結果
| 問題 | No.743 Segments on a Polygon |
| ユーザー |
 はむこ
|
| 提出日時 | 2018-01-22 08:34:39 |
| 言語 | C++11 (gcc 11.4.0) |
| 結果 |
AC
|
| 実行時間 | 842 ms / 2,000 ms |
| コード長 | 20,440 bytes |
| コンパイル時間 | 2,358 ms |
| コンパイル使用メモリ | 190,344 KB |
| 実行使用メモリ | 41,172 KB |
| 最終ジャッジ日時 | 2024-06-07 15:47:30 |
| 合計ジャッジ時間 | 12,396 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
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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 | 832 ms
41,040 KB |
| testcase_01 | AC | 837 ms
41,048 KB |
| testcase_02 | AC | 842 ms
41,168 KB |
| testcase_03 | AC | 830 ms
41,040 KB |
| testcase_04 | AC | 828 ms
41,168 KB |
| testcase_05 | AC | 825 ms
41,044 KB |
| testcase_06 | AC | 821 ms
41,172 KB |
| testcase_07 | AC | 822 ms
41,168 KB |
| testcase_08 | AC | 814 ms
41,168 KB |
| testcase_09 | AC | 472 ms
41,164 KB |
ソースコード
// 重要！！！！！！！！！！！！
// 何故か配列じゃないと動かないので、必ず使うときには配列に移してから使うこと！！
// v.data()みたいなのではバグる！！！！！！TODO なおす
//
// あと、出力がintになっていることが多いので、long longキャストに注意！！！！
#include <bits/stdc++.h>
#include <sys/time.h>
using namespace std;
#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
#define exists find_if
#define forall all_of
using ll = long long; using vll = vector<ll>; using vvll = vector<vll>; using P = pair<ll, ll>;
using ld = long double; using vld = vector<ld>;
using vi = vector<int>; using vvi = vector<vi>; vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; }
using Pos = complex<double>;
template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) { o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args>
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]"; return o; }
template <typename T> ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; }
template <typename T, typename U> ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; }
template <typename T, typename U, typename V> ostream &operator<<(ostream &o, const unordered_map<T, U, V> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]"; return o; }
vector<int> range(const int x, const int y) { vector<int> v(y - x + 1); iota(v.begin(), v.end(), x); return v; }
template <typename T> istream& operator>>(istream& i, vector<T>& o) { rep(j, o.size()) i >> o[j]; return i;}
string bits_to_string(ll input, ll n=64) { string s; rep(i, n) s += '0' + !!(input & (1ll << i)); return s; }
template <typename T> unordered_map<T, ll> counter(vector<T> vec){unordered_map<T, ll> ret; for (auto&& x : vec) ret[x]++; return ret;};
string substr(string s, P x) {return s.substr(x.fi, x.se - x.fi); }
struct ci : public iterator<forward_iterator_tag, ll> { ll n; ci(const ll n) : n(n) { } bool operator==(const ci& x) { return n == x.n; } bool operator!=(const ci& x) { return !(*this == x); } ci &operator++() { n++; return *this; } ll operator*() const { return n; } };
size_t random_seed; namespace std { using argument_type = P; template<> struct hash<argument_type> { size_t operator()(argument_type const& x) const { size_t seed = random_seed; seed ^= hash<ll>{}(x.fi); seed ^= (hash<ll>{}(x.se) << 1); return seed; } }; }; // hash for various class
namespace myhash{ const int Bsizes[]={3,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81}; const int xor_nums[]={0x100007d1,0x5ff049c9,0x14560859,0x07087fef,0x3e277d49,0x4dba1f17,0x709c5988,0x05904258,0x1aa71872,0x238819b3,0x7b002bb7,0x1cf91302,0x0012290a,0x1083576b,0x76473e49,0x3d86295b,0x20536814,0x08634f4d,0x115405e8,0x0e6359f2}; const int hash_key=xor_nums[rand()%20]; const int mod_key=xor_nums[rand()%20]; template <typename T> struct myhash{ std::size_t operator()(const T& val) const { return (hash<T>{}(val)%mod_key)^hash_key; } }; };
template <typename T> class uset:public std::unordered_set<T,myhash::myhash<T>> { using SET=std::unordered_set<T,myhash::myhash<T>>; public: uset():SET(){SET::rehash(myhash::Bsizes[rand()%20]);} };
template <typename T,typename U> class umap:public std::unordered_map<T,U,myhash::myhash<T>> { public: using MAP=std::unordered_map<T,U,myhash::myhash<T>>; umap():MAP(){MAP::rehash(myhash::Bsizes[rand()%20]);} };
struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; }
struct init_{init_(){ gettimeofday(&start, NULL); ios::sync_with_stdio(false); cin.tie(0); srand((unsigned int)time(NULL)); random_seed = RAND_MAX / 2 + rand() / 2; }} init__;
static const double EPS = 1e-14;
static const long long INF = 1e18;
static const long long mo = 1e9+7;
#define ldout fixed << setprecision(40)
#define double long double
/*****************/
// Dictionary
/*****************/
// Nはバケット数
template<int N> class FID {
static const int bucket = 512, block = 16;
// 整数iのpopcountをO(1)で求めるためのテーブル
// popcount[i] = __builtin_popcount(i), i<65536
static char popcount[];
// B[i]: s[0:512*i)のビット1の総数
int n, B[N/bucket+10];
// bs[i]: s[16*i:16*(i+1)]のビット列そのもの
unsigned short bs[N/block+10] = {};
// b[i]: s[i/32*512:i/32*512+i%32*32)のビット1の総数
// bs[i]を512bitずつリセットしながら、累積和を取ってる感じ。
unsigned short b[N/block+10] = {};
public:
FID(){}
FID(int n, bool s[]) : n(n) {
if(!popcount[1]) for (int i = 0; i < (1<<block); i++) popcount[i] = __builtin_popcount(i);
bs[0] = B[0] = b[0] = 0;
for (int i = 0; i < n; i++) {
if(i%block == 0) {
bs[i/block+1] = 0;
if(i%bucket == 0) {
B[i/bucket+1] = B[i/bucket];
b[i/block+1] = b[i/block] = 0;
}
else b[i/block+1] = b[i/block];
}
bs[i/block] |= short(s[i])<<(i%block);
b[i/block+1] += s[i];
B[i/bucket+1] += s[i];
}
if(n%bucket == 0) b[n/block] = 0;
}
// number of val in [0,r), O(1)
// 大ブロックの累積和(512bit)+中ブロックの累積和(16bit)+「余り分に適切なbitmaskをかけてpopcount」
int count(bool val, int r) { return val? B[r/bucket]+b[r/block]+popcount[bs[r/block]&((1<<(r%block))-1)]: r-count(1,r); }
// number of val in [l,r), O(1)
int count(bool val, int l, int r) { return count(val,r)-count(val,l); }
// position of ith in val, 0-indexed, O(log n)
// 範囲外を示していたら-1を返す
int select(bool val, int i) {
if(i < 0 or count(val,n) <= i) return -1;
i++;
int lb = 0, ub = n, md;
while(ub-lb>1) {
md = (lb+ub)>>1;
if(count(val,md) >= i) ub = md;
else lb = md;
}
return ub-1;
}
int select(bool val, int i, int l) { return select(val,i+count(val,l)); }
bool operator[](int i) { return bs[i/block]>>(i%block)&1; }
void print(void) {
/*
rep(i, 1+(N-1)/bucket) {
cout << B[i] << " ";
}
cout << endl;
rep(i, 1+(N-1)/block) {
cout << b[i] << " ";
}
cout << endl;
*/
rep(i, 1+(N-1)/block) {
cout << bits_to_string(bs[i], (i != (N-1)/block ? 16 : N - (N-1)/block*block)) << " ";
}
cout << endl;
}
};
template<int N> char FID<N>::popcount[1<<FID<N>::block];
/*****************/
// Wavelet Matrix
/*****************/
// 長さNで、値域[0, m=2^D)の整数を管理する
//#define ENABLE_SUM
template<class T, int N, int D> class wavelet {
int n, zs[D];
FID<N> dat[D];
public:
wavelet(void) { }
#ifdef ENABLE_SUM
T raw_data[D+1][N] = {};
T sum_data[D+1][N+1] = {};
wavelet(int n, T seq[]) : n(n) {
T l[N] = {}, r[N] = {};
bool b[N] = {};
memcpy(raw_data[0], seq, sizeof(T)*n);
for (int d = 0; d < D; d++) {
int lh = 0, rh = 0;
for (int i = 0; i < n; i++) {
b[i] = (raw_data[d][i]>>(D-d-1))&1;
if(b[i]) r[rh++] = raw_data[d][i];
else l[lh++] = raw_data[d][i];
}
dat[d] = FID<N>(n,b);
zs[d] = lh;
swap(l,raw_data[d+1]);
memcpy(raw_data[d+1]+lh, r, rh*sizeof(T));
}
rep(d, D+1) rep(i, N) sum_data[d][i+1] = sum_data[d][i] + raw_data[d][i];
}
// 深さdでの列の[l, r)での累積和を求める
T getSum(int d, int l, int r) {
return sum_data[d][r] - sum_data[d][l];
}
// get sum of elements in [l,r) in [a,b)
// O(log m)
T sum_dfs(int d, int l, int r, T val, T a, T b) {
// Wavelet Matrixの深さdで、
// [l, r)が[val, nv) = [val, val+(1ll<<(D-d)))の値域を表現している時、
// [a, b)の値域のものの和は？
if(l == r) return 0; // valは無いので0を返す
if(d == D) return (a <= val and val < b)? (r-l)*val: 0; // 深さDでは全部の値が同じなので、そのままかけて返す
T nv = 1ULL<<(D-d-1)|val, nnv = ((1ULL<<(D-d-1))-1)|nv;
if(nnv < a or b <= val) // どんなに1を選んでもaに満たなかったり、すでに最大を超えていたら0
return 0;
if (a <= val and nnv < b) // これからどう選んでも a <= [l, r) < bの場合、累積和を返す
return getSum(d, l, r);
int lc = dat[d].count(1,l), rc = dat[d].count(1,r);
return sum_dfs(d+1,l-lc,r-rc,val,a,b)+ sum_dfs(d+1,lc+zs[d],rc+zs[d],nv,a,b);
}
T sum(int l, int r, T a, T b) { return sum_dfs(0,l,r,0,a,b); }
#else
wavelet(int n, T seq[]) : n(n) {
T f[N], l[N], r[N];
bool b[N];
memcpy(f, seq, sizeof(T)*n);
for (int d = 0; d < D; d++) {
int lh = 0, rh = 0;
for (int i = 0; i < n; i++) {
bool k = (f[i]>>(D-d-1))&1;
if(k) r[rh++] = f[i];
else l[lh++] = f[i];
b[i] = k;
}
dat[d] = FID<N>(n,b);
zs[d] = lh;
swap(l,f);
memcpy(f+lh, r, rh*sizeof(T));
}
}
#endif
void print(void) {
rep(i, D) cout << zs[i] << " "; cout << endl;
rep(i, D) dat[i].print();
/*
cout << "Raw" << endl;
rep(d, D+1) { rep(i, N) cout << raw_data[d][i] << " "; cout << endl; }
cout << "Sum" << endl;
rep(d, D+1) { rep(i, N+1) cout << sum_data[d][i] << " "; cout << endl; }
*/
}
// get, []: i番目の要素
// O(1)
T get(int i) {
T ret = 0;
bool b;
for (int d = 0; d < D; d++) {
ret <<= 1;
b = dat[d][i];
ret |= b;
i = dat[d].count(b,i)+b*zs[d];
}
return ret;
}
T operator[](int i) { return get(i); }
// rank: 区間[0,r)にあるvalの個数
// O(log m)
int count(T val, int l, int r) {
for (int d = 0; d < D; d++) {
// ここで[l, r)にxのd桁目までが全て入っていることを保証(d>0)
bool b = (val>>(D-d-1))&1;
l = dat[d].count(b,l)+b*zs[d];
r = dat[d].count(b,r)+b*zs[d];
}
return r-l;
}
int count(T val, int r) { return count(val,0,r); }
// select: i番目のvalの位置
// O(log m log log m)
int select(T val, int k) {
int ls[D], rs[D], l = 0, r = n;
for (int d = 0; d < D; d++) {
ls[d] = l; rs[d] = r;
bool b = val>>(D-d-1)&1;
l = dat[d].count(b,l)+b*zs[d];
r = dat[d].count(b,r)+b*zs[d];
}
for (int d = D-1; d >= 0; d--) {
bool b = val>>(D-d-1)&1;
k = dat[d].select(b,k,ls[d]);
if(k >= rs[d] or k < 0) return -1;
k -= ls[d];
}
return k;
}
int select(T val, int k, int l) { return select(val,k+count(val,l)); }
// maximum: 区間[l,r)で大きい順にk個
// O(k log m)
void list_max_dfs(int d, int l, int r, int &k, T val, vector<T> &vs) {
if(l >= r or !k) return;
if(d == D) {
while(l++ < r and k > 0) vs.push_back(val), k--;
return;
}
int lc = dat[d].count(1,l), rc = dat[d].count(1,r);
// if min, change this order
list_max_dfs(d+1, lc+zs[d], rc+zs[d], k, 1ULL<<(D-d-1)|val,vs);
list_max_dfs(d+1, l-lc, r-rc, k, val, vs);
}
vector<T> list_max(int l, int r, int k) {
if (r-l < k) k = r-l;
if(k < 0) return {};
vector<T> ret;
list_max_dfs(0,l,r,k,0,ret);
return ret;
}
// 添字[l, r)の要素で、値が[a, b)のもののうち最大値を求める
// valは上からd bit決めて他0を埋めた時の値。
//
// O(log m)
T rangemax_dfs(int d, int l, int r, T val, T a, T b) {
if(r-l <= 0 or val >= b) return -1;
if(d == D) return val>=a? val: -1;
int lc = dat[d].count(1,l), rc = dat[d].count(1,r);
T ret = rangemax_dfs(d+1, lc+zs[d], rc+zs[d], 1ULL<<(D-d-1)|val, a, b);
if(~ret) return ret; // 1側を見て見つかったならそれに越したことはない
return rangemax_dfs(d+1, l-lc, r-rc, val, a, b); // なければ0側を見る
}
T rangemax(int l, int r, T a, T b) { return rangemax_dfs(0,l,r,0,a,b); }
// k is 0-indexed!!!!
// quantile: 区間[l,r)でk番目に大きい数
// O(log m)
T quantile(int l, int r, int k) {
if(r-l <= k or k < 0) return -1;
T ret = 0;
for (int d = 0; d < D; d++) {
int lc = dat[d].count(1,l), rc = dat[d].count(1,r);
// lc - rc = [l, r)で立っている1の数
if(rc-lc > k) { // 1の数にkが収まっていれば
l = lc+zs[d], r = rc+zs[d]; // 1側に遷移
ret |= 1ULL<<(D-d-1);
} else { // 0側ならば
k -= rc-lc; // 1側にあった数だけkを削って次へ
l -= lc, r -= rc;
}
}
return ret;
}
T min(int l, int r) { return quantile(l, r, 0); }
T max(int l, int r) { return quantile(l, r, r-l-1); }
// freq_list: 区間[l,r)で値が[lb,ub)になる値とその出現回数の組のリスト
// O(k log m), kはヒット数
void list_freq_dfs(int d, int l, int r, T val, T a, T b, vector<pair<T,int>> &vs) {
if(val >= b or r-l <= 0) return;
if(d == D) {
if(a <= val) vs.push_back(make_pair(val,r-l));
return;
}
T nv = val|(1LL<<(D-d-1)), nnv = nv|(((1LL<<(D-d-1))-1));
if(nnv < a) return;
int lc = dat[d].count(1,l), rc = dat[d].count(1,r);
list_freq_dfs(d+1,l-lc,r-rc,val,a,b,vs);
list_freq_dfs(d+1,lc+zs[d],rc+zs[d],nv,a,b,vs);
}
vector<pair<T,int>> list_freq(int l, int r, T a, T b) {
vector<pair<T,int>> ret;
list_freq_dfs(0,l,r,0,a,b,ret);
return ret;
}
// get_rect: 区間[l,r)で値が[lb,ub)になる要素の位置とその値の組(つまり矩形内にある点の座標)のリスト
// O(k log m), kはヒット数
vector<pair<int,T>> get_rect(int l, int r, T a, T b) {
vector<pair<T,int>> res = list_freq(l,r,a,b);
vector<pair<int,T>> ret;
for(auto &e: res)
for (int i = 0; i < e.second; i++)
ret.push_back(make_pair(select(e.first,i,l), e.first));
return ret;
}
// number of elements in [l,r) in [a,b)
// O(log m)
ll freq_dfs(int d, int l, int r, T val, T a, T b) {
if(l == r) return 0;
if(d == D) return (a <= val and val < b)? r-l: 0;
T nv = 1ULL<<(D-d-1)|val, nnv = ((1ULL<<(D-d-1))-1)|nv;
if(nnv < a or b <= val) return 0;
if(a <= val and nnv < b) return r-l;
int lc = dat[d].count(1,l), rc = dat[d].count(1,r);
return freq_dfs(d+1,l-lc,r-rc,val,a,b)+
freq_dfs(d+1,lc+zs[d],rc+zs[d],nv,a,b);
}
ll freq(int l, int r, T a, T b) { return freq_dfs(0,l,r,0,a,b); }
// TODO
// 普通に
// https://www.slideshare.net/pfi/ss-15916040
// rangemaxk, rangemink, prevvalue, nextvalue, intersectを実装するのが良さそう
};
// 二次元点群が与えられた時、
// 閉矩形領域の点群の数え上げをO(log n)で行う。
// 静的オンラインクエリ。
//
// 使い方
// rep(i, num_of_points)
// pc.insert(x[i], y[i]);
// pc.build();
//
// cout << pc.count(左下x, 左下y, 右上x, 右上y) << endl; // 閉矩形領域
//
#define SIZE 100010
#define BITS 18
class PointCloud2D {
// デバッグ用
ll countBrutal(ll ax, ll ay, ll bx, ll by) {
if (ax > bx || ay > by) return 0;
ll ret = 0;
rep(i, n) {
ret += (ax <= xy[i].fi && xy[i].fi <= bx && ay <= xy[i].se && xy[i].se <= by);
}
return ret;
}
public:
ll n;
ll* data;
wavelet<ll, SIZE, BITS> w;
vector<P> xy;
vll sx, ty;
map<ll, ll> xs;
map<ll, ll> yt;
void insert(ll x, ll y) {
xy.push_back(P(x, y));
}
void build(void) {
xy.pb(P(2ll*INF, 2ll*INF));
n = xy.size();
assert(n < SIZE);
assert(SIZE < (1ll<<BITS));
data = new ll[SIZE];
sx.resize(n), ty.resize(n);
sort(all(xy), [&](P& x, P& y){return x.se < y.se;});
rep(i, n) if (!yt.count(xy[i].se)) {
ll tmp = yt.size();
yt[xy[i].se] = tmp;
ty[tmp] = xy[i].se;
}
sort(all(xy));
rep(i, n) sx[i] = xy[i].fi;
rep(i, n) if (!xs.count(xy[i].fi)) xs[xy[i].fi] = i;
rep(i, n) {
data[i] = yt[xy[i].se];
}
w = wavelet<ll, SIZE, BITS>(n, data);
}
// 左下が(ax, ay), 右上が(bx, by)であるような閉矩形領域内部の点の数
// O(log n)
ll count(ll ax, ll ay, ll bx, ll by) {
if (ax > bx || ay > by) return 0;
// ax以上の最小のs
ll as = xs.lower_bound(ax)->se;
// bx以上の最小のs
ll bs = xs.upper_bound(bx)->se;
// ay以上の最小のt
ll at = yt.lower_bound(ay)->se;
// by以上の最小のt
ll bt = yt.upper_bound(by)->se;
ll ret = w.freq(as, bs, at, bt);
/*
if (ret != countBrutal(ax, ay, bx, by)) {
cout << "HIT " << mt(ax, ay, bx, by) << " "<< mt(as, bs, at, bt) << endl;
cout << "yours : " << ret << " v.s. brutal : " << countBrutal(ax, ay, bx, by)<<endl;
}
*/
return ret;
}
PointCloud2D(void) { }
};
int main(void) {
ll n, m; cin >> n >> m; assert(1<=n&&n<=1e5), assert(1<=m&&m<=2e5);
vll a(m, -1);
map<ll, ll> freq;
rep(i, n) {
ll x, y; cin >> x >> y;
a[x] = i;
a[y] = i;
freq[x]++, freq[y]++;
}
for (auto x : freq) {
assert(x.se <= 1);
}
vll p;
vector<P> pos(n, P(-1, -1));
rep(i, m) if (a[i] != -1) {
if (pos[a[i]].fi < 0)
pos[a[i]].fi = i;
else
pos[a[i]].se = i;
p.pb(a[i]);
}
PointCloud2D pc;
rep(i, n) {
pc.insert(pos[i].fi, pos[i].se);
}
pc.build();
vll ret(n, -1);
rep(i, n) {
ll l = pos[i].fi, r = pos[i].se;
ret[i] =
pc.count(l+1, -INF, r-1, INF)
+ pc.count(-INF, l+1, INF, r-1)
- 2 * pc.count(l+1, l+1, r-1, r-1);
}
cout << accumulate(all(ret), 0ll) / 2ll << endl;
return 0;
}