codeforces 438D

分析：对于数a，ba，b，满足a>=ba>=b， 则 (amodb)<a/2(a\mod b)< a/2

所以对aa最多取模log2alog_2a次

线段树维护区间最大值和区间和，

取模操作对ai>=ma_i>=m暴力修改即可

时间复杂度：O(n∗log2ai∗log2n+m∗log2x∗log2n)O(n*log_2a_i*log_2n+m*log_2x*log_2n)

#include<map>
#include<string>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>

const int MAXN = 100005;

int n , m;
int a[MAXN] = {0};

struct treenode
{
    long long sum;int max;
}tree[MAXN<<2] = {0};

#define L(x)  (x<<1)
#define R(x)  ((x<<1)|1)
long long query(int l,int r,int ll,int rr,int si)
{
    if(l == ll && r == rr)return tree[si].sum;
    else
    {
        int mid = (ll+rr)>>1;long long ret = 0;

        if(r <= mid)    ret =  query(l,r,ll,mid,L(si));
        else if(l > mid)ret =  query(l,r,mid+1,rr,R(si));
        else 
        {
         ret += query(l,mid,ll,mid,L(si));
         ret += query(mid+1,r,mid+1,rr,R(si));
        }
        return ret;
    }
}
void update(int x)
{
    tree[x].sum = tree[L(x)].sum + tree[R(x)].sum;
    tree[x].max = std::max(tree[L(x)].max, tree[R(x)].max);
}
void build(int ll,int rr,int si)
{
    if(ll == rr){tree[si].sum = tree[si].max = a[ll];}
    else
    {
        int mid = (ll+rr)>>1;
        if(ll<=mid)build(ll,mid,L(si));
        if(mid<rr)build(mid+1,rr,R(si));
        update(si);
    }
}
void modset(int l,int r,int ll,int rr,int si,int p)
{   
    if(tree[si].max < p)return;

    if(ll == rr){tree[si].max %= p; tree[si].sum = tree[si].max;}
    else
    { 
     int mid = (ll+rr)>>1;
     if(r <= mid)   modset(l,r,ll,mid,L(si),p);
     else if(l > mid)modset(l,r,mid+1,rr,R(si),p);
     else 
     {
        modset(l,mid,ll,mid,L(si),p);
        modset(mid+1,r,mid+1,rr,R(si),p);
     }
     update(si);
    }
}
void change(int k,int ll,int rr,int si,int val)
{
    if(ll == rr){tree[si].sum = tree[si].max = val;}
    else
    {
     int mid = (ll+rr)>>1;
     if(k <= mid) change(k,ll,mid,L(si),val);
     else       change(k,mid+1,rr,R(si),val);
     update(si);
    }
}
#undef L
#undef R

int main()
{
#ifndef ONLINE_JUDGE
    freopen("CF438D.in","r",stdin);
    freopen("CF438D.out","w",stdout);
#endif  

    scanf("%d%d",&n,&m);

    for(int i = 1 ; i <= n; i++)scanf("%d",&a[i]);

    build(1,n,1);

    while(m--)
    {
        int op;scanf("%d",&op);
        int l , r ,v;

        switch(op)
        {
            case 1:
              scanf("%d%d",&l,&r);
              printf("%I64d\n",query(l,r,1,n,1));
              break;
            case 2:
              scanf("%d%d%d",&l,&r,&v);
              modset(l,r,1,n,1,v);
              break;
            case 3:
              scanf("%d%d",&l,&v);
              change(l,1,n,1,v);
              break;    
        }
    }
#ifndef ONLINE_JUDGE
    fclose(stdin);
    fclose(stdout);
#endif
    return 0;       
}