lgP1253 扶苏的问题
给定长度为n的序列A，有如下3种操作：
- 1 l r x，将区间[l,r]中的每个数都修改为x。
- 2 l r x，将区间[l,r]中的每个数都加上x。
- 3 l r，查询区间[l,r]内的最大值。
分析：设置2个懒标记，先处理赋值标记，再处理增加标记。
#include <bits/stdc++.h>
using llong = long long;
const llong inf = 1e18;
template<class Info, class Tag>
struct LazySegmentTree {
int n;
std::vector<Info> info;
std::vector<Tag> tag;
LazySegmentTree():n(0) {}
LazySegmentTree(int _n, Info v=Info()) {
init(_n, v);
}
template<class T>
LazySegmentTree(std::vector<T> v) {
init(v);
}
void init(int _n, Info v=Info()) {
init(std::vector<Info>(_n, v));
}
template<class T>
void init(std::vector<T> v) {
n = v.size();
info.assign(4 << std::__lg(n), Info());
tag.assign(4 << std::__lg(n), Tag());
std::function<void(int,int,int)> build = [&](int x, int l, int r) {
if (l + 1 == r) {
info[x] = v[l];
return;
}
int m = (l + r) / 2;
build(2*x+1, l, m);
build(2*x+2, m, r);
pushup(x);
};
build(0, 0, n);
}
void pushup(int x) {
info[x] = info[2*x+1] + info[2*x+2];
}
void apply(int x, const Tag &t) {
info[x].apply(t);
tag[x].apply(t);
}
void pushdown(int x) {
apply(2*x+1, tag[x]);
apply(2*x+2, tag[x]);
tag[x] = Tag();
}
void assign(int x, int l, int r, int p, const Info &v) {
if (l + 1 == r) {
info[x] = v;
return;
}
int m = (l + r) / 2;
pushdown(x);
if (p < m) {
assign(2*x+1, l, m, p, v);
} else {
assign(2*x+2, m, r, p, v);
}
pushup(x);
}
void assign(int p, const Info &v) {
assign(0, 0, n, p, v);
}
void add(int x, int l, int r, int p, const Info &v) {
if (l + 1 == r) {
info[x] += v;
return;
}
int m = (l + r) / 2;
pushdown(x);
if (p < m) {
add(2*x+1, l, m, p, v);
} else {
add(2*x+2, m, r, p, v);
}
pushup(x);
}
void add(int p, const Info &v) {
add(0, 0, n, p, v);
}
Info rangeQuery(int x, int l, int r, int L, int R) {
if (R <= l || r <= L) {
return Info();
}
if (L <= l && r <= R) {
return info[x];
}
int m = (l + r) / 2;
pushdown(x);
return rangeQuery(2*x+1, l, m, L, R) + rangeQuery(2*x+2, m, r, L, R);
}
Info rangeQuery(int L, int R) {
return rangeQuery(0, 0, n, L, R);
}
void rangeApply(int x, int l, int r, int L, int R, const Tag &t) {
if (R <= l || r <= L) {
return;
}
if (L <= l && r <= R) {
apply(x, t);
return;
}
int m = (l + r) / 2;
pushdown(x);
rangeApply(2*x+1, l, m, L, R, t);
rangeApply(2*x+2, m, r, L, R, t);
pushup(x);
}
void rangeApply(int L, int R, const Tag &t) {
return rangeApply(0, 0, n, L, R, t);
}
template<class F>
int findFirst(int x, int l, int r, int L, int R, F && pred) {
if (R <= l || r <= L) {
return -1;
}
if (L <= l && r <= R && !pred(info[x])) {
return -1;
}
if (l + 1 == r) {
return l;
}
int m = (l + r) / 2;
pushdown(x);
int res = findFirst(2*x+1, l, m, L, R, pred);
if (res == -1) {
res = findFirst(2*x+2, m, r, L, R, pred);
}
return res;
}
template<class F>
int findFirst(int L, int R, F &&pred) {
return findFirst(0, 0, n, L, R, pred);
}
template<class F>
int findLast(int x, int l, int r, int L, int R, F &&pred) {
if (R <= l || r <= L) {
return -1;
}
if (L <= l && r <= R && !pred(info[x])) {
return -1;
}
if (l + 1 == r) {
return l;
}
int m = (l + r) / 2;
pushdown(x);
int res = findLast(2*x+2, m, r, L, R, pred);
if (res == -1) {
res = findLast(2*x+1, l, m, L, R, pred);
}
return res;
}
template<class F>
int findLast(int L, int R, F &&pred) {
return findLast(0, 0, n, L, R, pred);
}
void print(int x, int l, int r) {
std::cerr << x << "(" << l << "," << r << ") " << info[x] << " " << tag[x] << "\n";
if (l + 1 < r) {
int m = (l + r) / 2;
print(2*x+1, l, m);
print(2*x+2, m, r);
}
}
void print() {
std::cerr << "-----------------------------\n";
print(0, 0, n);
}
};
struct Tag {
llong set;
llong add;
Tag(llong s=inf, llong a=inf):set(s),add(a) {}
void apply(Tag t) {
if (t.set != inf) {
set = t.set;
add = inf;
}
if (t.add != inf) {
if (add == inf) {
add = t.add;
} else {
add += t.add;
}
}
}
friend std::ostream& operator<<(std::ostream &out, Tag &tag) {
out << "tag:(" << tag.set << "," << tag.add << ")";
return out;
}
};
struct Info {
llong max;
Info(llong a=-inf):max(a) {}
void apply(Tag t) {
if (t.set != inf) {
max = t.set;
}
if (t.add != inf) {
max += t.add;
}
}
friend Info operator+(const Info &a, const Info &b) {
Info ans;
ans.max = std::max(a.max, b.max);
return ans;
}
friend std::ostream& operator<<(std::ostream &out, Info &info) {
out << "info:(" << info.max << ")";
return out;
}
};
void solve() {
int n, m;
std::cin >> n >> m;
std::vector<llong> A(n);
for (int i = 0; i < n; i++) {
std::cin >> A[i];
}
LazySegmentTree<Info,Tag> tr(A);
for (int i = 0; i < m; i++) {
int op, l, r, x;
std::cin >> op >> l >> r;
if (op == 1) {
std::cin >> x;
tr.rangeApply(l-1, r, Tag(x, inf));
} else if (op == 2) {
std::cin >> x;
tr.rangeApply(l-1, r, Tag(inf, x));
} else if (op == 3) {
std::cout << tr.rangeQuery(l-1, r).max << "\n";
}
}
}
int main() {
std::cin.tie(0)->sync_with_stdio(0);
int t = 1;
while (t--) solve();
return 0;
}
