[AcWing 1277] 维护序列
作者:互联网
线段树
区间修改(加,乘),区间查询(求和)
点击查看代码
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N = 5e5 + 10;
int n, m, p;
LL w[N];
struct Node
{
int l, r;
LL sum, add, mul;
} tr[N << 2];
void pushup(int u)
{
tr[u].sum = (tr[u << 1].sum + tr[u << 1 | 1].sum) % p;
}
void eval(Node &t, LL add, LL mul)
{
t.sum = (t.sum * mul + (LL)(t.r - t.l + 1) * add) % p;
t.mul = t.mul * mul % p;
t.add = (t.add * mul + add) % p;
}
void pushdown(int u)
{
eval(tr[u << 1], tr[u].add, tr[u].mul);
eval(tr[u << 1 | 1], tr[u].add, tr[u].mul);
tr[u].add = 0;
tr[u].mul = 1;
}
void build(int u, int l, int r)
{
if (l == r)
tr[u] = {l, r, w[l], 0, 1};
else {
tr[u] = {l, r, 0, 0, 1};
int mid = l + r >> 1;
build(u << 1, l, mid);
build(u << 1 | 1, mid + 1, r);
pushup(u);
}
}
void modify(int u, int l, int r, LL add, LL mul)
{
if (tr[u].l >= l && tr[u].r <= r)
eval(tr[u], add, mul);
else {
pushdown(u);
int mid = tr[u].l + tr[u].r >> 1;
if (l <= mid)
modify(u << 1, l, r, add, mul);
if (r > mid)
modify(u << 1 | 1, l, r, add, mul);
pushup(u);
}
}
LL query(int u, int l, int r)
{
if (tr[u].l >= l && tr[u].r <= r)
return tr[u].sum;
else {
pushdown(u);
int mid = tr[u].l + tr[u].r >> 1;
LL res = 0;
if (l <= mid)
res = (res + query(u << 1, l, r)) % p;
if (r > mid)
res = (res + query(u << 1 | 1, l, r)) % p;
return res;
}
}
void solve()
{
cin >> n >> p;
for (int i = 1; i <= n; i ++)
cin >> w[i];
build(1, 1, n);
cin >> m;
while (m --) {
int t, l, r;
cin >> t >> l >> r;
if (t == 1) {
LL d;
cin >> d;
modify(1, l, r, 0, d);
}
else if (t == 2) {
LL d;
cin >> d;
modify(1, l, r, d, 1);
}
else
cout << query(1, l, r) << endl;
}
}
signed main()
{
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
solve();
return 0;
}
- 懒标记
先乘后加比较好维护
① 乘一个数 \(c\),\(x \cdot mul + add \rightarrow x \cdot (mul \cdot c) + (add \cdot c)\)
② 加一个数 \(d\),\(x \cdot mul + add \rightarrow x \cdot mul + (add + d)\)
上面两种操作可以合为一个操作,先乘 \(c\),再加上 \(d\)
\(x \cdot mul + add \rightarrow x \cdot (mul \cdot c) + (add \cdot c + d)\)
当 \(c \neq 1, d = 0\) 时,对应的是乘法操作,当 \(c = 1, d \neq 0\) 时,对应的是加法操作
标签:cdot,LL,cin,1277,int,add,序列,mul,AcWing 来源: https://www.cnblogs.com/wKingYu/p/16534491.html