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 <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <utility>
#include <cmath>
#include <ctime>
#include <cassert>
#include <set>
#include <stack>
#include <map>
#include <queue>
#include <random>
#include <chrono>
#include <array>
#include <bitset>
#include <sstream>
#include <unordered_map>
using ll = long long;
#define debug(x) cout << #x << " = " << x << '\n'
#define separator "===============================================\n"
#define all(a) a.begin(), a.end()
#define SZ(a) ((int)(a).size())
using namespace std;
const int mxn = 2e3 + 3;
const ll mod = 1e9 + 7;
const int inf32 = 2e9;
const ll inf64 = 7e18;
// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
struct point {
ll x, y, w;
};
using Line = tuple<int, int, int>; // ax + by + c = 0
ll S(point a, point b, point c){
return (b.x-a.x)*(b.y+a.y) + (c.x-b.x)*(c.y+b.y) + (a.x-c.x)*(a.y+c.y);
}
// determine which side point a is to line bc
bool cw(point a, point b, point c){
ll d = S(a, b, c);
return d > 0; // true = clockwise
}
Line get_line(point a, point b){
return make_tuple(a.y - b.y, b.x - a.x, a.x * b.y - a.y * b.x);
}
long double dist(point A, Line d){
ll a, b, c; tie(a, b, c) = d;
ll num = a * A.x + b * A.y + c;
ll denom = a * a + b * b;
return 1.0 * num * num / denom;
}
int n;
point a[mxn];
void sub2(){
ll res = 0;
for (int i = 1; i <= n; ++i){
for (int j = i + 1; j <= n; ++j){
vector<point> L, R;
for (int k = 1; k <= n; ++k){
if (k == i || k == j) continue;
if (cw(a[k], a[i], a[j])) L.push_back(a[k]);
else R.push_back(a[k]);
}
Line d = get_line(a[i], a[j]);
sort(all(L), [&](point a, point b){
return dist(a, d) < dist(b, d);
});
sort(all(R), [&](point a, point b){
return dist(a, d) < dist(b, d);
});
// tilt the line slightly to adjust
ll ini = max({0ll, a[i].w, a[j].w, a[i].w + a[j].w});
res = max(res, ini);
ll s = 0;
for (point p : L){
s += p.w;
res = max(res, ini + s);
}
s = 0;
for (point p : R){
s += p.w;
res = max(res, ini + s);
}
}
}
cout << res << '\n';
}
void solve(){
cin >> n;
bool flag_sub1 = true;
for (int i = 1; i <= n; ++i){
cin >> a[i].x >> a[i].y >> a[i].w;
flag_sub1 &= a[i].y == 0;
}
if (flag_sub1){
ll res = 0;
sort(a + 1, a + n + 1, [](point a, point b){
return a.x < b.x;
});
for (int i = 1; i <= n; ++i){
ll cur = 0;
for (int j = i; j <= n; ++j){
cur += a[j].w;
res = max(res, cur);
}
}
cout << res << '\n';
return;
}
sub2();
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);
clock_t tStart = clock();
int t = 1;
// cin >> t;
while(t--) solve();
fprintf(stderr,"\n>> Runtime: %.10fs\n",(double)(clock()-tStart)/CLOCKS_PER_SEC);
}
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