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| #include<bits/stdc++.h> using namespace std; int T, k, n, ans; int minn, maxn; struct vec { int v[4]; }a[50010]; int vis[50010]; struct tree { int v, laz, c; int ls, rs; tree() { v = laz = ls = rs = 0; } void cl() { v = laz = 0; c = 1; } }t[240010]; int cnt = 1; inline void update(int nod) { t[nod].v = max(t[t[nod].ls].v, t[t[nod].rs].v); } inline void pushdown(int nod) { if (t[nod].c) { t[t[nod].ls].cl(); t[t[nod].rs].cl(); t[nod].c = 0; } if (t[nod].laz) { t[t[nod].ls].v += t[nod].laz; t[t[nod].ls].laz += t[nod].laz; t[t[nod].rs].v += t[nod].laz; t[t[nod].rs].laz += t[nod].laz; t[nod].laz = 0; } } void build(int nod, int l, int r) { if (l == r) return; int mid = (l + r) >> 1; t[nod].ls = ++cnt; t[nod].rs = ++cnt; build(t[nod].ls, l, mid); build(t[nod].rs, mid + 1, r); } void add(int nod, int l, int r, int pl, int pr, int x) { if (l >= pl && r <= pr) { t[nod].v += x; t[nod].laz += x; return; } pushdown(nod); int mid = (l + r) >> 1; if (mid >= pl) add(t[nod].ls, l, mid, pl, pr, x); if (pr > mid) add(t[nod].rs, mid + 1, r, pl, pr, x); update(nod); } bool check3(int mid) { vector<pair<int, int> >v; for (int i = 1; i < 3; ++i) { v.clear(); for (int j = 0; j < n; ++j) { for (int l = 0; l < 3; ++l) { if (a[j].v[l] - minn <= mid && maxn - a[j].v[(l + i) % 3] <= mid) { v.emplace_back(make_pair(a[j].v[(3 - i + l) % 3], j)); } } } sort(v.begin(), v.end()); memset(vis, 0, sizeof(vis)); int tot = 0; for (int l = 0, r = 0; r < v.size();) { if (!vis[v[r].second]) ++tot; vis[v[r++].second]++; while (l < r && vis[v[l].second] > 1) --vis[v[l++].second]; if (tot == n && v[r - 1].first - v[l].first <= mid) return true; } } return false; } vector <pair<int, int > > cc[30010]; multiset <int> orz[30010]; set <int> ls; inline int xy(int x, int y) { if (orz[x].empty()) return 0; auto tmp = orz[x].upper_bound(y); if(tmp == orz[x].begin()) return 0; --tmp; return *tmp + 1; } inline int dx(int x, int y, int mid) { if (orz[x].empty()) return 30000; auto tmp = orz[x].lower_bound(y); if (tmp == orz[x].end()) return 30000; return *tmp - mid - 1; } bool check4(int mid) { pair<int, int> tmp; for (int i = 1; i < 4; ++i) { bool ppp = 0; ls.clear(); for (int j = 0; j < n; ++j) { orz[j].clear(); bool pp = 0; for (int l = 0; l < 4; ++l) { if (a[j].v[l] - minn <= mid && maxn - a[j].v[(l + i) % 4] <= mid) { bool p = 0; for (int m = 1; m < 4; ++m) { if (m == i) continue; if(!p) tmp.first = a[j].v[(m + l) % 4], p = 1; else tmp.second = a[j].v[(m + l) % 4]; } pp = 1; if (ls.find(tmp.first) == ls.end()) cc[tmp.first].clear(), ls.insert(tmp.first); cc[tmp.first].emplace_back(make_pair(j, tmp.second)); } } if (!pp) { ppp = 1; break; } } if (ppp) continue; t[1].cl(); for (auto l = ls.begin(), r = ls.begin(); r != ls.end(); ++r) { for (auto &j : cc[*r]) { int tl = max(j.second - mid, xy(j.first, j.second)); int tr = min(j.second, dx(j.first, j.second, mid)); tl = max(tl, minn); if (tl <= tr) { add(1, 1, 30000, tl, tr, 1); } orz[j.first].insert(j.second); } while (l != r && *r - *l > mid) { for (auto &j : cc[*l]) { orz[j.first].erase(orz[j.first].find(j.second)); int tl = max(j.second - mid, xy(j.first, j.second)); int tr = min(j.second, dx(j.first, j.second, mid)); tl = max(tl, minn); if (tl <= tr) { add(1, 1, 30000, tl, tr, -1); } } ++l; } if (t[1].v == n) return true; } } return false; } int main() { scanf("%d%d", &T, &k); if (k == 4) build(1, 1, 30000); while (T--) { ans = 30000; minn = 30000; maxn = 0; scanf("%d", &n); for (int i = 0; i < k; ++i) { for (int j = 0; j < n; ++j) { scanf("%d", &a[j].v[i]); maxn = max(maxn, a[j].v[i]); minn = min(minn, a[j].v[i]); } } switch(k){ case 1: { printf("%d\n", maxn - minn); break; } case 2: { int mi = 30000, ma = 0; for (int i = 0; i < n; ++i) { ma = max(ma, min(a[i].v[0], a[i].v[1])); mi = min(mi, min(a[i].v[0], a[i].v[1])); } ans = ma - mi; mi = 30000, ma = 0; for (int i = 0; i < n; ++i) { ma = max(ma, max(a[i].v[0], a[i].v[1])); mi = min(mi, max(a[i].v[0], a[i].v[1])); } ans = max(ans, ma - mi); printf("%d\n", ans); break; } case 3: { int l = 0, r = 30000, mid; while (l < r) { mid = (l + r) >> 1; if (check3(mid)) { r = mid; } else { l = mid + 1; } } printf("%d\n", l); break; } case 4: { int l = 0, r = 30000, mid; while (l < r) { mid = (l + r) >> 1; if (check4(mid)) { r = mid; } else { l = mid + 1; } } printf("%d\n", l); break; } } } return 0; }
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