Blog of RuSun

\begin {array}{c} \mathfrak {One Problem Is Difficult} \\\\ \mathfrak {Because You Don't Know} \\\\ \mathfrak {Why It Is Diffucult} \end {array}

P4314 CPU 监控

P4314 CPU 监控

线段树历史最值问题的模板。考虑每个操作对历史最大值的影响。对于区间覆盖操作,很好维护。事实上,对于加操作,同样的将 $tag$ 下传,历史上会出现不同的 $tag$ 需要下传,我们当然不能全部下传,而下面的没有被 pushdown ,值一直没有变,它的历史最大值就是最大的 $tag$ 加上原来的值。在区间覆盖后,所有的数都是一样的,所有的区间加操作都相当于区间覆盖操作。

查看代码
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#include <cstdio>
#include <algorithm>
using namespace std;
typedef long long LL;
const LL inf = 1e16;
const int N = 1e5 + 10;
template <class Type>
void read(Type &x)
{
char c;
bool flag = false;
while ((c = getchar()) < '0' || c > '9')
(c == '-') && (flag = true);
x = c - '0';
while ((c = getchar()) >= '0' && c <= '9')
x = (x << 3) + (x << 1) + c - '0';
(flag) && (x = ~x + 1);
}
void chkmax(LL &x, LL k)
{
(x < k) && (x = k);
}
struct Node
{
int l, r;
LL mx, _mx, add, _add, cvr, _cvr;
} tr[N << 2];
int n, m, w[N];
void pushup(int x)
{
tr[x].mx = max(tr[x << 1].mx, tr[x << 1 | 1].mx);
tr[x]._mx = max(tr[x << 1]._mx, tr[x << 1 | 1]._mx);
}
void pushadd(int x, LL v, LL _v)
{
chkmax(tr[x]._mx, tr[x].mx + _v);
tr[x].mx += v;
if (tr[x].cvr == -inf)
{
chkmax(tr[x]._add, tr[x].add + _v);
tr[x].add += v;
}
else
{
chkmax(tr[x]._cvr, tr[x].cvr + _v);
tr[x].cvr += v;
}
}
void pushcover(int x, LL v, LL _v)
{
chkmax(tr[x]._mx, _v);
chkmax(tr[x]._cvr, _v);
tr[x].mx = tr[x].cvr = v;
}
void pushdown(int x)
{
if (tr[x].add || tr[x]._add)
{
pushadd(x << 1, tr[x].add, tr[x]._add);
pushadd(x << 1 | 1, tr[x].add, tr[x]._add);
tr[x].add = tr[x]._add = 0;
}
if (tr[x].cvr != -inf || tr[x]._cvr != -inf)
{
pushcover(x << 1, tr[x].cvr, tr[x]._cvr);
pushcover(x << 1 | 1, tr[x].cvr, tr[x]._cvr);
tr[x].cvr = tr[x]._cvr = -inf;
}
}
void build(int l = 1, int r = n, int x = 1)
{
tr[x].cvr = tr[x]._cvr = -inf;
tr[x].l = l, tr[x].r = r;
if (l == r)
{
tr[x].mx = tr[x]._mx = w[l];
return;
}
int mid = l + r >> 1;
build(l, mid, x << 1);
build(mid + 1, r, x << 1 | 1);
pushup(x);
}
void add(int l, int r, int k, int x = 1)
{
if (tr[x].l >= l && tr[x].r <= r)
return pushadd(x, k, max(0, k));
pushdown(x);
int mid = tr[x].l + tr[x].r >> 1;
if (l <= mid)
add(l, r, k, x << 1);
if (r > mid)
add(l, r, k, x << 1 | 1);
pushup(x);
}
void cover(int l, int r, int k, int x = 1)
{
if (tr[x].l >= l && tr[x].r <= r)
return pushcover(x, k, k);
pushdown(x);
int mid = tr[x].l + tr[x].r >> 1;
if (l <= mid)
cover(l, r, k, x << 1);
if (r > mid)
cover(l, r, k, x << 1 | 1);
pushup(x);
}
LL query(int l, int r, int x = 1)
{
if (tr[x].l >= l && tr[x].r <= r)
return tr[x].mx;
pushdown(x);
int mid = tr[x].l + tr[x].r >> 1;
LL res = -inf;
if (l <= mid)
chkmax(res, query(l, r, x << 1));
if (r > mid)
chkmax(res, query(l, r, x << 1 | 1));
return res;
}
LL _query(int l, int r, int x = 1)
{
if (tr[x].l >= l && tr[x].r <= r)
return tr[x]._mx;
pushdown(x);
int mid = tr[x].l + tr[x].r >> 1;
LL res = -inf;
if (l <= mid)
chkmax(res, _query(l, r, x << 1));
if (r > mid)
chkmax(res, _query(l, r, x << 1 | 1));
return res;
}
int main()
{
read(n);
for (int i = 1; i <= n; i++)
read(w[i]);
build();
read(m);
for (char op; m; m--)
{
scanf("%c", &op);
if (op == 'Q')
{
int l, r;
read(l), read(r);
printf("%lld\n", query(l, r));
}
else if (op == 'A')
{
int l, r;
read(l), read(r);
printf("%lld\n", _query(l, r));
}
else if (op == 'P')
{
int l, r, k;
read(l), read(r), read(k);
add(l, r, k);
}
else if (op == 'C')
{
int l, r, k;
read(l), read(r), read(k);
cover(l, r, k);
}
}
return 0;
}