Submission #681131

#	Time	Username	Problem	Language	Result	Execution time	Memory
681131		sysia	Triangles (CEOI18_tri)	C++17	20 / 100	1 ms	340 KiB

tri

//Sylwia Sapkowska
#include <bits/stdc++.h>
#include "trilib.h"
#pragma GCC optimize("O3", "unroll-loops")
using namespace std;

void __print(int x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ", "; __print(x.second); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? ", " : ""), __print(i); cerr << "}";}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifdef LOCAL
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif

#define int long long
typedef pair<int, int> T;
const int oo = 1e18, oo2 = 1e9+7, K = 30;
const int mod = 998244353;
/*
Solution:
Creating convex hull requires 3 steps:
a) finding a point which lies on convex hull - ?? queries
b) angular sort with respect to the point from a) - O(n log n) queries
c) finding actual convex hull - O(n) queries

--At most one point not on the convex hull -> if we choose two different points, then one of them certainly lies on the
convex hull.
--Let's sort points with respect to some random point. Then this point lies on the convex hull iff first or last point of the sorted list creates a side with that random point (we can check how many points lie on which side of that line).
*/

mt19937 rng(chrono::steady_clock().now().time_since_epoch().count());
int p(int a, int b){return a+rng()%(b-a+1);}

int cw(int a, int b, int c){
    if (a == b || b == c || a == c) return 0;
    return is_clockwise(a, b, c) ? 1 : -1;
}

void solve(){
    int n = get_n();
    auto solve = [&](int v){
        vector<int>ord(n);
        // cout << v << "\n";
        iota(ord.begin(), ord.end(), 1);
        ord.erase(ord.begin()+v-1);
        stable_sort(ord.begin(), ord.end(), [&](auto x, auto y){return cw(v, x, y) == 1;});
        // for (auto x: ord) cout << x << " ";
        // cout << "\n";
        auto check = [&](int a, int b){
            int x = 0, y = 0;
            for (int i = 1; i<=n; i++){
                int u = cw(a, b, i);
                if (u == -1) x++;
                else if (u == 1) y++;
            }
            if (x > 0 && y > 0) return false;
            return true;
        };
        if (check(v, ord[0])){
            // cout << "found\n";
            vector<int>hull;
            hull.emplace_back(v);
            for (auto x: ord){
                if (x == v) continue;
                while (hull.size() >= 2 && cw(hull.end()[-2], hull.end()[-1], x) == -1) hull.pop_back();
                hull.emplace_back(x);
            }
            // for (auto x: hull) cout << x << " ";
            // cout << "\n;
            give_answer((int)hull.size());
            exit(0);
        } 
        return ord[0];
    };
    int v = solve(p(1, n));
    int u = solve(v);
    //use second algorithm -- upper and lower hull with respect to the line {v, ord[0]}
    vector<int>lower, upper;
    for (int i = 1; i<=n; i++){
        if (i == v || i == u) continue;
        if (cw(v, u, i) == 1) lower.emplace_back(i);
        else upper.emplace_back(i);
    }
    lower.emplace_back(u);
    upper.emplace_back(u);
    stable_sort(lower.begin(), lower.end(), [&](auto x, auto y){return cw(v, x, y) == 1;});
    stable_sort(upper.begin(), upper.end(), [&](auto x, auto y){return cw(v, x, y) == 1;});
    // reverse(upper.begin(), upper.end());
    // for (auto x: lower) cout << x << " ";
    // cout << "\n";
    // for (auto x: upper) cout << x << " ";
    // cout << "\n";
    int ans = 0;
    for (vector<int> curr: {lower, upper}){
        vector<int>hull = {v};
        for (auto x: curr){
            while ((int)hull.size() >= 2 && cw(hull.end()[-2], hull.end()[-1], x) == -1) hull.pop_back();
            hull.emplace_back(x);
        }
        // for (auto x: hull) cout << x << " ";
        // cout << "\n";
        ans += (int)hull.size()-2;
    }
    // cout << ans << "\n";
    give_answer(ans);
}

int32_t main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    int t = 1;
    // cin >> t;
    while (t--) solve();

    return 0;
}

• Subtask 1: 0 / 15
• Subtask 2: 0 / 20
• Subtask 3: 0 / 20
• Subtask 4: 20 / 20
• Subtask 5: 0 / 25