Codeforces Round #250 (Div. 1) D. The Child and Sequence 线段树 区间求和+点修改+区间取模

D. The Child and Sequence

 

At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite sequence of Picks.

Fortunately, Picks remembers how to repair the sequence. Initially he should create an integer array a[1], a[2], ..., a[n]. Then he should perform a sequence of m operations. An operation can be one of the following:

1. Print operation l, r. Picks should write down the value of .
2. Modulo operation l, r, x. Picks should perform assignment a[i] = a[i] mod x for each i (l ≤ i ≤ r).
3. Set operation k, x. Picks should set the value of a[k] to x (in other words perform an assignment a[k] = x).

Can you help Picks to perform the whole sequence of operations?

Input

The first line of input contains two integer: n, m (1 ≤ n, m ≤ 105). The second line contains n integers, separated by space:a[1], a[2], ..., a[n] (1 ≤ a[i] ≤ 109) — initial value of array elements.

Each of the next m lines begins with a number type .

• If type = 1, there will be two integers more in the line: l, r (1 ≤ l ≤ r ≤ n), which correspond the operation 1.
• If type = 2, there will be three integers more in the line: l, r, x (1 ≤ l ≤ r ≤ n; 1 ≤ x ≤ 109), which correspond the operation 2.
• If type = 3, there will be two integers more in the line: k, x (1 ≤ k ≤ n; 1 ≤ x ≤ 109), which correspond the operation 3.

Output

For each operation 1, please print a line containing the answer. Notice that the answer may exceed the 32-bit integer.

Sample test(s)

input

5 5
1 2 3 4 5
2 3 5 4
3 3 5
1 2 5
2 1 3 3
1 1 3

output

8
5


题意：
   操作1：l,r 求l到r之间的区间和
   操作2：l,r,c  将l到r之间的数分别取模x
   操作3：l,r  讲a[l]改成r；
题解：
   线段树的区间操作
   对于去摸：我们设置一个区间段最大值，要取得模要是大于这个最大则之间退出
   这就是优化

///1085422276
#include<bits/stdc++.h>
using namespace std ;
typedef long long ll;
#define mem(a) memset(a,0,sizeof(a))
#define meminf(a) memset(a,127,sizeof(a));
#define inf 1000000007
#define mod 1000000007
inline ll read()
{
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){
        if(ch=='-')f=-1;ch=getchar();
    }
    while(ch>='0'&&ch<='9'){
        x=x*10+ch-'0';ch=getchar();
    }return x*f;
}
//************************************************
const int maxn=100000+5;
int a[maxn],n,m,q;
struct ss{
  int  l,r;
  ll v,sum,tag;
}tr[maxn*5];
void build(int k,int s,int t)
{
    tr[k].l=s;tr[k].r=t;
    tr[k].v=0;tr[k].tag=0;tr[k].sum=0;
    if(s==t){
        tr[k].sum=a[s];
        tr[k].v=a[s];
        return ;
    }
    int mid=(s+t)>>1;
    build(k<<1,s,mid);
    build(k<<1|1,mid+1,t);
    tr[k].sum=tr[k<<1].sum+tr[k<<1|1].sum;
      tr[k].v=max(tr[k<<1].v,tr[k<<1|1].v);
}
ll ask(int k,int s,int t)
{
    if(tr[k].l==s&&tr[k].r==t){
        return tr[k].sum;
    }
    int mid=(tr[k].l+tr[k].r)>>1;
    ll ret=0;
    if(t<=mid)ret= ask(k<<1,s,t);
    else if(s>mid)ret= ask(k<<1|1,s,t);
    else {
        ret=(ask(k<<1,s,mid)+ask(k<<1|1,mid+1,t));
    } tr[k].sum=tr[k<<1].sum+tr[k<<1|1].sum;
    tr[k].v=max(tr[k<<1].v,tr[k<<1|1].v);
    return ret;
}
void modify(int k,int s,int t,ll c)
{
    if(tr[k].v<c)return ;
     if(tr[k].l==tr[k].r){
        tr[k].sum%=c;
        tr[k].v%=c;
        return ;
     }
    int mid=(tr[k].l+tr[k].r)>>1;
    if(t<=mid)modify(k<<1,s,t,c);
    else if(s>mid)modify(k<<1|1,s,t,c);
    else {
       modify(k<<1,s,mid,c);modify(k<<1|1,mid+1,t,c);
    }
     tr[k].sum=tr[k<<1].sum+tr[k<<1|1].sum;
     tr[k].v=max(tr[k<<1].v,tr[k<<1|1].v);
}
void update(int k,int x,int c)
{
    if(tr[k].l==x&&tr[k].r==x){
        tr[k].sum=c;
        tr[k].v=c;
        return;
    }
    int mid=(tr[k].l+tr[k].r)>>1;
    if(x<=mid)update(k<<1,x,c);
    else {
         update(k<<1|1,x,c);
    }
    tr[k].sum=tr[k<<1].sum+tr[k<<1|1].sum;
    tr[k].v=max(tr[k<<1].v,tr[k<<1|1].v);
}
int main(){

    n=read();m=read();
    for(int i=1;i<=n;i++){
        scanf("%d",&a[i]);
    }build(1,1,n);int x,y;ll c;
    for(int i=1;i<=m;i++){
        scanf("%d",&q);
        if(q==1){
            scanf("%d%d",&x,&y);
            printf("%I64d
",ask(1,x,y));
        }
        else if(q==2){
            scanf("%d%d%I64d",&x,&y,&c);
            modify(1,x,y,c);
        }
        else {
            scanf("%d%d",&x,&y);
            update(1,x,y);
        }

    }
  return 0;
}