线段树维护区间(平方和，立方和)修改区间(加，赋值，乘)

最新推荐文章于 2021-10-18 14:44:23 发布

hannibal_lecter_

最新推荐文章于 2021-10-18 14:44:23 发布

阅读量1.5k

点赞数 1

CC 4.0 BY-SA版权

分类专栏：线段树

本文链接：https://blog.youkuaiyun.com/qq_39921637/article/details/82958664

线段树专栏收录该内容

10 篇文章

订阅专栏

本文介绍了如何使用线段树数据结构有效地维护区间内的平方和与立方和，并详细阐述了如何进行区间加、赋值和乘等操作，提升区间查询与更新的效率。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

题目地址

/*
* @Author: hannibal
* @Date:   2018-08-07 10:42:26
* @Last Modified by:   hannibal
* @Last Modified time: 2018-08-07 17:08:44
*/
#pragma GCC optimize(2)
#include<bits/stdc++.h>
using namespace std;
typedef unsigned long long  ll;
const ll mod = 10007;
const ll maxn = 1e5+10;
ll Case = 1, n, m;
struct node{
	ll l, r;
	ll add, mul, set;
	ll p1, p2, p3;
	ll mid(){return (l+r)/2;}
}tr[maxn<<2];
void pushup(ll rt) {
	tr[rt].p1 = (tr[rt<<1].p1 + tr[rt<<1|1].p1)%mod;
	tr[rt].p2 = (tr[rt<<1].p2 + tr[rt<<1|1].p2)%mod;
	tr[rt].p3 = (tr[rt<<1].p3 + tr[rt<<1|1].p3)%mod;
}
void caladd(ll rt) {
	ll len1 = (tr[rt<<1].r-tr[rt<<1].l+1)%mod;
	ll len2 =( tr[rt<<1|1].r-tr[rt<<1|1].l+1)%mod;
	tr[rt<<1].add = (tr[rt<<1].add+tr[rt].add%mod);tr[rt<<1|1].add = (tr[rt<<1|1].add+tr[rt].add)%mod;
	ll temp = (tr[rt].add*tr[rt].add%mod)*tr[rt].add%mod;
	tr[rt<<1].p3 =(tr[rt<<1].p3+(temp*len1)%mod+3*tr[rt].add*((tr[rt<<1].p2+tr[rt<<1].p1*tr[rt].add)%mod)%mod)%mod;
	tr[rt<<1|1].p3 = (tr[rt<<1|1].p3+(temp*len2)%mod+3*tr[rt].add*((tr[rt<<1|1].p2+tr[rt<<1|1].p1*tr[rt].add)%mod)%mod)%mod;
	tr[rt<<1].p2 = (tr[rt<<1].p2+(tr[rt].add*tr[rt].add%mod*len1%mod)+2*tr[rt<<1].p1*tr[rt].add%mod)%mod;
	tr[rt<<1|1].p2 = (tr[rt<<1|1].p2+(tr[rt].add*tr[rt].add%mod*len2%mod)+2*tr[rt<<1|1].p1*tr[rt].add%mod)%mod;
	tr[rt<<1].p1 = (tr[rt<<1].p1+len1*tr[rt].add%mod)%mod;
	tr[rt<<1|1].p1 = (tr[rt<<1|1].p1+len2*tr[rt].add%mod)%mod;
	tr[rt].add = 0;
}
void calmul(ll rt) {
	ll x = tr[rt].mul;
	tr[rt<<1].mul = (x*tr[rt<<1].mul)%mod;
	tr[rt<<1|1].mul = (x*tr[rt<<1|1].mul)%mod;
	if(tr[rt<<1].add) tr[rt<<1].add = (tr[rt<<1].add*x)%mod;
	if(tr[rt<<1|1].add) tr[rt<<1|1].add = (tr[rt<<1|1].add*x)%mod;
	ll temp = (x*x)%mod*x%mod;
	tr[rt<<1].p1 = (tr[rt<<1].p1*x)%mod;
	tr[rt<<1|1].p1 = (tr[rt<<1|1].p1*x)%mod;
	tr[rt<<1].p2 = (tr[rt<<1].p2*x%mod*x)%mod;
	tr[rt<<1|1].p2 = (tr[rt<<1|1].p2*x%mod*x)%mod;
	tr[rt<<1].p3 = (tr[rt<<1].p3*temp%mod)%mod;
	tr[rt<<1|1].p3 = (tr[rt<<1|1].p3*temp%mod)%mod;
	tr[rt].mul = 1;
}
void calset(ll rt) {
	ll len1 = (tr[rt<<1].r-tr[rt<<1].l+1)%mod;
	ll len2 = (tr[rt<<1|1].r-tr[rt<<1|1].l+1)%mod;
	tr[rt<<1].set = tr[rt<<1|1].set = tr[rt].set;
	tr[rt<<1].add = tr[rt<<1|1].add = 0;
	tr[rt<<1].mul = tr[rt<<1|1].mul = 1;
	ll temp = (tr[rt].set*tr[rt].set)%mod*tr[rt].set%mod;
	tr[rt<<1].p1 = len1*(tr[rt].set%mod)%mod;
	tr[rt<<1|1].p1 = len2*(tr[rt].set%mod)%mod;
	tr[rt<<1].p2 = len1*(tr[rt].set*tr[rt].set%mod)%mod;
	tr[rt<<1|1].p2 = len2*(tr[rt].set*tr[rt].set%mod)%mod;
	tr[rt<<1].p3 = len1*temp%mod;
	tr[rt<<1|1].p3 = len2*temp%mod;
	tr[rt].set = 0;
}
void pushdown(ll rt) {
	if(tr[rt].set) calset(rt);
	if(tr[rt].mul != 1) calmul(rt);
	if(tr[rt].add) caladd(rt);
}
void build(ll rt, ll l, ll r){
	tr[rt].l = l; tr[rt].r = r;tr[rt].mul = 1;
	tr[rt].add =  tr[rt].set = 0;
	if(l == r) {tr[rt].p1 = tr[rt].p2 = tr[rt].p3 = 0;return;}
	ll mid = tr[rt].mid();
	build(rt<<1, l, mid);build(rt<<1|1, mid+1, r);
	pushup(rt);
}
void update(ll rt, ll l, ll r, ll flag, ll c) {
	if(tr[rt].l == l && tr[rt].r == r) {
		if(flag == 1){
			tr[rt].add += c;
			ll temp = c*c%mod*c%mod*(r-l+1)%mod;
			tr[rt].p3 = (tr[rt].p3+temp+3*c*((tr[rt].p2+tr[rt].p1*c)%mod))%mod;
			tr[rt].p2 = (tr[rt].p2+(c*c%mod*(r-l+1)%mod)+2*tr[rt].p1*c%mod)%mod;
			tr[rt].p1 = (tr[rt].p1+(r-l+1)*c%mod)%mod;
		}
		else if(flag == 2) {
			tr[rt].mul = (tr[rt].mul*c)%mod;
			if(tr[rt].add) tr[rt].add = (tr[rt].add*c)%mod;
			tr[rt].p1 = (tr[rt].p1*c)%mod;
			tr[rt].p2 = (tr[rt].p2*c%mod*c)%mod;
			tr[rt].p3 = (tr[rt].p3*c%mod*c%mod*c)%mod;
		}
		else if(flag == 3) {
			tr[rt].set = c; tr[rt].add = 0; tr[rt].mul = 1;
			tr[rt].p1 = (r-l+1)%mod*c%mod;
			tr[rt].p2 = (r-l+1)%mod*c%mod*c%mod;
			tr[rt].p3 = (r-l+1)%mod*c%mod*c%mod*c%mod;
		}
		return;
	}
	pushdown(rt);
	ll mid = tr[rt].mid();
	if(r <= mid) update(rt<<1, l, r, flag, c);
	else if(l > mid) update(rt<<1|1, l, r, flag, c);
	else update(rt<<1, l, mid, flag, c), update(rt<<1|1, mid+1, r, flag, c);
	pushup(rt);
}
ll query(ll rt, ll l, ll r, ll p) {
	if(tr[rt].l == l && tr[rt].r == r) {
		if(p == 1) return tr[rt].p1%mod;
		else if(p == 2) return tr[rt].p2%mod;
		else return tr[rt].p3%mod;
	}
	pushdown(rt);
	ll mid = tr[rt].mid();
	if(r <= mid) return query(rt<<1, l, r, p);
	else if(l > mid) return query(rt<<1|1, l, r, p);
	else return (query(rt<<1, l, mid, p)+query(rt<<1|1,mid+1, r, p)+mod)%mod;
}
void solve() {
	build(1, 1, n);
	for(ll i = 1; i <= m; i++){
		ll q, x, y, p;
		scanf("%llu%llu%llu%llu", &q, &x, &y, &p);
		if(q == 4) printf("%llu\n", query(1, x, y, p)%mod);
		else update(1, x, y, q, p);
	}
}
int main() {
    ios::sync_with_stdio(false);
#ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
#endif
    while(scanf("%llu%llu", &n, &m) == 2&&(n+m)) {
        solve();
    }
    return 0;
}