,0);
    tree[t].Min = tree[t].Mmin = mp(INF,0);
    if(l == r){
        if(flag) tree[t].Max = tree[t].Min = mp(node[l].x,node[l].c);
        else tree[t].Max = tree[t].Min = mp(node[l].y,node[l].c);
        return;
    }
    int m = l + r >> 1;
    Build(tree,t << 1,l,m,flag); Build(tree,t << 1 | 1,m + 1,r,flag);
    Pushup(tree[t],tree[t << 1],tree[t << 1 | 1]);
}
void update(Tree* tree,int t,int k,int x){
    if(tree[t].l == tree[t].r){
        tree[t].Max.fi += x;
        tree[t].Min.fi += x;
        return;
    }
    int m = tree[t].l + tree[t].r >> 1;
    if(k <= m) update(tree,t << 1,k,x);
    else update(tree,t << 1 | 1,k,x);
    Pushup(tree[t],tree[t << 1],tree[t << 1 | 1]);
}
void update2(Tree* tree,int t,int k,int c){
    if(tree[t].l == tree[t].r){
        tree[t].Max.se = tree[t].Min.se = c;
        return;
    }
    int m = tree[t].l + tree[t].r >> 1;
    if(k <= m) update2(tree,t << 1,k,c);
    else update2(tree,t << 1 | 1,k,c);
    Pushup(tree[t],tree[t << 1],tree[t << 1 | 1]);
}
Tree query(Tree *tree,int t,int l,int r){
    if(l <= tree[t].l && tree[t].r <= r) return tree[t];
    int m = tree[t].l + tree[t].r >> 1;
    if(r <= m) return query(tree,t << 1,l,r);
    else if(l > m) return query(tree,t << 1 | 1,l,r);
    else{
        Tree ans;
        Pushup(ans,query(tree,t << 1,l,m),query(tree,t << 1 | 1,m + 1,r));
        return ans;
    }
}
int main(){
    int T = read(); int CASE = 1;
    while(T--){
        Sca2(N,M);
        printf("Case #%d:
",CASE++);
        for(int i = 1; i <= N ; i ++){
            LL x = read(),y = read();
            Sca(node[i].c);
            node[i].x = x + y; node[i].y = x - y;
        }
        Build(tree[0],1,1,N,1);
        Build(tree[1],1,1,N,0);
        while(M--){
             int op = read();
             if(op == 1){
                 int k = read(),x = read(),y = read();  
                 update(tree[0],1,k,x + y);
                 update(tree[1],1,k,x - y);
             }else if(op == 2){
                 int k,c; Sca2(k,c);
                 update2(tree[0],1,k,c);
                 update2(tree[1],1,k,c);
             }else{
                 int l,r; Sca2(l,r);
                 LL ans = 0;
                Tree tmp = query(tree[0],1,l,r);
                if(tmp.Max.se != tmp.Min.se) ans = max(ans,tmp.Max.fi - tmp.Min.fi);
                else ans = max(ans,max(tmp.Max.fi - tmp.Mmin.fi,tmp.Mmax.fi - tmp.Min.fi));
                tmp = query(tree[1],1,l,r);
                if(tmp.Max.se != tmp.Min.se) ans = max(ans,tmp.Max.fi - tmp.Min.fi);
                else ans = max(ans,max(tmp.Max.fi - tmp.Mmin.fi,tmp.Mmax.fi - tmp.Min.fi));
                 Prl(ans);
             }
        }
    }
    return 0;
}