This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define For(i, a, b) for(int i = a; i <= b; i++)
#define Forr(i, a, b) for(int i = a; i >= b; i--)
#define F first
#define S second
#define all(x) x.begin(),x.end()
#define sz(x) ((int)x.size())
#define eb emplace_back
#define int LL
using namespace std;
using LL = long long;
using pii = pair<int, int>;
inline void chmax(int &l, const int &r) {
l = max(l, r);
}
inline void chmin(int &l, const int &r) {
l = min(l, r);
}
struct Owo {
int x, y, z;
};
void solve1(int n) {
vector<Owo> v(n);
for(auto &i:v) {
cin >> i.x >> i.y >> i.z;
}
sort(all(v), [](const auto &a, const auto &b) {
return a.z < b.z;
});
int ans = -1;
For(r, 2, n - 1) {
sort(v.begin(), v.begin() + r, [](const auto &a, const auto &b) {
return a.y < b.y;
});
int mxx = -1e18;
int tmp = -1e18;
For(m, 0, r - 1) {
if(v[m].z == v[r].z) continue;
if(v[m].y > v[r].y && mxx > max(v[m].x, v[r].x)) {
ans = max(ans, v[m].y + v[r].z + mxx);
}
tmp = max(tmp, v[m].x);
if(v[m + 1].y != v[m].y) mxx = tmp;
}
}
cout << ans << "\n";
}
const int MAX = 4010;
int oaox[MAX][MAX];
int oaoy[MAX][MAX];
int oaoz[MAX][MAX];
void solve2(int n) {
vector<Owo> v(n);
For(i, 0, MAX - 1) For(j, 0, MAX - 1) {
oaox[i][j] = 0;
oaoz[i][j] = oaoy[i][j] = 1e18;
}
for(auto &i:v) {
cin >> i.x >> i.y >> i.z;
chmin(oaoy[i.y][i.z + 1], i.x);
chmin(oaoz[i.y + 1][i.z], i.x);
chmax(oaox[i.y][i.z], i.x);
}
int ans = -1;
For(i, 1, MAX - 1) For(j, 1, MAX - 1) {
chmax(oaox[i][j], max(oaox[i - 1][j], oaox[i][j - 1]));
chmin(oaoy[i][j], oaoy[i][j - 1]);
chmin(oaoz[i][j], oaoz[i - 1][j]);
if(oaox[i - 1][j - 1] > max(oaoy[i][j], oaoz[i][j])) {
chmax(ans, oaox[i - 1][j - 1] + i + j);
}
}
cout << ans << "\n";
}
int32_t main() {
ios::sync_with_stdio(false);
cin.tie(0);
// OAO
int n; cin >> n;
if(n <= 4000) solve1(n);
else solve2(n);
return 0;
}
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