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maximize-the-distance-between-points-on-a-square.cpp
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// Time: O(nlogn + nlogs), s = side
// Space: O(n)
// sort, binary search, greedy, two pointers, sliding window
class Solution {
public:
int maxDistance(int side, vector<vector<int>>& points, int k) {
const auto& binary_search_right = [](auto left, auto right, const auto& check) {
while (left <= right) {
const auto mid = left + (right - left) / 2;
if (!check(mid)) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return right;
};
vector<int64_t> p;
for (const auto& x : points) {
if (x[0] == 0) {
p.emplace_back(0ll * side + x[1]);
} else if(x[1] == side) {
p.emplace_back(1ll * side + x[0]);
} else if(x[0] == side) {
p.emplace_back(2ll * side + (side - x[1]));
} else {
p.emplace_back(3ll * side + (side - x[0]));
}
}
sort(begin(p), end(p));
const auto& check = [&](int d) {
vector<tuple<int, int, int>> intervals = {{0, 0, 1}};
for (int right = 1, i = 0; right < size(p); ++right) {
int left = right, cnt = 1;
for (; i < size(intervals); ++i) {
const auto& [l, r, c] = intervals[i];
if (p[right] - p[r] < d) {
break;
}
if ((p[l] + 4ll * side) - p[right] >= d) {
if (c + 1 >= cnt) {
cnt = c + 1;
left = l;
}
}
}
intervals.emplace_back(left, right, cnt);
}
int mx = 0;
for (const auto& [l, r, c] : intervals) {
mx = max(mx, c);
}
return mx >= k;
};
return binary_search_right(1ll, 4ll * side / k, check);
}
};
// Time: O(nlogn + nlogs), s = side
// Space: O(n)
// sort, binary search, greedy, two pointers, sliding window
class Solution2 {
public:
int maxDistance(int side, vector<vector<int>>& points, int k) {
const auto& binary_search_right = [](auto left, auto right, const auto& check) {
while (left <= right) {
const auto mid = left + (right - left) / 2;
if (!check(mid)) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return right;
};
vector<vector<pair<int, int>>> p(4);
for (const auto& x : points) {
if (x[0] == 0) {
p[0].emplace_back(x[0], x[1]);
} else if (x[1] == side) {
p[1].emplace_back(x[0], x[1]);
} else if (x[0] == side) {
p[2].emplace_back(x[0], x[1]);
} else {
p[3].emplace_back(x[0], x[1]);
}
}
sort(begin(p[0]), end(p[0]));
sort(begin(p[1]), end(p[1]));
sort(begin(p[2]), end(p[2]), greater<pair<int, int>>());
sort(begin(p[3]), end(p[3]), greater<pair<int, int>>());
vector<pair<int, int>> sorted_points;
for (int i = 0; i < size(p); ++i) {
for (const auto& x : p[i]) {
sorted_points.emplace_back(x);
}
}
const auto& check = [&](int d) {
vector<tuple<int, int, int>> intervals = {{0, 0, 1}};
for (int right = 1, i = 0; right < size(points); ++right) {
int left = right, cnt = 1;
for (; i < size(intervals); ++i) {
const auto& [l, r, c] = intervals[i];
if (abs(sorted_points[right].first - sorted_points[r].first) + abs(sorted_points[right].second - sorted_points[r].second) < d) {
break;
}
if (abs(sorted_points[right].first - sorted_points[l].first) + abs(sorted_points[right].second - sorted_points[l].second) >= d) {
if (c + 1 >= cnt) {
cnt = c + 1;
left = l;
}
}
}
intervals.emplace_back(left, right, cnt);
}
int mx = 0;
for (const auto& [l, r, c] : intervals) {
mx = max(mx, c);
}
return mx >= k;
};
return binary_search_right(1ll, 4ll * side / k, check);
}
};
// Time: O(nlogn + n * (k * logn) * logs), s = side
// Space: O(n)
// sort, binary search, greedy
class Solution3 {
public:
int maxDistance(int side, vector<vector<int>>& points, int k) {
const auto& binary_search_right = [](auto left, auto right, const auto& check) {
while (left <= right) {
const auto mid = left + (right - left) / 2;
if (!check(mid)) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return right;
};
vector<int64_t> p;
for (const auto& x : points) {
if (x[0] == 0) {
p.emplace_back(0ll * side + x[1]);
} else if(x[1] == side) {
p.emplace_back(1ll * side + x[0]);
} else if(x[0] == side) {
p.emplace_back(2ll * side + (side - x[1]));
} else {
p.emplace_back(3ll * side + (side - x[0]));
}
}
sort(begin(p), end(p));
int64_t result = 1;
for (int i = 0; i < size(p) - k + 1; ++i) {
if (p.back() - p[i] <= result * (k - 1ll)) { // to speed up
break;
}
result = binary_search_right(result + 1ll, 4ll * side / k, [&](int d) {
int j = i;
for (int _ = 0; _ < k - 1; ++_) {
j = distance(cbegin(p), lower_bound(cbegin(p) + j + 1, cend(p), p[j] + d));
if (j == size(p)) {
return false;
}
}
return (p[i] + 4ll * side) - p[j] >= d;
});
}
return result;
}
};
// Time: O(nlogn + (n * k * logn) * logs), s = side
// Space: O(n)
// sort, binary search, greedy
class Solution4 {
public:
int maxDistance(int side, vector<vector<int>>& points, int k) {
const auto& binary_search_right = [](auto left, auto right, const auto& check) {
while (left <= right) {
const auto mid = left + (right - left) / 2;
if (!check(mid)) {
right = mid - 1;
} else {
left = mid + 1;
}
}
return right;
};
vector<int64_t> p;
for (const auto& x : points) {
if (x[0] == 0) {
p.emplace_back(0ll * side + x[1]);
} else if(x[1] == side) {
p.emplace_back(1ll * side + x[0]);
} else if(x[0] == side) {
p.emplace_back(2ll * side + (side - x[1]));
} else {
p.emplace_back(3ll * side + (side - x[0]));
}
}
sort(begin(p), end(p));
for (int i = 0; i < size(points); ++i) {
p.emplace_back(p[i] + 4ll * side);
}
const auto& check = [&](int d) {
for (int i = 0; i < size(points); ++i) {
int j = i;
int cnt = 0;
for (; cnt < k - 1; ++cnt) {
j = distance(cbegin(p), lower_bound(cbegin(p) + j + 1, cbegin(p) + (i + size(points)), p[j] + d));
if (j == i + size(points)) {
break;
}
}
if (cnt == k - 1) {
if ((p[i] + 4ll * side) - p[j] >= d) {
return true;
}
}
}
return false;
};
return binary_search_right(1ll, 4ll * side / k, check);
}
};