結果

問題 No.2173 Nightcord
コンテスト
ユーザー chineristAC
提出日時 2022-12-25 02:26:33
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 4,395 bytes
コンパイル時間 143 ms
コンパイル使用メモリ 82,164 KB
実行使用メモリ 84,052 KB
最終ジャッジ日時 2024-11-18 09:39:50
合計ジャッジ時間 19,625 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 36 WA * 12 RE * 6
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 # 

import sys,random,bisect
from collections import deque,defaultdict,Counter
from heapq import heapify,heappop,heappush
from itertools import cycle, permutations
from math import log,gcd

input = lambda :sys.stdin.readline().rstrip()
mi = lambda :map(int,input().split())
li = lambda :list(mi())

def cross3(a, b, c):
    return (b[0]-a[0])*(c[1]-a[1]) - (b[1]-a[1])*(c[0]-a[0])

# ps = [(x, y), ...]: ソートされた座標list
def convex_hull(ps):
    qs = []
    N = len(ps)
    for p in ps:
        # 一直線上で高々2点にする場合は ">=" にする
        while len(qs) > 1 and cross3(qs[-1], qs[-2], p) > 0:
            qs.pop()
        qs.append(p)
    t = len(qs)
    for i in range(N-2, -1, -1):
        p = ps[i]
        while len(qs) > t and cross3(qs[-1], qs[-2], p) > 0:
            qs.pop()
        qs.append(p)
    return qs

# O(N)
def inside_convex_polygon0(p0, qs):
    L = len(qs)
    D = [cross3(qs[i-1], p0, qs[i]) for i in range(L)]
    return all(e >= 0 for e in D) or all(e <= 0 for e in D)

# O(log N)
def inside_convex_polygon(p0, qs):
    L = len(qs)
    left = 1; right = L
    q0 = qs[0]
    while left+1 < right:
        mid = (left + right) >> 1
        if cross3(q0, p0, qs[mid]) <= 0:
            left = mid
        else:
            right = mid
    if left == L-1:
        left -= 1
    qi = qs[left]; qj = qs[left+1]
    v0 = cross3(q0, qi, qj)
    v1 = cross3(q0, p0, qj)
    v2 = cross3(q0, qi, p0)
    if v0 < 0:
        v1 = -v1; v2 = -v2
    return 0 <= v1 and 0 <= v2 and v1 + v2 <= v0

def find_zero(x0, x1, f):
    v0 = f(x0)
    if v0 == 0:
        return x0+1
    left = x0; right = x1+1
    while left+1 < right:
        mid = (left + right) >> 1
        if v0 * f(mid) >= 0:
            left = mid
        else:
            right = mid
    return right

def binary_search(f, L):
    left = 0; right = L
    while left+1 < right:
        mid = (left + right) >> 1
        if f(mid) < 0:
            left = mid
        else:
            right = mid
    return right

def line_polygon_intersection(p0, p1, qs):
    x0, y0 = p0; x1, y1 = p1
    dx = x1 - x0; dy = y1 - y0
    h = lambda p: (p[0] - x0)*dy - (p[1] - y0)*dx
    L = len(qs)

    i0 = i1 = -1

    v0 = h(qs[0])
    v1 = h(qs[L-1])
    if v0 == v1:
        v2 = h(qs[1])
        # assert v0 != v2
        if v0 < v2:
            i0 = L-1
        else:
            i1 = L-1
    else:
        v2 = h(qs[1])
        if v1 > v0 <= v2:
            i0 = 0
        elif v1 < v0 >= v2:
            i1 = 0
        else:
            g = lambda x: min((v1 - v0)*x/(L-1) + v0, h(qs[x]))
            i0 = binary_search(lambda x: g(x+1) - g(x), L-1)

    if i1 == -1:
        B = i0 - L
        k = binary_search(lambda x: h(qs[B+x]) - h(qs[B+x+1]), L)
        i1 = (i0 + k) % L
    else:
        B = i1 - L
        k = binary_search(lambda x: h(qs[B+x+1]) - h(qs[B+x]), L)
        i0 = (i1 + k) % L

    if h(qs[i0]) * h(qs[i1]) > 0:
        # a line and a polygon are disjoint
        return []

    # a vertex to the left side of a line: i0
    # a vertex to the right side of a line: i1

    f = lambda i: h(qs[i-L])
    k0 = find_zero(i1, i0 if i1 < i0 else i0+L, f) % L
    k1 = find_zero(i0, i1 if i0 < i1 else i1+L, f) % L
    # vertices to the left side of a line: k0, k0+1, ..., k1-2, k1-1
    # vertices to the right side of a line: k1, k1+1, ..., k0-2, k0-1
    if k0 == k1:
        return [k0]
    return [k0, k1]





def solve_3(N,K,star):

    for p in range(2):
        for x,y in star[p]:
            S = set()
            for xx,yy in star[p^1]:
                xx,yy = xx-x,yy-y
                g = gcd(xx,yy)
                xx,yy = xx//g,yy//g
                if (-xx,-yy) in S:
                    return "Yes"
                S.add((xx,yy))

    return "No"

def solve_4(N,K,star):

    star[0].sort()
    star[1].sort()

    ch = [convex_hull(star[p]) for p in range(2)]
    for p in range(2):
        for i in range(len(ch[p])):
            x,y = ch[p][i]
            if inside_convex_polygon((x,y),ch[p^1]):
                return "Yes"
            xx,yy = ch[p][i+1]
            if line_polygon_intersection((x,y),(xx,yy),ch[p^1]):
                return "Yes"
    
    return "No"


N,K = mi()
star = [[] for p in range(2)]
for _ in range(N):
    x,y,c = mi()
    star[c-1].append((x,y))

if K == 3:
    print(solve_3(N,K,star))
else:
    print(solve_4(N,K,star))
0