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test/library-checker/manhattanmst.test.cpp
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- Last update: 2024-07-05 09:06:01+09:00
- Problem: https://judge.yosupo.jp/problem/manhattanmst
Depends on
Code
#define PROBLEM "https://judge.yosupo.jp/problem/manhattanmst"
#include <atcoder/dsu>
#include <iostream>
#include "graph/manhattan_mst.hpp"
int main() {
int n;
std::cin >> n;
std::vector<long long> x(n), y(n);
for (int i = 0; i < n; i++) {
std::cin >> x[i] >> y[i];
}
atcoder::dsu uf(n);
long long sum = 0;
std::vector<std::pair<int, int>> ans;
for (auto [u, v, w] : manhattan_mst(x, y)) {
if (!uf.same(u, v)) {
uf.merge(u, v);
sum += w;
ans.emplace_back(u, v);
}
}
std::cout << sum << '\n';
for (auto [u, v] : ans) {
std::cout << u << ' ' << v << '\n';
}
}#line 1 "test/library-checker/manhattanmst.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/manhattanmst"
#include <atcoder/dsu>
#include <iostream>
#line 2 "graph/manhattan_mst.hpp"
#include <algorithm>
#include <cassert>
#line 5 "graph/manhattan_mst.hpp"
#include <limits>
#include <map>
#include <numeric>
#include <vector>
#line 1 "atcoder/segtree.hpp"
#line 7 "atcoder/segtree.hpp"
#line 1 "atcoder/internal_bit.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
constexpr int bsf_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#line 9 "atcoder/segtree.hpp"
namespace atcoder {
template <class S, S (*op)(S, S), S (*e)()> struct segtree {
public:
segtree() : segtree(0) {}
explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
log = internal::ceil_pow2(_n);
size = 1 << log;
d = std::vector<S>(2 * size, e());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
S get(int p) const {
assert(0 <= p && p < _n);
return d[p + size];
}
S prod(int l, int r) const {
assert(0 <= l && l <= r && r <= _n);
S sml = e(), smr = e();
l += size;
r += size;
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() const { return d[1]; }
template <bool (*f)(S)> int max_right(int l) const {
return max_right(l, [](S x) { return f(x); });
}
template <class F> int max_right(int l, F f) const {
assert(0 <= l && l <= _n);
assert(f(e()));
if (l == _n) return _n;
l += size;
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!f(op(sm, d[l]))) {
while (l < size) {
l = (2 * l);
if (f(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;
}
template <bool (*f)(S)> int min_left(int r) const {
return min_left(r, [](S x) { return f(x); });
}
template <class F> int min_left(int r, F f) const {
assert(0 <= r && r <= _n);
assert(f(e()));
if (r == 0) return 0;
r += size;
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(op(d[r], sm))) {
while (r < size) {
r = (2 * r + 1);
if (f(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;
std::vector<S> d;
void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};
} // namespace atcoder
#line 11 "graph/manhattan_mst.hpp"
namespace manhattan_mst_internal {
template <typename T>
struct S {
T val;
int id;
};
template <typename T>
S<T> op(S<T> a, S<T> b) {
return a.val < b.val ? a : b;
}
template <typename T>
S<T> e() {
return {std::numeric_limits<T>::max(), -1};
}
} // namespace manhattan_mst_internal
template <typename T>
std::vector<std::tuple<int, int, T>> manhattan_mst(std::vector<T> x,
std::vector<T> y) {
int n = x.size();
assert(int(x.size()) == n && int(y.size()) == n);
std::vector<int> id(n);
std::iota(id.begin(), id.end(), 0);
std::vector<int> y_id(n);
std::vector<std::tuple<int, int, T>> ret;
for (int a = 0; a < 2; a++) {
for (int b = 0; b < 2; b++) {
for (int c = 0; c < 2; c++) {
sort(id.begin(), id.end(), [&](int i, int j) {
if (y[i] - x[i] == y[j] - x[j] && y[i] == y[j])
return i < j;
if (y[i] - x[i] == y[j] - x[j]) return y[i] > y[j];
return y[i] - x[i] < y[j] - x[j];
});
std::vector<T> _y = y;
std::sort(_y.begin(), _y.end());
for (int i = 0; i < n; i++) {
y_id[i] = std::lower_bound(_y.begin(), _y.end(), y[i]) -
_y.begin();
}
atcoder::segtree<manhattan_mst_internal::S<T>,
manhattan_mst_internal::op<T>,
manhattan_mst_internal::e<T>>
segt(n);
for (int i : id) {
manhattan_mst_internal::S<T> p = segt.prod(y_id[i], n);
if (p.id != -1) {
ret.emplace_back(i, p.id, p.val - (x[i] + y[i]));
}
segt.set(y_id[i], {x[i] + y[i], i});
}
std::swap(x, y);
}
for (T &x : x) x = -x;
}
for (T &y : y) y = -y;
}
sort(ret.begin(), ret.end(),
[](auto a, auto b) { return std::get<2>(a) < std::get<2>(b); });
return ret;
}
#line 7 "test/library-checker/manhattanmst.test.cpp"
int main() {
int n;
std::cin >> n;
std::vector<long long> x(n), y(n);
for (int i = 0; i < n; i++) {
std::cin >> x[i] >> y[i];
}
atcoder::dsu uf(n);
long long sum = 0;
std::vector<std::pair<int, int>> ans;
for (auto [u, v, w] : manhattan_mst(x, y)) {
if (!uf.same(u, v)) {
uf.merge(u, v);
sum += w;
ans.emplace_back(u, v);
}
}
std::cout << sum << '\n';
for (auto [u, v] : ans) {
std::cout << u << ' ' << v << '\n';
}
}