题目地址


易错点:

  • 线段树查询时直接保留查询范围即可.
  • 线段树递归结束后,返回gcd结果时应取绝对值.
  • 本题线段树初始化时需要使用差分数组(更相减损术);同样地,在进行区间修改时[l~r]的修改会影响到线段树内[l~r+1]的值.
  • 修改时应特判r>n的情况.

#include<cstdio>
#include<iostream>
#include<cstring>
#include<cmath>
#define ll long long
using namespace std;
const int MAXN=6e5;
struct Node{
    int l,r;
    ll val;
}tr[MAXN*4];
ll gcd(ll a,ll b){
    return b?gcd(b,a%b):a;
}
ll b[MAXN];
void build(int p,int l,int r){
    tr[p].l=l,tr[p].r=r;
    if(l==r){
        tr[p].val=b[l];
        return;
    }
    int mid=(l+r)>>1;
    build(p<<1,l,mid);
    build((p<<1)|1,mid+1,r);
    tr[p].val=gcd(tr[p<<1].val,tr[(p<<1)|1].val);
}
ll query(int p,int l,int r){
    if(tr[p].l>=l&&tr[p].r<=r){
        return abs(tr[p].val);
    }
    int mid=(tr[p].l+tr[p].r)>>1;
    ll ans=0;
    if(l<=mid)ans=gcd(ans,query(p<<1,l,r));
    if(r>mid)ans=gcd(ans,query((p<<1)|1,l,r));
    return abs(ans);
}
void change(int p,int x,ll val){
    if(tr[p].l==tr[p].r){
        tr[p].val+=val;
        return;
    }
    int mid=(tr[p].l+tr[p].r)>>1;
    if(x<=mid)change(p<<1,x,val);
    else change((p<<1)|1,x,val);
    tr[p].val=gcd(tr[p<<1].val,tr[(p<<1)|1].val);
}
int lowbit(int x){
    return x&-x;
}
int n;
ll c[MAXN];
void add(int x,ll val){
    while(x<=n){
        c[x]+=val;
        x+=lowbit(x);
    }
}
ll ask(int x){
    ll ans=0;
    while(x){
        ans+=c[x];
        x-=lowbit(x);
    }
    return ans;
}
ll a[MAXN];
int root=1;
int main(){
    int m;
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++){
        scanf("%lld",&a[i]);
        b[i]=a[i]-a[i-1];
    }
    build(root,1,n);
    char tmp[2];
    for(int i=1;i<=m;i++){
        int l,r;
        scanf("%s%d%d",tmp,&l,&r);
        if(tmp[0]=='C'){
            ll delta;
            scanf("%lld",&delta);
            change(root,l,delta);
            if(r<n)change(root,r+1,-delta);
            add(l,delta),add(r+1,-delta);
        }else{
            ll alValue=a[l]+ask(l);
            ll val=l<r?query(root,l+1,r):0;
            printf("%lld\n",gcd(alValue,val));
        }
    }
    return 0;
}