#include <bits/stdc++.h>
using namespace std;
using lint = long long;
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int N, K;
cin >> N >> K;
vector<lint> X(N), Y(N);
for (int i = 0; i < N; i++) {
cin >> X[i] >> Y[i];
}
// There is a vertical or horizontal line which divides K = 3 -> {1, 2}.
// Binary search the answer L. If cuts are shaped like (|-), then we
// can greedily take big left part. If cuts are shaped like (| |), we
// brute force middle (as we can greedily take middle), precompute left part
// and right part.
//
// This takes O(N log MAX).
vector<int> sortByX(N);
vector<int> sortByY(N);
iota(begin(sortByX), end(sortByX), 0);
iota(begin(sortByY), end(sortByY), 0);
sort(begin(sortByX), end(sortByX), [&](int i, int j) {
return pair(X[i], Y[i]) < pair(X[j], Y[j]);
});
sort(begin(sortByY), end(sortByY), [&](int i, int j) {
return pair(Y[i], X[i]) < pair(Y[j], X[j]);
});
vector<int> posInSortByX(N);
vector<int> posInSortByY(N);
for (int i = 0; i < N; i++) {
posInSortByX[sortByX[i]] = i;
posInSortByY[sortByY[i]] = i;
}
const auto CountingSort = [&](vector<int> &a, const vector<int> &sorted, const vector<int> &pos) {
static vector<int> res(N);
fill(begin(res), end(res), 0);
for (auto i : a) {
res[pos[i]] = 1;
}
a.clear();
for (int i = 0; i < N; i++) {
if (res[i]) {
a.emplace_back(sorted[i]);
}
}
};
vector<array<lint, 3>> ans;
const auto SolveK1 = [&](lint L, vector<int> alive, int config) {
if (alive.empty()) return true;
lint minX = +2e9;
lint maxX = -2e9;
lint minY = +2e9;
lint maxY = -2e9;
for (auto i : alive) {
minX = min(minX, X[i]);
maxX = max(maxX, X[i]);
minY = min(minY, Y[i]);
maxY = max(maxY, Y[i]);
}
if (maxX - minX <= L && maxY - minY <= L) {
lint len = max({1ll, maxX - minX, maxY - minY});
if (config == 0) ans.push_back({minX, minY, len});
if (config == 1) ans.push_back({maxX - len, minY, len});
if (config == 2) ans.push_back({maxX - len, maxY - len, len});
if (config == 3) ans.push_back({minX, maxY - len, len});
return true;
}
return false;
};
const auto SolveK2 = [&](int L, vector<int> alive, int vert, int config) {
if (alive.empty()) return true;
if (!vert) {
CountingSort(alive, sortByY, posInSortByY);
} else {
CountingSort(alive, sortByX, posInSortByX);
}
vector<lint> prefMinX(alive.size());
vector<lint> prefMaxX(alive.size());
vector<lint> prefMinY(alive.size());
vector<lint> prefMaxY(alive.size());
vector<lint> suffMinX(alive.size());
vector<lint> suffMaxX(alive.size());
vector<lint> suffMinY(alive.size());
vector<lint> suffMaxY(alive.size());
for (int i = 0; i < int(alive.size()); i++) {
int id = alive[i];
prefMinX[i] = prefMaxX[i] = X[id];
prefMinY[i] = prefMaxY[i] = Y[id];
suffMinX[i] = suffMaxX[i] = X[id];
suffMinY[i] = suffMaxY[i] = Y[id];
}
for (int i = 1; i < int(alive.size()); i++) {
prefMinX[i] = min(prefMinX[i], prefMinX[i - 1]);
prefMaxX[i] = max(prefMaxX[i], prefMaxX[i - 1]);
prefMinY[i] = min(prefMinY[i], prefMinY[i - 1]);
prefMaxY[i] = max(prefMaxY[i], prefMaxY[i - 1]);
}
for (int i = int(alive.size()) - 2; i >= 0; i--) {
suffMinX[i] = min(suffMinX[i], suffMinX[i + 1]);
suffMaxX[i] = max(suffMaxX[i], suffMaxX[i + 1]);
suffMinY[i] = min(suffMinY[i], suffMinY[i + 1]);
suffMaxY[i] = max(suffMaxY[i], suffMaxY[i + 1]);
}
const auto CalcPref = [&](int i) -> lint {
if (i < 0 || i >= alive.size()) return 0;
return max(prefMaxX[i] - prefMinX[i], prefMaxY[i] - prefMinY[i]);
};
const auto CalcSuff = [&](int i) -> lint {
if (i < 0 || i >= alive.size()) return 0;
return max(suffMaxX[i] - suffMinX[i], suffMaxY[i] - suffMinY[i]);
};
vector<int> pref;
vector<int> suff = alive;
reverse(begin(suff), end(suff));
for (int i = 0; i < int(alive.size()); i++) {
pref.emplace_back(alive[i]);
suff.pop_back();
if (!(i + 1 == alive.size() ||
(vert == 0 && Y[alive[i + 1]] != Y[alive[i]]) ||
(vert == 1 && X[alive[i + 1]] != X[alive[i]]))) {
continue;
}
if (CalcPref(i) <= L && CalcSuff(i + 1) <= L) {
assert(SolveK1(L, pref, 2));
assert(SolveK1(L, suff, 0));
return true;
}
}
return false;
};
const auto SolveK3 = [&](int K, lint L) {
// Configuration: |-
// Configuration: -|
// Configuration: -,-
// Configuration: -`-
// Configuration: | |
// Configuration: =
};
const auto Solve = [&](int K, lint L) {
vector<int> alive(N);
iota(begin(alive), end(alive), 0);
if (K == 1) {
ans.clear();
return SolveK1(L, alive, 0);
} else if (K == 2) {
ans.clear();
if (SolveK2(L, alive, 0, 0)) {
return true;
}
ans.clear();
if (SolveK2(L, alive, 1, 0)) {
return true;
}
}
return false;
};
lint lo = 1;
lint hi = 2e9;
while (lo < hi) {
lint md = (lo + hi) / 2;
if (Solve(K, md)) {
hi = md;
} else {
lo = md + 1;
}
}
assert(Solve(K, lo));
int it = 0;
while (ans.size() < K) {
ans.push_back({lint(3e9 - 2 * it), lint(3e9), 1});
it++;
}
for (int i = 0; i < K; i++) {
cout << ans[i][0] << ' ' << ans[i][1] << ' ' << ans[i][2] << '\n';
}
return 0;
}
Compilation message
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:121:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
121 | if (i < 0 || i >= alive.size()) return 0;
| ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:125:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
125 | if (i < 0 || i >= alive.size()) return 0;
| ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:136:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
136 | if (!(i + 1 == alive.size() ||
| ~~~~~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In function 'int main()':
izvanzemaljci.cpp:194:21: warning: comparison of integer expressions of different signedness: 'std::vector<std::array<long long int, 3> >::size_type' {aka 'long unsigned int'} and 'int' [-Wsign-compare]
194 | while (ans.size() < K) {
| ~~~~~~~~~~~^~~
izvanzemaljci.cpp:151:14: warning: variable 'SolveK3' set but not used [-Wunused-but-set-variable]
151 | const auto SolveK3 = [&](int K, lint L) {
| ^~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
204 KB |
Output is correct |
| 2 |
Correct |
1 ms |
204 KB |
Output is correct |
| 3 |
Correct |
1 ms |
204 KB |
Output is correct |
| 4 |
Correct |
1 ms |
204 KB |
Output is correct |
| 5 |
Correct |
1 ms |
204 KB |
Output is correct |
| 6 |
Correct |
0 ms |
204 KB |
Output is correct |
| 7 |
Correct |
73 ms |
4220 KB |
Output is correct |
| 8 |
Correct |
75 ms |
4348 KB |
Output is correct |
| 9 |
Correct |
71 ms |
4224 KB |
Output is correct |
| 10 |
Correct |
81 ms |
4276 KB |
Output is correct |
| 11 |
Correct |
72 ms |
4224 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
304 KB |
Output is correct |
| 2 |
Correct |
1 ms |
204 KB |
Output is correct |
| 3 |
Correct |
1 ms |
204 KB |
Output is correct |
| 4 |
Correct |
0 ms |
204 KB |
Output is correct |
| 5 |
Correct |
1 ms |
204 KB |
Output is correct |
| 6 |
Correct |
0 ms |
204 KB |
Output is correct |
| 7 |
Correct |
1 ms |
204 KB |
Output is correct |
| 8 |
Correct |
1 ms |
204 KB |
Output is correct |
| 9 |
Correct |
1 ms |
204 KB |
Output is correct |
| 10 |
Correct |
456 ms |
12324 KB |
Output is correct |
| 11 |
Correct |
502 ms |
12864 KB |
Output is correct |
| 12 |
Correct |
487 ms |
12892 KB |
Output is correct |
| 13 |
Correct |
461 ms |
12960 KB |
Output is correct |
| 14 |
Correct |
457 ms |
12976 KB |
Output is correct |
| 15 |
Correct |
424 ms |
12932 KB |
Output is correct |
| 16 |
Correct |
481 ms |
12844 KB |
Output is correct |
| 17 |
Correct |
299 ms |
11844 KB |
Output is correct |
| 18 |
Correct |
280 ms |
11496 KB |
Output is correct |
| 19 |
Correct |
300 ms |
10636 KB |
Output is correct |
| 20 |
Correct |
333 ms |
11196 KB |
Output is correct |
| 21 |
Correct |
324 ms |
12840 KB |
Output is correct |
| 22 |
Correct |
513 ms |
12956 KB |
Output is correct |
| 23 |
Correct |
405 ms |
12836 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
1 ms |
460 KB |
Execution killed with signal 6 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
2 ms |
460 KB |
Execution killed with signal 6 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
1 ms |
460 KB |
Execution killed with signal 6 |
| 2 |
Halted |
0 ms |
0 KB |
- |
