結果

問題 No.3154 convex polygon judge
ユーザー deuteridayo
提出日時 2025-05-20 22:17:05
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 218 ms / 2,000 ms
コード長 4,235 bytes
コンパイル時間 6,749 ms
コンパイル使用メモリ 335,428 KB
実行使用メモリ 12,764 KB
最終ジャッジ日時 2025-05-20 22:17:15
合計ジャッジ時間 9,368 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 44
権限があれば一括ダウンロードができます

ソースコード

diff # 

#ifndef MY_HEADER
#define MY_HEADER

#include<bits/stdc++.h>
#include<atcoder/all>
using namespace std;
using namespace atcoder;
using lint = long long;
using ulint = unsigned long long;
using llint = __int128_t;
struct edge;
using graph = vector<vector<edge>>;
#define endl '\n'
constexpr int INF = 1<<30;
constexpr lint INF64 = 1LL<<61;
constexpr lint mod107 = 1e9+7;
using mint107 = modint1000000007;
constexpr long mod = 998244353;
using mint = modint998244353;
lint ceilDiv(lint x, lint y){if(x >= 0){return (x+y-1)/y;}else{return x/y;}}
lint floorDiv(lint x, lint y){if(x >= 0){return x/y;}else{return (x-y+1)/y;}}
lint Sqrt(lint x) {assert(x >= 0); lint ans = sqrt(x); while(ans*ans > x)ans--; while((ans+1)*(ans+1)<=x)ans++; return ans;}
lint gcd(lint a,lint b){if(a<b)swap(a,b);if(a%b==0)return b;else return gcd(b,a%b);}
lint lcm(lint a,lint b){return (a / gcd(a,b)) * b;}
double Dist(double x1, double y1, double x2, double y2){return sqrt(pow(x1-x2, 2) + pow(y1-y2,2));}
lint DistSqr(lint x1, lint y1, lint x2, lint y2){return (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2); }
string toString(lint n){string ans = "";if(n == 0){ans += "0";}else{while(n > 0){int a = n%10;char b = '0' + a;string c = "";c += b;n /= 10;ans = c + ans;}}return ans;}
string toString(lint n, lint k){string ans = toString(n);string tmp = "";while(ans.length() + tmp.length() < k){tmp += "0";}return tmp + ans;}
vector<lint>prime;void makePrime(lint n){prime.push_back(2);for(lint i=3;i<=n;i+=2){bool chk = true;for(lint j=0;j<prime.size() && prime[j]*prime[j] <= i;j++){if(i % prime[j]==0){chk=false;break;}}if(chk)prime.push_back(i);}}
lint Kai[20000001]; bool firstCallnCr = true; 
lint ncrmodp(lint n,lint r,lint p){ if(firstCallnCr){ Kai[0] = 1; for(int i=1;i<=20000000;i++){ Kai[i] = Kai[i-1] * i; Kai[i] %= p;} firstCallnCr = false;} if(n<0)return 0; if(r<0)return 0;
if(n < r)return 0;if(n==0)return 1;lint ans = Kai[n];lint tmp = (Kai[r] * Kai[n-r]) % p;for(lint i=1;i<=p-2;i*=2){if(i & p-2){ans *= tmp;ans %= p;}tmp *= tmp;tmp %= p;}return ans;}
#define rep(i, n) for(int i = 0; i < n; i++)
#define repp(i, x, y) for(int i = x; i < y; i++)
#define rrep(i, x) for(int i = x-1; i >= 0; i--)
#define vec vector
#define pb push_back
#define eb emplace_back
#define se second
#define fi first
#define al(x) x.begin(),x.end()
#define ral(x) x.rbegin(),x.rend()

struct edge{
    edge(lint v, lint c = 1) {to = v, cost = c;}
    lint to;
    lint cost;
};

#endif
struct Point {
    long long x, y; int quad;
    Point(long long X, long long Y) {
        x = X;
        y = Y;
        quad = getQuad();
    }
    int getQuad() {
        if(x >= 0) {
            if(y >= 0) return 1;
            else return 4;
        } else {
            if(y >= 0) return 2;
            else return 3;
        }
    }
};

bool operator<(const Point &left, const Point &right) {
    if(left.quad == right.quad) {
        return left.y * right.x < left.x * right.y;
    } else {
        return left.quad < right.quad;
    }
}

lint isup(lint dx1, lint dy1, lint dx2, lint dy2) {
    return (dy1 *dx2 < dx1 * dy2);
}

int main(){
    lint N;
    cin >> N;
    vec<lint>X(N), Y(N);
    vec<pair<lint, lint>>P;
    rep(i, N) {
        cin >> X[i] >> Y[i];
        P.pb({X[i], Y[i]});
    }
    sort(al(P));
    stack<pair<lint, lint>>up, down;
    up.push(P[0]);
    up.push(P[1]);
    down.push(P[0]);
    down.push(P[1]);
    // 上側
    repp(i,2, N) {
        while(up.size() >= 2) {
            auto p1 = up.top();
            up.pop();
            auto p2 = up.top();
            if(isup(p2.first - p1.first, p2.second - p1.second, P[i].first - p2.first, P[i].second - p2.second)) {
                up.push(p1);
                break;
            }
        }
        up.push(P[i]);
    }

    //下側
    repp(i, 2, N) {
        while(down.size() >= 2) {
            auto p1 = down.top();
            down.pop();
            auto p2 = down.top();
            if(isup( P[i].first - p2.first, P[i].second - p2.second, p2.first - p1.first, p2.second - p1.second)) {
                down.push(p1);
                break;
            }
        }
        down.push(P[i]);
    }

    if(up.size() + down.size() == N+2) cout << "Yes";
    else cout << "No";
    
    
    
}
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