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| 1 | +#include <bits/stdc++.h> |
| 2 | +typedef long long ll; |
| 3 | +using namespace std; |
| 4 | + |
| 5 | +const ll INF = 3e9 - 4; |
| 6 | + |
| 7 | +struct Point { |
| 8 | + ll x, y; |
| 9 | +} points[100001]; |
| 10 | + |
| 11 | +struct Square { |
| 12 | + Point p; |
| 13 | + ll l; |
| 14 | +}; |
| 15 | + |
| 16 | +int n, k; |
| 17 | + |
| 18 | +pair<ll, vector<Square>> one() { |
| 19 | + // Bounding box |
| 20 | + ll mn_x = INT_MAX, mn_y = INT_MAX; |
| 21 | + ll mx_x = INT_MIN, mx_y = INT_MIN; |
| 22 | + for (int i = 1; i <= n; i++) { |
| 23 | + mn_x = min(mn_x, points[i].x); |
| 24 | + mx_x = max(mx_x, points[i].x); |
| 25 | + mn_y = min(mn_y, points[i].y); |
| 26 | + mx_y = max(mx_y, points[i].y); |
| 27 | + } |
| 28 | + ll l = max({1ll, mx_x - mn_x, mx_y - mn_y}); |
| 29 | + return {l, {{{mn_x, mn_y}, l}, {{INF, INF}, 1}, {{INF + 2, INF + 2}, 1}}}; |
| 30 | +} |
| 31 | + |
| 32 | +pair<ll, vector<Square>> two() { |
| 33 | + // Sweep line |
| 34 | + ll l_best = INT_MAX; |
| 35 | + Square s1_best, s2_best; |
| 36 | + |
| 37 | + multiset<ll> ys; |
| 38 | + for (int i = 1; i <= n; i++) ys.insert(points[i].y); |
| 39 | + sort(points + 1, points + n + 1, |
| 40 | + [](Point A, Point B) { return A.x < B.x; }); |
| 41 | + ll mn_y = INT_MAX, mx_y = INT_MIN; |
| 42 | + for (int i = 1; i < n; i++) { |
| 43 | + mn_y = min(mn_y, points[i].y); |
| 44 | + mx_y = max(mx_y, points[i].y); |
| 45 | + ys.erase(ys.find(points[i].y)); |
| 46 | + if (points[i].x == points[i + 1].x) continue; |
| 47 | + ll l = max({points[i].x - points[1].x, mx_y - mn_y, |
| 48 | + points[n].x - points[i + 1].x, *ys.rbegin() - *ys.begin(), |
| 49 | + 1ll}); |
| 50 | + if (l < l_best) { |
| 51 | + l_best = l; |
| 52 | + s1_best = {{points[i].x - |
| 53 | + max({points[i].x - points[1].x, mx_y - mn_y, 1ll}), |
| 54 | + mn_y}, |
| 55 | + max({points[i].x - points[1].x, mx_y - mn_y, 1ll})}; |
| 56 | + s2_best = {{points[i + 1].x, *ys.begin()}, |
| 57 | + max({points[n].x - points[i + 1].x, |
| 58 | + *ys.rbegin() - *ys.begin(), 1ll})}; |
| 59 | + } |
| 60 | + } |
| 61 | + |
| 62 | + multiset<ll> xs; |
| 63 | + for (int i = 1; i <= n; i++) xs.insert(points[i].x); |
| 64 | + sort(points + 1, points + n + 1, |
| 65 | + [](Point A, Point B) { return A.y < B.y; }); |
| 66 | + ll mn_x = INT_MAX, mx_x = INT_MIN; |
| 67 | + for (int i = 1; i < n; i++) { |
| 68 | + mn_x = min(mn_x, points[i].x); |
| 69 | + mx_x = max(mx_x, points[i].x); |
| 70 | + xs.erase(xs.find(points[i].x)); |
| 71 | + if (points[i].y == points[i + 1].y) continue; |
| 72 | + ll l = max({points[i].y - points[1].y, mx_x - mn_x, |
| 73 | + points[n].y - points[i + 1].y, *xs.rbegin() - *xs.begin(), |
| 74 | + 1ll}); |
| 75 | + if (l < l_best) { |
| 76 | + l_best = l; |
| 77 | + s1_best = {{mn_x, points[i].y - max({points[i].y - points[1].y, |
| 78 | + mx_x - mn_x, 1ll})}, |
| 79 | + max({points[i].y - points[1].y, mx_x - mn_x, 1ll})}; |
| 80 | + s2_best = {{*xs.begin(), points[i + 1].y}, |
| 81 | + max({points[n].y - points[i + 1].y, |
| 82 | + *xs.rbegin() - *xs.begin(), 1ll})}; |
| 83 | + } |
| 84 | + } |
| 85 | + |
| 86 | + return {l_best, {s1_best, s2_best, {{INF, INF}, 1}}}; |
| 87 | +} |
| 88 | + |
| 89 | +pair<ll, vector<Square>> three() { |
| 90 | + // Sweep line + greedy |
| 91 | + ll l_best = INT_MAX; |
| 92 | + Square s1_best, s2_best, s3_best; |
| 93 | + |
| 94 | + sort(points + 1, points + n + 1, |
| 95 | + [](Point A, Point B) { return A.x < B.x; }); |
| 96 | + for (int i = 2; i <= n; i++) { |
| 97 | + for (int j = i + 1; j <= n; j++) { |
| 98 | + |
| 99 | + } |
| 100 | + |
| 101 | + sort(points + i + 1, points + n + 1, |
| 102 | + [](Point A, Point B) { return A.y < B.y; }); |
| 103 | + for (int j = i + 1; j <= n; j++) { |
| 104 | + |
| 105 | + } |
| 106 | + sort(points + i + 1, points + n + 1, |
| 107 | + [](Point A, Point B) { return A.x < B.x; }); |
| 108 | + } |
| 109 | + |
| 110 | + return {l_best, {s1_best, s2_best, s3_best}}; |
| 111 | +} |
| 112 | + |
| 113 | +int main() { |
| 114 | + cin.tie(0)->sync_with_stdio(0); |
| 115 | + cin >> n >> k; |
| 116 | + for (int i = 1; i <= n; i++) cin >> points[i].x >> points[i].y; |
| 117 | + |
| 118 | + vector<pair<ll, vector<Square>>> ans; |
| 119 | + if (k >= 1) ans.push_back(one()); |
| 120 | + if (k >= 2) ans.push_back(two()); |
| 121 | + if (k >= 3) ans.push_back(three()); |
| 122 | + sort(ans.begin(), ans.end(), |
| 123 | + [](pair<ll, vector<Square>> A, pair<ll, vector<Square>> B) { |
| 124 | + return A.first < B.first; |
| 125 | + }); |
| 126 | + for (int i = 0; i < k; i++) |
| 127 | + cout << ans[0].second[i].p.x << ' ' << ans[0].second[i].p.y << ' ' |
| 128 | + << ans[0].second[i].l << '\n'; |
| 129 | + return 0; |
| 130 | +} |
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