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DataStructure/test/area_of_union_of_rectangles.test.cpp
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- Last update: 2023-01-07 02:15:55+08:00
- Problem: https://judge.yosupo.jp/problem/area_of_union_of_rectangles
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Code
#define PROBLEM "https://judge.yosupo.jp/problem/area_of_union_of_rectangles"
#include <bits/stdc++.h>
using namespace std;
#include "../misc/area_of_union_of_rectangles.h"
using namespace area_of_union_of_rectangles;
int main() {
int n; cin >> n;
vector<Rect> rects(n);
for (auto& r : rects) cin >> r;
cout << solve(rects) << endl;
}#line 1 "DataStructure/test/area_of_union_of_rectangles.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/area_of_union_of_rectangles"
#include <bits/stdc++.h>
using namespace std;
#line 1 "DataStructure/LazySegTree.h"
// Lazy Segment Tree, copied from AtCoder {{{
// Source: https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp
// Doc: https://atcoder.github.io/ac-library/master/document_en/lazysegtree.html
//
// Notes:
// - Index of elements from 0
// - Range queries are [l, r-1]
// - composition(f, g) should return f(g())
//
// Tested:
// - https://oj.vnoi.info/problem/qmax2
// - https://oj.vnoi.info/problem/lites
// - (range set, add, mult, sum) https://oj.vnoi.info/problem/segtree_itmix
// - (range add (i-L)*A + B, sum) https://oj.vnoi.info/problem/segtree_itladder
// - https://atcoder.jp/contests/practice2/tasks/practice2_l
// - https://judge.yosupo.jp/problem/range_affine_range_sum
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
template<
class S, // node data type
S (*op) (S, S), // combine 2 nodes
S (*e) (), // identity element
class F, // lazy propagation tag
S (*mapping) (F, S), // apply tag F on a node
F (*composition) (F, F), // combine 2 tags
F (*id)() // identity tag
>
struct LazySegTree {
LazySegTree() : LazySegTree(0) {}
explicit LazySegTree(int n) : LazySegTree(vector<S>(n, e())) {}
explicit LazySegTree(const vector<S>& v) : _n((int) v.size()) {
log = ceil_pow2(_n);
size = 1 << log;
d = std::vector<S>(2 * size, e());
lz = std::vector<F>(size, id());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
// 0 <= p < n
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
// 0 <= p < n
S get(int p) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return d[p];
}
// Get product in range [l, r-1]
// 0 <= l <= r <= n
// For empty segment (l == r) -> return e()
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return e();
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
S sml = e(), smr = e();
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() {
return d[1];
}
// 0 <= p < n
void apply(int p, F f) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = mapping(f, d[p]);
for (int i = 1; i <= log; i++) update(p >> i);
}
// Apply f on all elements in range [l, r-1]
// 0 <= l <= r <= n
void apply(int l, int r, F f) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return;
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
// Binary search on SegTree to find largest r:
// f(op(a[l] .. a[r-1])) = true (assuming empty array is always true)
// f(op(a[l] .. a[r])) = false (assuming op(..., a[n]), which is out of bound, is always false)
template <bool (*g)(S)> int max_right(int l) {
return max_right(l, [](S x) { return g(x); });
}
template <class G> int max_right(int l, G g) {
assert(0 <= l && l <= _n);
assert(g(e()));
if (l == _n) return _n;
l += size;
for (int i = log; i >= 1; i--) push(l >> i);
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!g(op(sm, d[l]))) {
while (l < size) {
push(l);
l = (2 * l);
if (g(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
// Binary search on SegTree to find smallest l:
// f(op(a[l] .. a[r-1])) = true (assuming empty array is always true)
// f(op(a[l-1] .. a[r-1])) = false (assuming op(a[-1], ..), which is out of bound, is always false)
template <bool (*g)(S)> int min_left(int r) {
return min_left(r, [](S x) { return g(x); });
}
template <class G> int min_left(int r, G g) {
assert(0 <= r && r <= _n);
assert(g(e()));
if (r == 0) return 0;
r += size;
for (int i = log; i >= 1; i--) push((r - 1) >> i);
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!g(op(d[r], sm))) {
while (r < size) {
push(r);
r = (2 * r + 1);
if (g(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
vector<S> d;
vector<F> lz;
void update(int k) {
d[k] = op(d[2*k], d[2*k+1]);
}
void all_apply(int k, F f) {
d[k] = mapping(f, d[k]);
if (k < size) lz[k] = composition(f, lz[k]);
}
void push(int k) {
all_apply(2*k, lz[k]);
all_apply(2*k+1, lz[k]);
lz[k] = id();
}
};
// }}}
// Examples {{{
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_D
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_E
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_F
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_G
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_H
// https://onlinejudge.u-aizu.ac.jp/courses/library/3/DSL/2/DSL_2_I
// supports:
// - set a(l -> r) to val; val > NOT_SET
// - add a(l -> r) += val
// - find sum a(l -> r)
// - find min a(l -> r)
struct RangeSetAddMinSumOps {
struct S { long long sum, min, sz; };
static S op(S l, S r) { return S { l.sum + r.sum, min(l.min, r.min), l.sz + r.sz }; }
static S e() { return S {0LL, INT_MAX, 0}; }
static const long long NOT_SET = -1000111000;
struct F { long long set, add; };
static S mapping(F f, S s) {
if (f.set == NOT_SET) {
return S {
s.sum + f.add * s.sz,
s.min + f.add,
s.sz,
};
}
return S {
(f.set + f.add) * s.sz,
f.set + f.add,
s.sz,
};
}
static F composition(F f, F g) {
if (f.set == NOT_SET) {
return F { g.set, g.add + f.add };
}
return f;
}
static F id() {
return F { NOT_SET, 0 };
}
};
// }}}
#line 2 "DataStructure/misc/area_of_union_of_rectangles.h"
// Area of union of rectangles {{{
namespace area_of_union_of_rectangles {
using ll = long long;
const int INF = std::numeric_limits<int>::max() / 2;
struct Rect {
int x1, y1, x2, y2;
};
istream& operator >> (istream& cin, Rect& r) {
cin >> r.x1 >> r.y1 >> r.x2 >> r.y2;
return cin;
}
struct S {
int min_cnt;
ll sum;
};
S op(S x, S y) {
if (x.min_cnt < y.min_cnt) return x;
if (y.min_cnt < x.min_cnt) return y;
return { x.min_cnt, x.sum + y.sum };
}
S e() { return { INF, 0 }; }
S mapping(int f, S s) { return { s.min_cnt + f, s.sum }; }
int composition(int f, int g) { return f + g; }
int id() { return 0; }
using ST = LazySegTree<S, op, e, int, mapping, composition, id>;
ll solve(const std::vector<Rect>& rects) {
if (rects.empty()) return ll(0);
const int n = rects.size();
std::vector<std::tuple<int, int, int, int>> events; events.reserve(2*n);
std::vector<int> ys; ys.reserve(2*n);
for (const auto& r : rects) {
events.emplace_back(r.x1, r.y1, r.y2, +1);
events.emplace_back(r.x2, r.y1, r.y2, -1);
ys.push_back(r.y1);
ys.push_back(r.y2);
}
std::sort(events.begin(), events.end(), [] (const auto& e1, const auto& e2) {
return std::get<0>(e1) < std::get<0>(e2); });
std::sort(ys.begin(), ys.end());
ys.erase(std::unique(ys.begin(), ys.end()), ys.end());
const int nys = ys.size();
std::vector<S> init(nys - 1);
for (int i = 0; i < nys - 1; ++i) {
init[i] = { 0, ys[i+1] - ys[i] };
}
ST st(init);
ll res = 0;
ll lx = std::get<0>(events.front()); // events[i-1].x
for (int i = 0; lx != std::get<0>(events.back());) {
for (;; ++i) {
auto [xi, d, u, add] = events[i];
if (xi != lx) break;
int ly = std::lower_bound(ys.begin(), ys.end(), d) - ys.begin();
int ry = std::lower_bound(ys.begin(), ys.end(), u) - ys.begin();
st.apply(ly, ry, add);
}
ll rx = std::get<0> (events[i]);
auto [min_cnt, sum] = st.all_prod();
res += (rx - lx) * (ys.back() - ys.front() - (min_cnt == 0 ? sum : ll(0)));
lx = rx;
}
return res;
}
}
// }}}
#line 6 "DataStructure/test/area_of_union_of_rectangles.test.cpp"
using namespace area_of_union_of_rectangles;
int main() {
int n; cin >> n;
vector<Rect> rects(n);
for (auto& r : rects) cin >> r;
cout << solve(rects) << endl;
}