HDU - 1542: Atlantis
解法
概要
\(O(n^2 \log n)\)
座標圧縮して通常の遅延伝搬segment木などでsweepline
\(O(n^2)\)
座標圧縮してimos法
\(O(n \log n)\)
座標圧縮して部分性拡張した遅延伝搬segment木 https://kimiyuki.net/blog/2018/11/03/lazy-propagation-segment-tree/
メモ
https://github.com/kmyk/competitive-programming-library/issues/3
実装
#include <bits/stdc++.h>
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = int(n) - 1; (i) >= 0; -- (i))
#define ALL(x) begin(x), end(x)
using namespace std;
template <class Monoid, class OperatorMonoid>
struct lazy_propagation_segment_tree { // on monoids
static_assert (is_same<typename Monoid::underlying_type, typename OperatorMonoid::target_type>::value, "");
typedef typename Monoid::underlying_type underlying_type;
typedef typename OperatorMonoid::underlying_type operator_type;
const Monoid mon;
const OperatorMonoid op;
int n;
vector<underlying_type> a;
vector<operator_type> f;
lazy_propagation_segment_tree() = default;
lazy_propagation_segment_tree(int a_n, underlying_type initial_value = Monoid().unit(), Monoid const & a_mon = Monoid(), OperatorMonoid const & a_op = OperatorMonoid())
: mon(a_mon), op(a_op) {
n = 1; while (n <= a_n) n *= 2;
a.resize(2 * n - 1, mon.unit());
fill(a.begin() + (n - 1), a.begin() + ((n - 1) + a_n), initial_value); // set initial values
REP_R (i, n - 1) a[i] = mon.append(a[2 * i + 1], a[2 * i + 2]); // propagate initial values
f.resize(max(0, (2 * n - 1) - n), op.identity());
}
void point_set(int i, underlying_type z) {
assert (0 <= i and i < n);
point_set(0, 0, n, i, z);
}
void point_set(int i, int il, int ir, int j, underlying_type z) {
if (i == n + j - 1) { // 0-based
a[i] = z;
} else if (ir <= j or j+1 <= il) {
// nop
} else {
flush(i, il, ir, false);
point_set(2 * i + 1, il, (il + ir) / 2, j, z);
point_set(2 * i + 2, (il + ir) / 2, ir, j, z);
a[i] = mon.append(a[2 * i + 1], a[2 * i + 2]);
}
}
void range_apply(int l, int r, operator_type z) {
assert (0 <= l and l <= r and r <= n);
if (z == op.identity()) return;
range_apply(0, 0, n, l, r, z);
}
void range_apply(int i, int il, int ir, int l, int r, operator_type z) {
if (l <= il and ir <= r) { // 0-based
if (i < f.size()) f[i] = op.compose(z, f[i]);
try {
a[i] = op.apply(z, a[i]);
} catch (typename OperatorMonoid::domain_error e) {
if (i < f.size()) {
flush(i, il, ir, false);
a[i] = mon.append(a[2 * i + 1], a[2 * i + 2]);
} else {
assert (false);
}
}
} else if (ir <= l or r <= il) {
// nop
} else {
flush(i, il, ir, false);
range_apply(2 * i + 1, il, (il + ir) / 2, l, r, z);
range_apply(2 * i + 2, (il + ir) / 2, ir, l, r, z);
a[i] = mon.append(a[2 * i + 1], a[2 * i + 2]);
}
}
underlying_type range_concat(int l, int r) {
assert (0 <= l and l <= r and r <= n);
return range_concat(0, 0, n, l, r);
}
underlying_type range_concat(int i, int il, int ir, int l, int r) {
if (l <= il and ir <= r) { // 0-based
return a[i];
} else if (ir <= l or r <= il) {
return mon.unit();
} else {
try {
return op.apply(f[i], mon.append(
range_concat(2 * i + 1, il, (il + ir) / 2, l, r),
range_concat(2 * i + 2, (il + ir) / 2, ir, l, r)));
} catch (typename OperatorMonoid::domain_error e) {
flush(i, il, ir, true);
return mon.append(
range_concat(2 * i + 1, il, (il + ir) / 2, l, r),
range_concat(2 * i + 2, (il + ir) / 2, ir, l, r));
}
}
}
private:
void flush(int i, int il, int ir, bool pred) {
if (f[i] == op.identity()) return;
range_apply(2 * i + 1, il, (il + ir) / 2, 0, n, f[i]);
range_apply(2 * i + 2, (il + ir) / 2, ir, 0, n, f[i]);
f[i] = op.identity();
if (pred) a[i] = mon.append(a[2 * i + 1], a[2 * i + 2]);
}
};
template <typename T>
struct count_monoid_with_range {
typedef struct {
T l, r; // of range
bool is_atomic;
int multiplicity;
T covered;
} underlying_type;
underlying_type unit() const {
return (underlying_type) { -1, -1, false, -1, -1 };
}
underlying_type append(underlying_type a, underlying_type b) const {
if (a.multiplicity == -1) return b;
if (b.multiplicity == -1) return a;
underlying_type c;
c.l = a.l;
c.r = b.r;
c.is_atomic = false;
c.multiplicity = min(a.multiplicity, b.multiplicity);
c.covered = a.covered + b.covered;
return c;
}
};
template <typename T>
struct increment_operator_monoid_with_range {
typedef int underlying_type;
typedef typename count_monoid_with_range<T>::underlying_type target_type;
typedef struct {} domain_error;
underlying_type identity() const {
return 0;
}
target_type apply(underlying_type a, target_type b) const {
if (a == 0) return b;
b.multiplicity += a;
if (b.multiplicity > 0) {
b.covered = b.r - b.l;
} else if (b.is_atomic) {
b.covered = 0;
} else {
throw (domain_error) {};
}
return b;
}
underlying_type compose(underlying_type a, underlying_type b) const {
return a + b;
}
};
double solve(int n, vector<double> const & x1, vector<double> const & y1, vector<double> const & x2, vector<double> const & y2) {
// coordinate compression
vector<double> xs;
xs.insert(xs.end(), ALL(x1));
xs.insert(xs.end(), ALL(x2));
sort(ALL(xs));
xs.erase(unique(ALL(xs)), xs.end());
auto compress = [&](double x) { return lower_bound(ALL(xs), x) - xs.begin(); };
// prepare segtree
lazy_propagation_segment_tree<count_monoid_with_range<double>, increment_operator_monoid_with_range<double> > segtree(xs.size() - 1);
REP (i, xs.size() - 1) {
typename count_monoid_with_range<double>::underlying_type a;
a.l = xs[i];
a.r = xs[i + 1];
a.is_atomic = true;
a.multiplicity = 0;
a.covered = 0;
segtree.point_set(i, a);
}
// prepare events
vector<tuple<double, int, int, int> > events;
REP (i, n) {
events.emplace_back(y1[i], compress(x1[i]), compress(x2[i]), +1);
events.emplace_back(y2[i], compress(x1[i]), compress(x2[i]), -1);
}
sort(ALL(events));
// use sweepline
double acc = 0;
double last_y = 0;
for (auto event : events) {
double y; int l, r, delta; tie(y, l, r, delta) = event;
acc += (y - last_y) * segtree.range_concat(0, xs.size()).covered;
segtree.range_apply(l, r, delta);
last_y = y;
}
return acc;
}
int main() {
for (int testcase = 1; ; ++ testcase) {
int n; cin >> n;
if (n == 0) break;
vector<double> x1(n), y1(n), x2(n), y2(n);
REP (i, n) {
cin >> x1[i] >> y1[i] >> x2[i] >> y2[i];
}
cout << "Test case #" << testcase << endl;
cout << "Total explored area: " << fixed << setprecision(2) << solve(n, x1, y1, x2, y2) << endl;
cout << endl;
}
return 0;
}