結果
| 問題 | No.622 点と三角柱の内外判定 |
| ユーザー |
 T101010101
|
| 提出日時 | 2024-04-29 18:23:06 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 33,059 bytes |
| コンパイル時間 | 7,304 ms |
| コンパイル使用メモリ | 314,896 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-11-19 00:26:24 |
| 合計ジャッジ時間 | 8,890 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
5,248 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,248 KB |
| testcase_03 | AC | 2 ms
5,248 KB |
| testcase_04 | AC | 2 ms
5,248 KB |
| testcase_05 | AC | 3 ms
5,248 KB |
| testcase_06 | AC | 2 ms
5,248 KB |
| testcase_07 | AC | 2 ms
5,248 KB |
| testcase_08 | AC | 2 ms
5,248 KB |
| testcase_09 | AC | 3 ms
5,248 KB |
| testcase_10 | AC | 3 ms
5,248 KB |
| testcase_11 | AC | 2 ms
5,248 KB |
| testcase_12 | AC | 2 ms
5,248 KB |
| testcase_13 | AC | 2 ms
5,248 KB |
| testcase_14 | AC | 2 ms
5,248 KB |
| testcase_15 | AC | 2 ms
5,248 KB |
| testcase_16 | AC | 2 ms
5,248 KB |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | WA | - |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
| testcase_22 | WA | - |
| testcase_23 | WA | - |
| testcase_24 | WA | - |
| testcase_25 | WA | - |
| testcase_26 | WA | - |
| testcase_27 | WA | - |
| testcase_28 | WA | - |
| testcase_29 | WA | - |
| testcase_30 | WA | - |
| testcase_31 | WA | - |
コンパイルメッセージ
main.cpp: In function 'll round2(ll, ll)':
main.cpp:199:9: warning: 'z' may be used uninitialized [-Wmaybe-uninitialized]
199 | int z = z / y;
| ^
main.cpp:199:9: note: 'z' was declared here
199 | int z = z / y;
| ^
ソースコード
#pragma region Macros
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,abm,mmx,avx,avx2")
#include <bits/extc++.h>
// #include <atcoder/all>
// using namespace atcoder;
using namespace std;
using namespace __gnu_pbds;
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// using Bint = mp::cpp_int;
// using Bdouble = mp::number<mp::cpp_dec_float<256>>;
// Bdouble Beps = 0.00000000000000000000000000000001; // 1e-32
// const bool equals(Bdouble a, Bdouble b) { return mp::fabs(a - b) < Beps; }
#define pb emplace_back
#define int ll
#define endl '\n'
// #define unordered_map<int, int> gp_hash_table<int, int, custom_hash>
#define sqrt __builtin_sqrtl
#define cbrt __builtin_cbrtl
#define hypot __builtin_hypotl
#define next asdnext
#define prev asdprev
using ll = long long;
using ld = long double;
const ld PI = acosl(-1);
const int INF = 1 << 30;
const ll INFL = 1LL << 61;
// const int MOD = 998244353;
const int MOD = 1000000007;
const ld EPS = 1e-10;
const bool equals(ld a, ld b) { return fabs((a) - (b)) < EPS; }
const vector<int> dx = {0, 1, 0, -1, 1, 1, -1, -1}; // → ↓ ← ↑ ↘ ↙ ↖ ↗
const vector<int> dy = {1, 0, -1, 0, 1, -1, -1, 1};
struct Edge {
int from, to, cost;
Edge() : from(-1), to(-1), cost(-1) {}
Edge(int to, int cost) : to(to), cost(cost) {}
Edge(int from, int to, int cost) : from(from), to(to), cost(cost) {}
bool operator ==(const Edge& e) {
return this->from == e.from && this->to == e.to && this->cost == e.cost;
}
bool operator !=(const Edge& e) {
return this->from != e.from or this->to != e.to or this->cost != e.cost;
}
};
chrono::system_clock::time_point start;
__attribute__((constructor))
void constructor() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(10);
start = chrono::system_clock::now();
}
random_device seed_gen;
mt19937_64 rng(seed_gen());
uniform_int_distribution<int> dist_x(0, 1e9);
struct RNG {
unsigned Int(unsigned l, unsigned r) {
return dist_x(rng) % (r - l + 1) + l;
}
ld Double() {
return ld(dist_x(rng)) / 1e9;
}
} rnd;
using i64 = ll;
// using i64 = uint64_t;
// bit演算, x==0の場合は例外処理した方がよさそう. 区間は [l, r)
i64 lrmask(i64 l, i64 r) { return (1LL << r) - (1LL << l); }
i64 sub_bit(i64 x, i64 l, i64 r) { i64 b = x & ((1LL << r) - (1LL << l)); return b >> l; } // r溢れ可
i64 bit_width(i64 x) { return 64 - __builtin_clzll(x) + (x == 0); }
i64 popcount(i64 x) { return __builtin_popcountll(x); }
i64 popcount(i64 x, i64 l, i64 r) { return __builtin_popcountll(sub_bit(x, l, r)); }
i64 unpopcount(i64 x) { return bit_width(x) - __builtin_popcountll(x); }
i64 unpopcount(i64 x, i64 l, i64 r) { return r - l - __builtin_popcountll(sub_bit(x, l, r)); }
bool is_pow2(i64 x) { return __builtin_popcountll(x) == 1; }
i64 top_bit(i64 x) { return 63 - __builtin_clzll(x);} // 2^kの位 (x > 0)
i64 bot_bit(i64 x) { return __builtin_ctz(x);} // 2^kの位 (x > 0)
// i64 next_bit(i64 x, i64 k) { return 0; }
// i64 prev_bit(i64 x, i64 k) { return 0; }
// i64 kth_bit(i64 x, i64 k) { return 0; }
i64 MSB(i64 x) { if (x == 0) return 0; return 1LL << (63 - __builtin_clzll(x)); } // mask
i64 LSB(i64 x) { return (x & -x); } // mask
i64 countl_zero(i64 x) { return __builtin_clzll(x); }
i64 countl_one(i64 x) {
i64 ret = 0, k = 63 - __builtin_clzll(x);
while (k != -1 && (x & (1LL << k))) { k--; ret++; }
return ret;
}
i64 countr_zero(i64 x) { return __builtin_ctzll(x); } // x==0のとき64が返ることに注意
i64 countr_one(i64 x) { i64 ret = 0; while (x & 1) { x >>= 1; ret++; } return ret; }
i64 floor_log2(i64 x) { if (x == 0) return 0; return 63 - __builtin_clzll(x); }
i64 bit_floor(i64 x) { if (x == 0) return 0; return 1LL << (63 - __builtin_clzll(x)); } // MSBと同じ
i64 ceil_log2(i64 x) { if (x == 0) return 0; return 64 - __builtin_clzll(x - 1); }
i64 bit_ceil(i64 x) { if (x == 0) return 0; return 1LL << (64 - __builtin_clzll(x - 1)); }
i64 rotl(i64 x, i64 k) { // 有効bit内でrotate. オーバーフロー注意
i64 w = bit_width(x); k %= w;
return ((x << k) | (x >> (w - k))) & ((1LL << w) - 1);
}
// i64 rotl(i64 x, i64 l, i64 m, i64 r) {}
i64 rotr(i64 x, i64 k) {
i64 w = bit_width(x); k %= w;
return ((x >> k) | (x << (w - k))) & ((1LL << w) - 1);
}
// i64 rotr(i64 x, i64 l, i64 m, i64 r) {}
i64 bit_reverse(i64 x) { // 有効bit内で左右反転
i64 r = 0, w = bit_width(x);
for (i64 i = 0; i < w; i++) r |= ((x >> i) & 1) << (w - i - 1);
return r;
}
// i64 bit_reverse(i64 x, i64 l, i64 r) { return 0; }
bool is_palindrome(i64 x) { return x == bit_reverse(x); }
bool is_palindrome(i64 x, i64 l, i64 r) { i64 b = sub_bit(x, l, r); return b == bit_reverse(b); }
i64 concat(i64 a, i64 b) { return (a << bit_width(b)) | b; } // オーバーフロー注意
i64 erase(i64 x, i64 l, i64 r) { return x>>r<<l | x&(1LL<<l - 1); } // [l, r) をカット
i64 hamming(i64 a, i64 b) { return __builtin_popcountll(a ^ b); }
i64 hamming(i64 a, i64 b, i64 l, i64 r) { return __builtin_popcountll(sub_bit(a, l, r) ^ sub_bit(b, l, r)); }
i64 compcount(i64 x) { return (__builtin_popcountll(x ^ (x >> 1)) + (x & 1)) / 2; }
i64 compcount2(i64 x) { return compcount(x & (x >> 1)); } // 長さ2以上の連結成分の個数
i64 adjacount(i64 x) { return __builtin_popcountll(x & (x >> 1)); } // 隣接する1のペアの個数
i64 next_combination(i64 x) {
i64 t = x | (x - 1); return (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctz(x) + 1));
}
__int128_t POW(__int128_t x, int n) {
__int128_t ret = 1;
assert(n >= 0);
if (x == 1 or n == 0) ret = 1;
else if (x == -1 && n % 2 == 0) ret = 1;
else if (x == -1) ret = -1;
else if (n % 2 == 0) {
assert(x < INFL);
ret = POW(x * x, n / 2);
} else {
assert(x < INFL);
ret = x * POW(x, n - 1);
}
return ret;
}
int per(int x, int y) { // x = qy + r (0 <= r < y) を満たすq
assert(y != 0);
if (x >= 0 && y > 0) return x / y;
if (x >= 0 && y < 0) return x / y - (x % y < 0);
if (x < 0 && y < 0) return x / y + (x % y < 0);
return x / y - (x % y < 0); // (x < 0 && y > 0)
}
int mod(int x, int y) { // x = qy + r (0 <= r < y) を満たすr
assert(y != 0);
if (x >= 0) return x % y;
__int128_t ret = x % y; // (x < 0)
ret += (__int128_t)abs(y) * INFL;
ret %= abs(y);
return ret;
}
int floor(int x, int y) { // (ld)x / y 以下の最大の整数
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x >= 0 ? x / y : (x + 1) / y - 1;
}
int ceil(int x, int y) { // (ld)x / y 以上の最小の整数
assert(y != 0);
if (y < 0) x = -x, y = -y;
return x > 0 ? (x - 1) / y + 1 : x / y;
}
int round(int x, int y) {
assert(y != 0);
return (x * 2 + y) / (y * 2);
}
int round(int x, int y, int k) { // (ld)(x/y)を10^kの位に関して四捨五入
assert(y != 0); // TODO
return INF;
}
int round2(int x, int y) { // 五捨五超入 // 未verify
assert(y != 0);
if (y < 0) y = -y, x = -x;
int z = z / y;
if ((z * 2 + 1) * y <= y * 2) z++;
return z;
}
// int round(ld x, int k) { // xを10^kの位に関して四捨五入
// }
// int floor(ld x, int k) { // xを10^kの位に関してflooring
// }
// int ceil(ld x, int k) { // xを10^kの位に関してceiling
// }
// int kth(int x, int y, int k) { // x / yの10^kの位の桁
// }
int floor(ld x, ld y) { // 誤差対策TODO
assert(!equals(y, 0));
return floor(x / y);
// floor(x) = ceil(x - 1) という話も
}
int ceil(ld x, ld y) { // 誤差対策TODO // ceil(p/q) = -floor(-(p/q))らしい
assert(!equals(y, 0));
return ceil(x / y);
// ceil(x) = floor(x + 1)
}
int perl(ld x, ld y) { // x = qy + r (0 <= r < y, qは整数) を満たす q
// 未verify. 誤差対策TODO. EPS外してもいいかも。
assert(!equals(y, 0));
if (x >= 0 && y > 0) return floor(x / y)+EPS;
if (x >= 0 && y < 0) return -floor(x / fabs(y));
if (x < 0 && y < 0) return floor(x / y) + (x - floor(x/y)*y < -EPS);
return floor(x / y) - (x - floor(x/y)*y < -EPS); // (x < 0 && y > 0)
}
ld modl(ld x, ld y) { // x = qy + r (0 <= r < y, qは整数) を満たす r
// 未verify. 誤差対策TODO. -0.0が返りうる。
assert(!equals(y, 0));
if (x >= 0) return x - fabs(y)*fabs(per(x, y));
return x - fabs(y)*floor(x, fabs(y));
}
int seisuu(ld x) { return (int)x; } // 整数部分. 誤差対策TODO
int modf(ld x) {
if (x < 0) return ceill(x);
else return floorl(x);
}
// 正なら+EPS, 負なら-EPSしてから、文字列に直して小数点以下を捨てる?
int seisuu(int x, int y) {
assert(y != 0);
return x / y;
}
int seisuu(ld x, ld y) { // 誤差対策TODO
assert(!equals(y, 0));
return (int)(x / y);
}
template <class T> pair<T, T> max(const pair<T, T> &a, const pair<T, T> &b) {
if (a.first > b.first or a.first == b.first && a.second > b.second) return a;
return b;
}
template <class T> pair<T, T> min(const pair<T, T> &a, const pair<T, T> &b) {
if (a.first < b.first or a.first == b.first && a.second < b.second) return a;
return b;
}
template <class T> bool chmax(T &a, const T& b) {
if (a < b) { a = b; return true; } return false;
}
template <class T> bool chmin(T &a, const T& b) {
if (a > b) { a = b; return true; } return false;
}
template <class T> T mid(T a, T b, T c) { // 誤差対策TODO
return a + b + c - max({a, b, c}) - min({a, b, c});
}
template <class T> void Sort(T &a, T &b, bool rev = false) {
if (rev == false) { // TODO テンプレート引数
if (a > b) swap(a, b);
} else {
if (b > a) swap(b, a);
}
}
template <class T> void sort(T &a, T &b, T &c, bool rev = false) {
if (rev == false) {
if (a > b) swap(a, b); if (a > c) swap(a, c); if (b > c) swap(b, c);
} else {
if (c > b) swap(c, b); if (c > a) swap(c, a); if (b > a) swap(b, a);
}
}
template <class T> void sort(T &a, T &b, T &c, T &d, bool rev = false) {
if (rev == false) {
if (a > b) swap(a, b); if (a > c) swap(a, c); if (a > d) swap(a, d);
if (b > c) swap(b, c); if (b > d) swap(b, d); if (c > d) swap(c, d);
} else {
if (d > c) swap(d, c); if (d > b) swap(d, b); if (d > a) swap(d, a);
if (c > b) swap(c, b); if (c > a) swap(c, a); if (b > a) swap(b, a);
}
}
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
class Compress {
public:
int sz = 0;
// gp_hash_table<int, int, custom_hash> Z, UZ;
unordered_map<int, int> Z; // 元の値 -> 圧縮した値
unordered_map<int, int> UZ; // 圧縮した値 -> 元の値
Compress(const vector<int> &V, int base = 0) {
this->sz = base;
set<int> s(V.begin(), V.end());
for (int x : s) {
this->Z[x] = this->sz;
this->UZ[this->sz] = x;
this->sz++;
}
}
Compress(const vector<int> &V1, const vector<int> &V2, int base = 0) {
this->sz = base;
vector<int> V3 = V2;
V3.insert(V3.end(), V1.begin(), V1.end());
set<int> s(V3.begin(), V3.end());
for (int x : s) {
this->Z[x] = this->sz;
this->UZ[this->sz] = x;
this->sz++;
}
}
Compress(const vector<int> &V1, const vector<int> &V2, const vector<int> &V3, int base = 0) {
this->sz = base;
vector<int> V4 = V1;
V4.insert(V4.end(), V2.begin(), V2.end());
V4.insert(V4.end(), V3.begin(), V3.end());
set<int> s(V4.begin(), V4.end());
for (int x : s) {
this->Z[x] = this->sz;
this->UZ[this->sz] = x;
this->sz++;
}
}
Compress(const vector<int> &V1, const vector<int> &V2,
const vector<int> &V3, const vector<int> &V4, int base = 0) {
this->sz = base;
vector<int> V5 = V1;
V5.insert(V5.end(), V2.begin(), V2.end());
V5.insert(V5.end(), V3.begin(), V3.end());
V5.insert(V5.end(), V4.begin(), V4.end());
set<int> s(V5.begin(), V5.end());
for (int x : s) {
this->Z[x] = this->sz;
this->UZ[this->sz] = x;
this->sz++;
}
}
vector<int> zip(const vector<int> &V) {
vector<int> ret = V;
for (int i = 0; i < (int)V.size(); i++) {
ret[i] = Z[ret[i]];
}
return ret;
}
vector<int> unzip(const vector<int> &V) {
vector<int> ret = V;
for (int i = 0; i < (int)V.size(); i++) {
ret[i] = UZ[ret[i]];
}
return ret;
}
int size() { return sz; }
int encode(int x) { return Z[x]; }
int decode(int x) {
if (UZ.find(x) == UZ.end()) return -1; // xが元の配列に存在しないとき
return UZ[x];
}
};
class UnionFind {
public:
UnionFind() = default;
UnionFind(int N) : par(N), sz(N, 1) {
iota(par.begin(), par.end(), 0);
}
int root(int x) {
if (par[x] == x) return x;
return (par[x] = root(par[x]));
}
bool unite(int x, int y) {
int rx = root(x);
int ry = root(y);
if (rx == ry) return false;
if (sz[rx] < sz[ry]) swap(rx, ry);
sz[rx] += sz[ry];
par[ry] = rx;
return true;
}
bool issame(int x, int y) { return (root(x) == root(y)); }
int size(int x) { return sz[root(x)]; }
vector<vector<int>> groups(int N) {
vector<vector<int>> G(N);
for (int x = 0; x < N; x++) {
G[root(x)].push_back(x);
}
G.erase( remove_if(G.begin(), G.end(),
[&](const vector<int>& V) { return V.empty(); }), G.end());
return G;
}
private:
vector<int> par, sz;
};
template<typename T>
struct BIT {
int N; // 要素数
vector<T> bit[2]; // データの格納先
BIT(int N_, int x = 0) {
N = N_ + 1;
bit[0].assign(N, 0); bit[1].assign(N, 0);
if (x != 0) {
for (int i = 0; i < N; i++) add(i, x);
}
}
BIT(const vector<int> &A) {
N = A.size() + 1;
bit[0].assign(N, 0); bit[1].assign(N, 0);
for (int i = 0; i < (int)A.size(); i++) add(i, A[i]);
}
void add_sub(int p, int i, T x) {
while (i < N) { bit[p][i] += x; i += (i & -i); }
}
void add(int l, int r, T x) {
add_sub(0, l + 1, -x * l); add_sub(0, r + 1, x * r);
add_sub(1, l + 1, x); add_sub(1, r + 1, -x);
}
void add(int i, T x) { add(i, i + 1, x); }
T sum_sub(int p, int i) {
T ret = 0;
while (i > 0) { ret += bit[p][i]; i -= (i & -i); }
return ret;
}
T sum(int i) { return sum_sub(0, i) + sum_sub(1, i) * i; }
T sum(int l, int r) { return sum(r) - sum(l); }
T get(int i) { return sum(i, i + 1); }
void set(int i, T x) { T s = get(i); add(i, -s + x); }
};
template<int mod> class Modint {
public:
int val = 0;
Modint(int x = 0) { while (x < 0) x += mod; val = x % mod; }
Modint(const Modint &r) { val = r.val; }
Modint operator -() { return Modint(-val); } // 単項
Modint operator +(const Modint &r) { return Modint(*this) += r; }
Modint operator +(const int &q) { Modint r(q); return Modint(*this) += r; }
Modint operator -(const Modint &r) { return Modint(*this) -= r; }
Modint operator -(const int &q) { Modint r(q); return Modint(*this) -= r; }
Modint operator *(const Modint &r) { return Modint(*this) *= r; }
Modint operator *(const int &q) { Modint r(q); return Modint(*this) *= r; }
Modint operator /(const Modint &r) { return Modint(*this) /= r; }
Modint operator /(const int &q) { Modint r(q); return Modint(*this) /= r; }
Modint& operator ++() { val++; if (val >= mod) val -= mod; return *this; } // 前置
Modint operator ++(signed) { ++*this; return *this; } // 後置
Modint& operator --() { val--; if (val < 0) val += mod; return *this; }
Modint operator --(signed) { --*this; return *this; }
Modint &operator +=(const Modint &r) { val += r.val; if (val >= mod) val -= mod; return *this; }
Modint &operator +=(const int &q) { Modint r(q); val += r.val; if (val >= mod) val -= mod; return *this; }
Modint &operator -=(const Modint &r) { if (val < r.val) val += mod; val -= r.val; return *this; }
Modint &operator -=(const int &q) { Modint r(q); if (val < r.val) val += mod; val -= r.val; return *this; }
Modint &operator *=(const Modint &r) { val = val * r.val % mod; return *this; }
Modint &operator *=(const int &q) { Modint r(q); val = val * r.val % mod; return *this; }
Modint &operator /=(const Modint &r) {
int a = r.val, b = mod, u = 1, v = 0;
while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
val = val * u % mod; if (val < 0) val += mod;
return *this;
}
Modint &operator /=(const int &q) {
Modint r(q); int a = r.val, b = mod, u = 1, v = 0;
while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);}
val = val * u % mod; if (val < 0) val += mod;
return *this;
}
bool operator ==(const Modint& r) { return this -> val == r.val; }
bool operator <(const Modint& r) { return this -> val < r.val; }
bool operator >(const Modint& r) { return this -> val > r.val; }
bool operator !=(const Modint& r) { return this -> val != r.val; }
};
using mint = Modint<MOD>;
istream &operator >>(istream &is, mint& x) {
int t; is >> t; x = t; return (is);
}
ostream &operator <<(ostream &os, const mint& x) {
return os << x.val;
}
mint modpow(const mint &x, int n) {
if (n < 0) return (mint)1 / modpow(x, -n); // 未verify
assert(n >= 0);
if (n == 0) return 1;
mint t = modpow(x, n / 2);
t = t * t;
if (n & 1) t = t * x;
return t;
}
int modpow(__int128_t x, int n, int mod) {
assert(n >= 0 && mod > 0); // TODO: n <= -1
__int128_t ret = 1;
while (n > 0) {
if (n % 2 == 1) ret = ret * x % mod;
x = x * x % mod;
n /= 2;
}
return ret;
}
int modinv(__int128_t x, int mod) {
assert(mod > 0);
// assert(x > 0);
if (x == 1 or x == 0) return 1;
return mod - modinv(mod % x, mod) * (mod / x) % mod;
}
istream &operator >>(istream &is, __int128_t& x) {
string S; is >> S;
__int128_t ret = 0;
int f = 1;
if (S[0] == '-') f = -1;
for (int i = 0; i < S.length(); i++)
if ('0' <= S[i] && S[i] <= '9')
ret = ret * 10 + S[i] - '0';
x = ret * f;
return (is);
}
ostream &operator <<(ostream &os, __int128_t x) {
ostream::sentry s(os);
if (s) {
__uint128_t tmp = x < 0 ? -x : x;
char buffer[128]; char *d = end(buffer);
do {
--d; *d = "0123456789"[tmp % 10]; tmp /= 10;
} while (tmp != 0);
if (x < 0) { --d; *d = '-'; }
int len = end(buffer) - d;
if (os.rdbuf()->sputn(d, len) != len) os.setstate(ios_base::badbit);
}
return os;
}
__int128_t stoll(string &S) {
__int128_t ret = 0; int f = 1;
if (S[0] == '-') f = -1;
for (int i = 0; i < S.length(); i++)
if ('0' <= S[i] && S[i] <= '9') ret = ret * 10 + S[i] - '0';
return ret * f;
}
__int128_t gcd(__int128_t a, __int128_t b) { return b ? gcd(b, a % b) : a; }
__int128_t lcm(__int128_t a, __int128_t b) {
return a / gcd(a, b) * b;
// lcmが__int128_tに収まる必要あり
}
string to_string(ld x, int k) { // xの小数第k位までをstring化する
assert(k >= 0);
stringstream ss;
ss << setprecision(k + 2) << x;
string s = ss.str();
if (s.find('.') == string::npos) s += '.';
int pos = s.find('.');
for (int i = 0; k >= (int)s.size() - 1 - pos; i++) s += '0';
s.pop_back();
if (s.back() == '.') s.pop_back();
return s;
// stringstream ss; // 第k+1位を四捨五入して第k位まで返す
// ss << setprecision(k + 1) << x;
// string s = ss.str();
// if (s.find('.') == string::npos) s += '.';
// int pos = s.find('.');
// for (int i = 0; k > (int)s.size() - 1 - pos; i++) s += '0';
// if (s.back() == '.') s.pop_back();
// return s;
}
string to_string(__int128_t x) {
string ret = "";
if (x < 0) { ret += "-"; x *= -1; }
while (x) { ret += (char)('0' + x % 10); x /= 10; }
reverse(ret.begin(), ret.end());
return ret;
}
string to_string(char c) { string s = ""; s += c; return s; }
template<class T> size_t HashCombine(const size_t seed,const T &v) {
return seed^(hash<T>()(v)+0x9e3779b9+(seed<<6)+(seed>>2));
}
template<class T,class S> struct hash<pair<T,S>>{
size_t operator()(const pair<T,S> &keyval) const noexcept {
return HashCombine(hash<T>()(keyval.first), keyval.second);
}
};
template<class T> struct hash<vector<T>>{
size_t operator()(const vector<T> &keyval) const noexcept {
size_t s=0;
for (auto&& v: keyval) s=HashCombine(s,v);
return s;
}
};
template<int N> struct HashTupleCore{
template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{
size_t s=HashTupleCore<N-1>()(keyval);
return HashCombine(s,get<N-1>(keyval));
}
};
template <> struct HashTupleCore<0>{
template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{ return 0; }
};
template<class... Args> struct hash<tuple<Args...>>{
size_t operator()(const tuple<Args...> &keyval) const noexcept {
return HashTupleCore<tuple_size<tuple<Args...>>::value>()(keyval);
}
};
vector<mint> _fac, _finv, _inv;
void COMinit(int N) {
_fac.resize(N + 1); _finv.resize(N + 1); _inv.resize(N + 1);
_fac[0] = _fac[1] = 1; _finv[0] = _finv[1] = 1; _inv[1] = 1;
for (int i = 2; i <= N; i++) {
_fac[i] = _fac[i-1] * mint(i);
_inv[i] = -_inv[MOD % i] * mint(MOD / i);
_finv[i] = _finv[i - 1] * _inv[i];
}
}
mint FAC(int N) {
if (N < 0) return 0; return _fac[N];
}
mint COM(int N, int K) {
if (N < K) return 0; if (N < 0 or K < 0) return 0;
return _fac[N] * _finv[K] * _finv[N - K];
}
mint PERM(int N, int K) {
if (N < K) return 0; if (N < 0 or K < 0) return 0;
return _fac[N] * _finv[N - K];
}
mint NHK(int N, int K) { // initのサイズに注意
if (N == 0 && K == 0) return 1;
return COM(N + K - 1, K);
}
#pragma endregion
class Point3d {
public:
double x, y, z;
Point3d(double x = 0, double y = 0, double z = 0) : x(x), y(y), z(z) {}
Point3d operator+(const Point3d& a) {
return Point3d(x + a.x, y + a.y, z + a.z);
}
Point3d operator-(const Point3d& a) {
return Point3d(x - a.x, y - a.y, z - a.z);
}
Point3d operator*(const double& d) {
return Point3d(x * d, y * d, z * d);
}
Point3d operator/(const double& d) {
return Point3d(x / d, y / d, z / d);
}
bool operator<(const Point3d& p) const {
if (!equals(x, p.x)) return x < p.x;
if (!equals(y, p.y)) return y < p.y;
if (!equals(z, p.z)) return z < p.z;
return false;
}
bool operator==(const Point3d& p) const {
return equals(x, p.x) && equals(y, p.y) && equals(z, p.z);
}
friend istream& operator>>(istream& is, Point3d& p) {
is >> p.x >> p.y >> p.z;
return is;
}
friend ostream& operator<<(ostream& os, Point3d& p) {
os << p.x << " " << p.y << " " << p.z;
return os;
}
};
int sign(double x) { return x < -EPS ? -1 : x > EPS; } // -1(負)/0/1(正)
struct Segment3d {
Point3d p[2], d; // pは端点、dは向き
Segment3d(Point3d p1 = Point3d(), Point3d p2 = Point3d()) {
p[0] = p1, p[1] = p2;
d = p[1] - p[0];
}
bool operator==(const Segment3d& S) const {
return (p[0] == S.p[0] && p[1] == S.p[1]) || (p[0] == S.p[1] && p[1] == S.p[0]);
}
};
using Line3d = Segment3d;
using Vector3d = Point3d;
bool is_parallel(Vector3d v1, Vector3d v2) {
if (equals(v1.x*v2.y, v1.y*v2.x) &&
equals(v1.y*v2.z, v1.z*v2.y) &&
equals(v1.z*v2.x, v1.x*v2.z)) return true;
return false;
}
bool is_orthogonal(Vector3d v1, Vector3d v2) {
if (equals(v1.x*v2.x + v1.y*v2.y + v1.z*v2.z, 0)) return true;
return false;
}
bool is_parallel(Line3d &l, Line3d &m) {
return is_parallel(l.p[1] - l.p[0], m.p[1] - m.p[0]);
}
bool is_orthogonal(Line3d &l, Line3d &m) {
return is_orthogonal(l.p[1] - l.p[0], m.p[1] - m.p[0]);
}
ostream& operator<<(ostream& os, const Point3d& p) {
return os << "(" << p.x << "," << p.y << "," << p.z << ")";
}
ostream& operator<<(ostream& os, const Segment3d& S) {
return os << "(" << S.p[0] << "," << S.p[1] << ")";
}
double dot(const Point3d& a, const Point3d& b) {
return a.x * b.x + a.y * b.y + a.z * b.z;
}
Vector3d cross(const Point3d& a, const Point3d& b) {
return Vector3d(a.y * b.z - a.z * b.y, a.z * b.x - a.x * b.z, a.x * b.y - a.y * b.x);
}
inline double norm(const Point3d& p) {
return p.x * p.x + p.y * p.y + p.z * p.z;
}
inline double abs(const Point3d& p) {
return sqrt(norm(p));
}
double rad_to_deg(double r) { return (r * 180.0 / PI); }
double deg_to_rad(double d) { return (d * PI / 180.0); }
double angle(Point3d a, Point3d b) {
double costheta = dot(a, b) / norm(a) / norm(b);
return acos(max(-1.0, min(1.0, costheta)));
}
Point3d rotateccw90(Point3d a) { return Point3d(-a.y, a.x); }
Point3d rotatecw90(Point3d a) { return Point3d(a.y, -a.x); }
Point3d rotateccw(Point3d a, double t) { return Point3d(a.x * cos(t) - a.y * sin(t), a.x * sin(t) + a.y * cos(t)); }
Point3d rotatecw(Point3d a, double t) { return Point3d(a.x * cos(t) + a.y * sin(t), -a.x * sin(t) + a.y * cos(t)); }
double distanceLP(Line3d L, Point3d p) {
return abs(cross(L.p[1] - L.p[0], p - L.p[0])) / abs(L.p[1] - L.p[0]);
}
double dist(Point3d p1, Point3d p2) {
return sqrt(norm(p1 - p2));
}
Point3d project(Segment3d S, Point3d p) {
Vector3d base = S.p[1] - S.p[0];
double t = dot(p - S.p[0], base) / norm(base);
return S.p[0] + base * t;
}
Point3d reflect(Segment3d S, Point3d p) {
return p + (project(S, p) - p) * 2.0;
}
bool on_line3d(Line3d L, Point3d p) {
return equals(abs(cross(L.p[1] - p, L.p[0] - p)), 0);
}
bool on_segment3d(Segment3d S, Point3d p) {
if (!on_line3d(S, p)) return false;
double dist[3] = {abs(S.p[1] - S.p[0]), abs(p - S.p[0]), abs(p - S.p[1])};
return on_line3d(S, p) && equals(dist[0], dist[1] + dist[2]);
}
double distanceSP(Segment3d S, Point3d p) {
Point3d r = project(S, p);
if (on_segment3d(S, r)) return abs(p - r);
return min(abs(S.p[0] - p), abs(S.p[1] - p));
}
class Plane3d {
public:
Point3d normal_vector; // 法線ベクトル
double d; // 平面方程式 normal_vector = (a,b,c), a*x + b*y + c*z + d = 0
Plane3d(Point3d normal_vector = Point3d(), double d = 0) : normal_vector(normal_vector), d(d) {}
Plane3d(Vector3d a, Vector3d b, Vector3d c) {
Vector3d v1 = b - a;
Vector3d v2 = c - a;
Vector3d tmp = cross(v1, v2);
normal_vector = tmp / abs(tmp);
set_d(a);
}
// From three non-collinear points P,Q,R
// Plane3d(Point3d p, Point3d q, Point3d r) : Plane3d((q - p) * (r - p), p) {}
// 点pの平面に対する位置(正/負)
double side(Point3d p) { return dot(normal_vector, p) - d; }
// shift the Plane3d perpendicular to normal_vector by distance dist
Plane3d shiftUp(double dist) { return {normal_vector, d + dist * abs(normal_vector)}; }
pair<Point3d, Point3d> get_two_points_on_plane() {
assert(sign(normal_vector.x) != 0 or sign(normal_vector.y) != 0 or sign(normal_vector.z) != 0);
if (sign(normal_vector.x) == 0 && sign(normal_vector.y) == 0) return make_pair(Point3d(1, 0, d/normal_vector.z), Point3d(0, 1, d/normal_vector.z));
if (sign(normal_vector.y) == 0 && sign(normal_vector.z) == 0) return make_pair(Point3d(d/normal_vector.x, 1, 0), Point3d(d/normal_vector.x, 0, 1));
if (sign(normal_vector.z) == 0 && sign(normal_vector.x) == 0) return make_pair(Point3d(1, d/normal_vector.y, 0), Point3d(0, d/normal_vector.y, 1));
if (sign(normal_vector.x) == 0) return make_pair(Point3d(1, d/normal_vector.y, 0), Point3d(0, 0, d/normal_vector.z));
if (sign(normal_vector.y) == 0) return make_pair(Point3d(0, 1, d/normal_vector.z), Point3d(d/normal_vector.x, 0, 0));
if (sign(normal_vector.z) == 0) return make_pair(Point3d(d/normal_vector.x, 0, 1), Point3d(0, d/normal_vector.y, 0));
if (sign(d)!=0) return make_pair(Point3d(d/normal_vector.x, 0, 0), Point3d(0, d/normal_vector.y, 0));
return make_pair(Point3d(normal_vector.y, -normal_vector.x, 0), Point3d(-normal_vector.y, normal_vector.x, 0));
}
// 法線ベクトルnormal_vectorと平面上の１点からdを計算する
void set_d(Point3d p) {
d = dot(normal_vector, p);
}
// 平面と点pの距離を求める
double distanceP(Point3d p) {
Point3d a = normal_vector * d; // 平面上の適当な点をつくる
return abs(dot(p - a, normal_vector));
}
// 平面上でもっとも点pと近い点を求める
Point3d projection(Point3d p) {
Point3d a = normal_vector * d;
return p - (normal_vector * dot(p - a, normal_vector));
}
Point3d reflection(Point3d p) { // 未
return p + (projection(p) - p) * 2.;
}
// 平面と線分が交差するか
bool intersectS(Segment3d seg) {
Point3d a = normal_vector * d;
double res1 = dot(a - seg.p[0], normal_vector);
double res2 = dot(a - seg.p[1], normal_vector);
if (res1 > res2) swap(res1, res2);
if ((equals(res1, 0.0) || res1 < 0) && (equals(res2, 0.0) || res2 > 0)) return true;
return false;
}
// 平面と線分の交点を求める
Point3d crosspointS(Segment3d seg) {
Point3d a = normal_vector * d;
double dot_p0a = fabs(dot(seg.p[0] - a, normal_vector));
double dot_p1a = fabs(dot(seg.p[1] - a, normal_vector));
if (equals(dot_p0a + dot_p1a, 0)) return seg.p[0];
return seg.p[0] + (seg.p[1] - seg.p[0]) * (dot_p0a / (dot_p0a + dot_p1a));
}
};
bool is_parallel(Plane3d P, Line3d &L) {
return is_orthogonal(P.normal_vector, L.p[1] - L.p[0]);
}
bool is_orthogonal(Plane3d P, Line3d &L) {
return is_parallel(P.normal_vector, L.p[1] - L.p[0]);
}
bool is_parallel(Plane3d P1, Plane3d P2) {
return cross(P1.normal_vector, P2.normal_vector) == Vector3d(0, 0);
}
bool is_orthogonal(Plane3d P1, Plane3d P2) {
return sign(dot(P1.normal_vector, P2.normal_vector)) == 0;
}
double angle(Plane3d p, Line3d l) {
return PI / 2. - acos(min(fabs(dot(p.normal_vector, l.d)) / abs(p.normal_vector) / abs(l.d), 1.0));
}
double distPL(Plane3d P, Line3d L) {
return is_parallel(P, L) ? P.distanceP(L.p[0]) : 0;
}
double distPS(Plane3d P, Segment3d S) {
Point3d ha = P.projection(S.p[0]), hb = P.projection(S.p[1]);
double ipa = dot(S.p[0] - ha, S.p[1] - S.p[0]), ipb = dot(S.p[1] - hb, S.p[0] - S.p[1]);
return sign(ipa) < 0 && sign(ipb) < 0 ? 0 : min(P.distanceP(S.p[0]), P.distanceP(S.p[1]));
}
using P3db = pair<Point3d, bool>;
double area(Point3d a, Point3d b, Point3d c) {
return abs(cross(b - a, c - a)) / 2.;
}
double orient_by_normal(Point3d p, Point3d q, Point3d r, Point3d n) {
return dot(cross(q - p, r - p), n);
}
double distance_from_segment_to_point(Point3d a, Point3d b, Point3d c) {
if (sign(dot(b - a, c - a)) < 0) return dist(a, c);
if (sign(dot(a - b, c - b)) < 0) return dist(b, c);
return fabs(abs(cross((b - a) / abs(b - a), c - a)));
}
double distance_from_triangle_to_point(Point3d a, Point3d b, Point3d c, Point3d d) {
Plane3d P(a, b, c);
Point3d proj = P.projection(d);
double dis = min(distance_from_segment_to_point(a, b, d), min(distance_from_segment_to_point(b, c, d), distance_from_segment_to_point(c, a, d)));
int o = sign(orient_by_normal(a, b, proj, P.normal_vector));
int inside = o == sign(orient_by_normal(b, c, proj, P.normal_vector));
inside &= o == sign(orient_by_normal(c, a, proj, P.normal_vector));
if (inside) return abs(d - proj);
return dis;
}
signed main() {
Point3d a, b, c, p;
cin >> a >> b >> c >> p;
Plane3d f(a, b, c);
int d = f.distanceP(p); // 平面ABCとの距離
// 三角形ABCとの距離
double mind = distance_from_triangle_to_point(a, b, c, p);
if (equals(mind, d)) cout << "YES" << endl;
else cout << "NO" << endl;
}