#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);
// }
sort(begin(alive), end(alive), [&](int i, int j) {
if (!vert) {
return pair(Y[i], X[i]) < pair(Y[j], X[j]);
} else {
return pair(X[i], Y[i]) < pair(X[j], Y[j]);
}
});
static vector<lint> prefMinX; prefMinX.resize(alive.size());
static vector<lint> prefMaxX; prefMaxX.resize(alive.size());
static vector<lint> prefMinY; prefMinY.resize(alive.size());
static vector<lint> prefMaxY; prefMaxY.resize(alive.size());
static vector<lint> suffMinX; suffMinX.resize(alive.size());
static vector<lint> suffMaxX; suffMaxX.resize(alive.size());
static vector<lint> suffMinY; suffMinY.resize(alive.size());
static vector<lint> suffMaxY; suffMaxY.resize(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]);
};
static vector<int> pref, suff;
pref.clear();
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) {
static vector<int> alive;
alive.resize(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;
}
} else if (K == 3) {
} else {
assert(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:128:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
128 | if (i < 0 || i >= alive.size()) return 0;
| ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:132:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
132 | if (i < 0 || i >= alive.size()) return 0;
| ~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:144:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
144 | if (!(i + 1 == alive.size() ||
| ~~~~~~^~~~~~~~~~~~~~~
izvanzemaljci.cpp: In function 'int main()':
izvanzemaljci.cpp:206:21: 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]
206 | while (ans.size() < K) {
| ~~~~~~~~~~~^~~
izvanzemaljci.cpp:43:14: warning: variable 'CountingSort' set but not used [-Wunused-but-set-variable]
43 | const auto CountingSort = [&](vector<int> &a, const vector<int> &sorted, const vector<int> &pos) {
| ^~~~~~~~~~~~
izvanzemaljci.cpp:159:14: warning: variable 'SolveK3' set but not used [-Wunused-but-set-variable]
159 | const auto SolveK3 = [&](int K, lint L) {
| ^~~~~~~
izvanzemaljci.cpp: In lambda function:
izvanzemaljci.cpp:191:3: warning: control reaches end of non-void function [-Wreturn-type]
191 | };
| ^
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
256 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 |
0 ms |
204 KB |
Output is correct |
| 6 |
Correct |
0 ms |
204 KB |
Output is correct |
| 7 |
Correct |
67 ms |
3812 KB |
Output is correct |
| 8 |
Correct |
77 ms |
3804 KB |
Output is correct |
| 9 |
Correct |
68 ms |
3808 KB |
Output is correct |
| 10 |
Correct |
82 ms |
3780 KB |
Output is correct |
| 11 |
Correct |
81 ms |
3780 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
204 KB |
Output is correct |
| 2 |
Correct |
0 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 |
1 ms |
204 KB |
Output is correct |
| 7 |
Correct |
1 ms |
204 KB |
Output is correct |
| 8 |
Correct |
1 ms |
256 KB |
Output is correct |
| 9 |
Incorrect |
1 ms |
204 KB |
Output isn't correct |
| 10 |
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 |
- |
| # |
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 |
1 ms |
460 KB |
Execution killed with signal 6 |
| 2 |
Halted |
0 ms |
0 KB |
- |
