题解

#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
const int maxn = 200000 + 3;
int x[maxn], y[maxn], n, m, len;
long long  nex[maxn], nexx[maxn], maxv[maxn << 2], C[maxn];
inline long long dist(int i,int j){ return abs(x[i] - x[j]) + abs(y[i] - y[j]); }
void build(int l,int r , int o)
{
    if(l > r) return ;
    if(l == r)
    {
        maxv[o] = nexx[l];
        return;
    }
    int mid = (l + r) >> 1, ls = (o << 1), rs = (o << 1)|1;
    build(l, mid , ls);
    build(mid + 1, r, rs);
    maxv[o] = max(maxv[ls], maxv[rs]);
}
inline long long query(int l,int r,int L,int R,int o)
{
    if(l > r || r < L || l > R) return 0;
    if(l >= L && r <= R) 
    {
        return maxv[o];
    }
    int mid = (l + r) >> 1, ls = (o << 1), rs = (o << 1) | 1;
    long long ans = 0;
    ans = max(ans, query(l, mid,L,R,ls));
    ans = max(ans, query(mid + 1, r, L,R,rs));
    return ans;
}
void change(int l,int r,int pos,int o)
{
    if(l > r || r < pos || l > pos) return ;
    if(l == r)
    {
        maxv[o] = nexx[pos];
        return ;
    }
    int mid = (l + r) >> 1, ls = (o<<1), rs = (o << 1) |1;
    change(l,mid,pos,ls);
    change(mid + 1,r,pos,rs);
    maxv[o] = max(maxv[ls], maxv[rs]);
}
int lowbit(int t){ return t & (-t); }
inline void update(int x,long long delta)
{
    while(x <= n)
    {
        C[x] += delta;
        x += lowbit(x);
    }
}
inline long long ask(int x)
{
    long long sums = 0;
    while(x > 0)
    {
        sums += C[x];
        x -= lowbit(x);
    }
    return sums;
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i = 1;i <= n; ++i)    scanf("%d%d",&x[i],&y[i]);
    for(int i = 1;i <= n;  ++i)  { if(i < n)nex[i] = dist(i, i + 1); update(i, dist(i,i - 1));}
    for(int i = 1;i <= n - 2; ++i) nexx[i] = nex[i] + nex[i + 1] - dist(i, i + 2);
    len = n - 2;
    build(1, len, 1);
    for(int i = 1;i <= m; ++i)
    {
        char op[10];
        scanf("%s",op);
        if(op[0] == 'Q')
        {
            int st, ed;
            scanf("%d%d",&st,&ed);
            long long s_ed = ask(ed);
            long long s_st = ask(st);
            printf("%lld\n",s_ed - s_st - query(1,len,st,ed - 2,1));
        }
        else
        {
            int id, a,b;
            scanf("%d%d%d",&id,&a,&b);
            update(id, -dist(id - 1, id));
            update(id + 1, -dist(id, id + 1));
            x[id] = a, y[id] = b;
            nex[id - 1] = dist(id - 1, id);
            nex[id] = dist(id, id + 1); 
            if(id + 2 <= n)
            {
                nexx[id] = nex[id] + nex[id + 1] - dist(id, id + 2);
                change(1,len, id, 1);
            }
            if(id - 1 > 0 )
            {
                nexx[id - 1] = nex[id - 1] + nex[id] - dist(id - 1, id + 1);
                change(1,len,id - 1,1);
            }
            if(id - 2 >= 1)
            {
                nexx[id -2] = nex[id - 2] + nex[id - 1] - dist(id - 2, id);
                change(1,len,id - 2,1);
            }
            update(id, dist(id - 1, id));
            update(id + 1, dist(id, id + 1));
        }
    }
    return 0;
}