codeforces 438D 分类： codeforces ...

最新推荐文章于 2025-04-09 21:24:36 发布

转载最新推荐文章于 2025-04-09 21:24:36 发布 · 65 阅读

0 ·

CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/dashgua/p/4723071.html

本文介绍了一种使用线段树数据结构处理数组中元素的取模操作的方法，通过维护区间最大值和区间和，优化了处理效率，适用于动态更新和查询场景。

分析：对于数a，b，满足a>=b，则 (amodb)<a/2

所以对a最多取模log2a次
线段树维护区间最大值和区间和，
取模操作对ai>=m暴力修改即可

时间复杂度：O(n∗log2ai∗log2n+m∗log2x∗log2n)

#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;       
}