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 pii pair<ll, ll>
typedef long long ll;
using namespace std;
const int SZ = 1 << 11;
int PN[SZ], IP[SZ];
struct Point {
ll x, y, s;
Point(ll x = 0, ll y = 0, ll s = 0) : x(x), y(y), s(s) {};
} P[SZ];
struct Seg {
struct Data {
ll LS, RS, T, S;
Data(ll LS = 0, ll RS = 0, ll T = 0, ll S = 0) : LS(LS), RS(RS), T(T), S(S) {};
Data operator+(const Data& a) {
Data ret;
ret.LS = max(LS, T + a.LS);
ret.RS = max(a.RS, RS + a.T);
ret.S = max({S, a.S, RS + a.LS});
ret.T = T + a.T;
return ret;
}
} T[SZ << 1];
void Update(int i, int v) {
T[i += SZ - 1] = Data(max(0, v), max(0, v), v, max(0, v));
while (i >>= 1) T[i] = T[i * 2] + T[i * 2 + 1];
}
ll Query() { return T[1].S; }
} T;
struct Comp {
bool operator()(const pii& a, const pii& b) const {
return a.second * b.first > a.first * b.second;
}
};
void Swap(int a, int b) {
ll sa = P[a].s, sb = P[b].s;
swap(IP[PN[a]], IP[PN[b]]);
swap(PN[a], PN[b]);
swap(P[a], P[b]);
T.Update(a, sb);
T.Update(b, sa);
}
int main() {
ios::sync_with_stdio(0); cin.tie(0);
int N;
cin >> N;
for (int i = 1; i <= N; ++i) {
cin >> P[i].x >> P[i].y >> P[i].s;
PN[i] = IP[i] = i;
}
sort(P + 1, P + N + 1, [&](Point a, Point b) {
if (a.x != b.x) return a.x < b.x;
return a.y < b.y;
});
for (int i = 1; i <= N; ++i) T.Update(i, P[i].s);
ll ans = T.Query();
map<pii, vector<pii>, Comp> ord;
for (int a = 1; a <= N; ++a) for (int b = a + 1; b <= N; ++b) {
ll xd = P[b].x - P[a].x, yd = P[b].y - P[a].y;
if (xd < 0) xd *= -1, yd *= -1;
ll g = gcd(abs(xd), abs(yd)); xd /= g; yd /= g;
if (xd == 0) yd = 1LL << 31;
ord[pii{xd, yd}].emplace_back(a, b);
}
for (auto& [_, V] : ord) {
for (auto [a, b] : V) Swap(IP[a], IP[b]);
ans = max(ans, T.Query());
}
cout << ans;
return 0;
}
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