[AcWing 243] 一个简单的整数问题2(线段树)
作者:互联网
线段树
区间修改,区间查询(和)
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#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int N = 5e5 + 10;
int n, m;
LL w[N];
struct Node
{
int l, r;
LL sum, add;
} tr[N << 2];
void pushup(int u)
{
tr[u].sum = tr[u << 1].sum + tr[u << 1 | 1].sum;
}
void pushdown(int u)
{
auto &root = tr[u], &left = tr[u << 1], &right = tr[u << 1 | 1];
if (root.add) {
left.add += root.add;
left.sum += (LL)(left.r - left.l + 1) * root.add;
right.add += root.add;
right.sum += (LL)(right.r - right.l + 1) * root.add;
root.add = 0;
}
}
void build(int u, int l, int r)
{
if (l == r)
tr[u] = {l, r, w[l], 0};
else {
tr[u] = {l, r};
int mid = l + r >> 1;
build(u << 1, l, mid);
build(u << 1 | 1, mid + 1, r);
pushup(u);
}
}
void update(int u, int l, int r, LL d)
{
if (tr[u].l >= l && tr[u].r <= r) {
tr[u].sum += (LL)(tr[u].r - tr[u].l + 1) * d;
tr[u].add += d;
}
else {
pushdown(u);
int mid = tr[u].l + tr[u].r >> 1;
if (l <= mid)
update(u << 1, l, r, d);
if (r > mid)
update(u << 1 | 1, l, r, d);
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 += query(u << 1, l, r);
if (r > mid)
res += query(u << 1 | 1, l, r);
return res;
}
}
void solve()
{
cin >> n >> m;
for (int i = 1; i <= n; i ++)
cin >> w[i];
build(1, 1, n);
while (m --) {
char op;
int l, r;
cin >> op >> l >> r;
if (op == 'Q')
cout << query(1, l, r) << endl;
else {
LL d;
cin >> d;
update(1, l, r, d);
}
}
}
signed main()
{
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
solve();
return 0;
}
- 区间修改需要用到懒标记
懒标记为需要加的数 \(d\),对于节点 \(root\),以及它的两个子节点 \(left\) 和 \(right\),进行 \(pushdown\) 操作时的更新如下:
① 给左区间加懒标记,\(left.add \ += root.add\)
② 修改左区间的区间和,\(left.sum \ += (left.r - left.l + 1) \cdot root.add\)
③ 给右区间加懒标记,\(right.add \ += root.add\)
④ 修改右区间的区间和,\(right.sum \ += (right.r - right.l + 1) \cdot root.add\)
⑤ 清空 \(root\) 节点的懒标记,\(root.add = 0\)
标签:right,int,线段,add,243,区间,left,root,AcWing 来源: https://www.cnblogs.com/wKingYu/p/16502764.html