cug1702&&CCNU校赛J题分块

最新推荐文章于 2023-03-08 01:26:15 发布

原创最新推荐文章于 2023-03-08 01:26:15 发布 · 309 阅读

0 ·

CC 4.0 BY-SA版权

区间查询同时被 2 个专栏收录

5 篇文章

订阅专栏

平方分割

1 篇文章

订阅专栏

本文介绍了一种利用平方分割和Lazy标记进行区间更新的方法，适用于处理大规模数据集的查询和更新操作。通过维护二维矩阵的值并使用无符号整形进行2^32取模，实现了高效的区间操作。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

题目大意：

思路：平方分割，区间更新是用lazy标记，需要时更新。这个需要不仅仅是在query是需要，update时也可能需要，如处理两端的时候就需要。标记的同事需要记录每次的p , q , r , s对a[i],b[i]的影响，相当于维护一个二维矩阵的值，这里就不推了，写一遍就知道了，一个简单的代换。还有一个就是对2^32取模，直接无符号整形即可。做的时候因为solve函数没写好，还有一些边界问题错了好多。。。时限2s，跑了1s7刚刚卡过去…………很水

#include <iostream>
#include <cstdio>
#include <string>
#include <cstring>
#include <fstream>
#include <algorithm>
#include <cmath>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <iomanip>

using namespace std;
//#pragma comment(linker, "/STACK:102400000,102400000")
#define maxn 100050
#define MOD 1000000007
#define mem(a , b) memset(a , b , sizeof(a))
#define LL long long
#define ULL unsigned long long
#define FOR(i , n) for(int i = 1 ;  i<= n ; i ++)
typedef pair<int , int> pii;
const long long INF= 0x3fffffff;
int n , m;
int  dis ;
unsigned int a[maxn] , b[maxn];
unsigned int p[maxn];
unsigned int tmp1 , tmp2;
struct node
{
    unsigned int ra ,sa , rb , sb , val;
}flag[maxn];

unsigned int solve(int x)
{
    int l = x * dis;
    int r = (x + 1) * dis ;
    unsigned ans = 0;
    for(int i = l ; i < r && i <= n; i ++)
    {
        tmp1 = a[i] , tmp2 = b[i];
        a[i] = tmp1 * flag[x].ra + tmp2 * flag[x].sa;
        b[i] = tmp1 * flag[x].rb + tmp2 * flag[x].sb;
        ans += (a[i] * b[i]);
    }
    flag[x].val = 0;
    return p[x] = ans;
}

unsigned int get(int x)
{
    int l = x * dis;
    int r = (x + 1) * dis ;
    unsigned int ans = 0;
    for(int i = l ; i < r && i <= n; i ++)
    {
        ans += (a[i] * b[i]);
    }
    return  ans;
}

void update(int l , int r , unsigned int ra , unsigned int sa , unsigned int rb , unsigned int sb)
{
    int st = (l)/dis ;
    int ed = (r)/dis ;
    for(int i = st+1 ; i < ed ; i ++)
    {
        if(!flag[i].val)
        {
            flag[i].ra = ra;
            flag[i].sa = sa;
            flag[i].rb = rb;
            flag[i].sb = sb;
            flag[i].val = 1;
        }
        else
        {
            unsigned int t1 = flag[i].ra , t2 = flag[i].sa , t3 = flag[i].rb , t4 = flag[i].sb;
            flag[i].ra = (t1*ra + t3*sa);
            flag[i].rb = (t1*rb + t3*sb);
            flag[i].sa = (t2*ra + t4*sa);
            flag[i].sb = (t2*rb + t4*sb);
         }
    }
    if(flag[st].val) solve(st);
    if(st != ed && flag[ed].val) solve(ed);
    int up = (st+1)*dis;
    for(int i = l ; i < up && i <= r; i ++)
    {
        tmp1 = a[i] , tmp2 = b[i];
        a[i] = tmp1 * ra + tmp2 * sa;
        b[i] = tmp1 * rb + tmp2 * sb;
    }
    p[st] = get(st);
    if(st == ed) return;
    for(int i = ed*dis ; i <= r ; i ++)
    {
        tmp1 = a[i] , tmp2 = b[i];
        a[i] = tmp1 * ra + tmp2 * sa;
        b[i] = tmp1 * rb + tmp2 * sb;
    }
    p[ed] = get(ed);
}

unsigned int query(int l , int r)
{
    int st = (l)/dis ;
    int ed = (r)/dis ;
    unsigned int ans = 0;
    for(int i = st+1 ; i < ed ; i ++)
    {
        if(flag[i].val)
        {
            ans += solve(i);
        }
        else ans += p[i];
    }
    if(flag[st].val) solve(st);
    if(st != ed && flag[ed].val) solve(ed);
    int up = (st+1)*dis;
    for(int i = l ; i < up && i <= r; i ++)
    {
        ans += (a[i] * b[i]);
    }
    if(st == ed) return ans;
    for(int i = ed*dis ; i <= r ; i ++)
    {
        ans += (a[i] * b[i]);
    }
    return ans ;
}

int main()
{
   // freopen("D:\\J.in", "r", stdin);
   // freopen("D:\\ss.out", "w", stdout);

    while(scanf("%d %d" , &n , &m) != EOF)
    {
        mem(p , 0) ; mem(flag , 0);mem(a ,0) ; mem(b , 0);
        dis = (int)sqrt(1.0*n);
        for(int i = 1 ; i <= n ; i ++)
            scanf("%u" , &a[i]);
        for(int i = 1 ; i <= n ; i ++)
            scanf("%u" , &b[i]);
        for(int i = 1 ; i <= n ; i ++)
        {
            p[(int)(i/dis)] += a[i]*b[i];
        }
        while(m--)
        {
            int op , x , y ;
            unsigned int  ra , sa , rb , sb;
            scanf("%d" , &op);
            if(op == 1)
            {
                scanf("%d %d %u %u %u %u" ,&x , &y , &ra , &sa , &rb , &sb);
                update(x , y , ra  ,sa , rb , sb);
            }
            else
            {
                scanf("%d %d" , &x , &y);
                printf("%u\n" , query(x , y));
            }
        }
    }
    return 0;
}