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>
using namespace std;
using point = complex<long long>;
#define X real()
#define Y imag()
const int N = 2000;
struct segtree {
segtree *left = nullptr, *right = nullptr;
long long prefix = 0, suffix = 0, sum = 0, maxi = 0;
void update(int a, int x, int l, int r) {
if (l == r) {
prefix = suffix = maxi = max(0, x);
sum = x;
} else {
if (!left) {
left = new segtree();
right = new segtree();
}
int m = (l + r) / 2;
if (a <= m) {
left->update(a, x, l, m);
} else {
right->update(a, x, m + 1, r);
}
prefix = max(left->prefix, left->sum + right->prefix);
suffix = max(left->suffix + right->sum, right->suffix);
sum = left->sum + right->sum;
maxi = max({left->maxi, right->maxi, left->suffix + right->prefix});
}
}
};
long long cross(point a, point b) {
return a.X * b.Y - a.Y * b.X;
}
bool comp(point a, point b) {
if (a.X == b.X) {
return a.Y < b.Y;
} else {
return a.X < b.X;
}
}
int w[N], where[N], perm[N];
point p[N];
int main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n;
cin >> n;
for (int i = 0; i < n; ++i) {
int x, y;
cin >> x >> y >> w[i];
p[i] = point(x, y);
}
iota(perm, perm + n, 0);
sort(perm, perm + n, [&](int i, int j) {
return comp(p[i], p[j]);
});
segtree *maxi = new segtree();
for (int i = 0; i < n; ++i) {
maxi->update(i, w[perm[i]], 0, n - 1);
where[perm[i]] = i;
}
vector<tuple<point, int, int>> vec;
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
if (i != j && comp(p[i], p[j])) {
vec.push_back({p[j] - p[i], i, j});
}
}
}
sort(vec.begin(), vec.end(), [&](auto i, auto j) {
return cross(get<0>(i), get<0>(j)) < 0;
});
long long ans = 0;
for (int i = 0, j = 0; i < (int) vec.size(); i = j) {
while (j < (int) vec.size() && cross(get<0>(vec[i]), get<0>(vec[j])) == 0) {
auto [v, a, b] = vec[j++];
maxi->update(where[a], w[b], 0, n - 1);
maxi->update(where[b], w[a], 0, n - 1);
swap(where[a], where[b]);
}
ans = max(ans, maxi->maxi);
}
cout << ans << "\n";
}
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