結果

問題 No.3154 convex polygon judge
ユーザー ArcAki
提出日時 2025-05-25 06:01:40
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 40 ms / 2,000 ms
コード長 4,860 bytes
コンパイル時間 13,084 ms
コンパイル使用メモリ 390,272 KB
実行使用メモリ 18,000 KB
最終ジャッジ日時 2025-05-25 06:01:55
合計ジャッジ時間 13,917 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 44
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ソースコード

diff # 

pub trait SortD{
    fn sort_d(&mut self);
}

impl<T: Ord> SortD for Vec<T>{
    fn sort_d(&mut self) {
        self.sort_by(|u, v| v.cmp(&u));
    }
}
pub struct F64Ord(f64);
impl PartialEq<Self> for F64Ord {
    fn eq(&self, other: &Self) -> bool {
        self.0==other.0
    }
}
impl Eq for F64Ord{}
impl Ord for F64Ord{
    fn cmp(&self, other: &Self) -> Ordering {
        self.0.total_cmp(&other.0)
    }
}
impl PartialOrd for F64Ord{
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        Some(self.cmp(&other))
    }
}
pub trait Mx{
    fn max(&self, rhs: Self)->Self;
}
impl Mx for f64{
    fn max(&self, rhs: Self)->Self{
        if *self < rhs{
            rhs
        } else {
            *self
        }
    }
}
pub trait Mi{
    fn min(&self, rhs: Self)->Self;
}
impl Mi for f64{
    fn min(&self, rhs: Self)->Self{
        if *self < rhs{
            rhs
        } else {
            *self
        }
    }
}
pub fn chmax<T: PartialOrd+Clone>(a: &mut T, b: &T){
    if *a < *b{
        *a = b.clone();
    }
}
pub fn chmin<T: PartialOrd+Clone>(a: &mut T, b: &T){
    if *a > *b{
        *a = b.clone();
    }
}
pub fn gcd(mut a: i64, mut b: i64)->i64{
    if b==0{return a;}
    while b!=0{
        let c = a;
        a = b;
        b = c%b;
    }
    a
}
pub fn floor(a:i64, b:i64)->i64{let res=(a%b+b)%b;(a-res)/b}
pub fn extended_gcd(a:i64,b:i64)->(i64,i64,i64)
{if b==0{(a,1,0)}else{let(g,x,y)=extended_gcd(b,a%b);(g,y,x-floor(a,b)*y)}}
pub fn mod_inverse(a:i64,m:i64)->i64{let(_,x,_) =extended_gcd(a,m);(x%m+m)%m}
pub fn comb(a: i64, b: i64, f: &Vec<(i64, i64)>)->i64{
    if a<b{return 0;}if b==0 || a==b{ return 1; }
    else{let x=f[a as usize].0;
        let y=f[(a-b) as usize].1;let z=f[b as usize].1;return((x*y)%MOD)*z%MOD;}}
pub fn factorial(x: i64)->Vec<(i64, i64)>{
    let mut f=vec![(1i64,1i64),(1, 1)];let mut z = 1i64;
    let mut inv = vec![0; x as usize+10];inv[1] = 1;
    for i in 2..x+1{z=(z*i)%MOD;
        let w=(MOD-inv[(MOD%i)as usize]*(MOD/i)%MOD)%MOD;
        inv[i as usize] = w;
        f.push((z, (f[i as usize-1].1*w)%MOD));}return f;}
pub fn fast_mod_pow(x: i64,p: usize, m: i64)->i64{
    let mut res=1;let mut t=x;let mut z=p;while z > 0{
        if z%2==1{res = (res*t)%m;}t = (t*t)%m;z /= 2; }res}
#[allow(unused_imports)]
use std::{
    convert::{Infallible, TryFrom, TryInto as _}, fmt::{self, Debug, Display, Formatter,},
    fs::{File}, hash::{Hash, Hasher}, iter::{Product, Sum}, marker::PhantomData,
    ops::{Add, AddAssign, Sub, SubAssign, Div, DivAssign, Mul, MulAssign, Neg, RangeBounds},
    str::FromStr, sync::{atomic::{self, AtomicU32, AtomicU64}, Once},
    collections::{*, btree_set::Range, btree_map::Range as BTreeRange}, mem::{swap},
    cmp::{self, Reverse, Ordering, Eq, PartialEq, PartialOrd},
    thread::LocalKey, f64::consts::PI, time::Instant, cell::RefCell,
    io::{self, stdin, Read, read_to_string, BufWriter, BufReader, stdout, Write},
};
#[allow(unused_imports)]
use proconio::{input, input_interactive, marker::{*}};
#[allow(unused_imports)]
//use rand::{thread_rng, Rng, seq::SliceRandom};
#[allow(unused_imports)]
//use ac_library::{*, ModInt1000000007 as mint};
#[allow(dead_code)]
//type MI = StaticModInt<Mod1000000007>;

#[allow(dead_code)]
const INF: i64 = 1<<60;
#[allow(dead_code)]
const MOD: i64 = 998244353;
#[allow(dead_code)]
const D: [(usize, usize); 4] = [(1, 0), (0, 1), (!0, 0), (0, !0)];
#[allow(dead_code)]
const D2: [(usize, usize); 8] = [(1, 0), (1, 1), (0, 1), (!0, 1), (!0, 0), (!0, !0), (0, !0), (1, !0)];

pub fn cross_product(a: (i64, i64), b: (i64, i64), c: (i64, i64)) -> i64 {
    (b.0 - a.0) * (c.1 - a.1) - (b.1 - a.1) * (c.0 - a.0)
}

pub fn convex_hull(point: &Vec<(i64, i64)>) -> (Vec<(i64, i64)>, Vec<(i64, i64)>) {
    if point.len() < 3 {
        let mut res = point.clone();
        res.sort();
        return (res.clone(), res.clone());
    }
    let mut sort_set = point.clone();
    sort_set.sort();
    let mut up_side = Vec::new();
    let mut low_side = Vec::new();
    for p in sort_set {
        while up_side.len() >= 2 &&
            cross_product(up_side[up_side.len() - 2], up_side[up_side.len() - 1], p) >= 0 {
            up_side.pop();
        }
        up_side.push(p);
        while low_side.len() >= 2 &&
            cross_product(low_side[low_side.len() - 2], low_side[low_side.len() - 1], p) <= 0{
            low_side.pop();
        }
        low_side.push(p);
    }
    let res1 = up_side.iter().map(|&x| x).collect::<Vec<_>>();
    let res2 = low_side.iter().map(|&x| x).collect::<Vec<_>>();
    (res1, res2)
}

//use proconio::fastout;
//#[fastout]
fn main() {
    input!{
        n: usize,
        p: [(i64, i64); n],
    }
    let (mut x, y) = convex_hull(&p);
    x.extend(y);
    x.sort(); x.dedup();
    if x.len()==n{
        println!("Yes");
    } else {
        println!("No");
    }
}
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