#650422 (C++17) No.1115 二つの数列 / Two Sequences

提出ソース
結果

問題	No.1115 二つの数列 / Two Sequences
コンテスト
ユーザー	ningenMe
提出日時	2021-04-23 16:27:27
言語	C++17 (gcc 13.3.0 + boost 1.89.0)
結果	AC
実行時間	599 ms / 2,000 ms
コード長	11,401 bytes
記録記録タグの例: 初AC ショートコード純ショートコード純主流ショートコード最速実行時間
コンパイル時間	3,440 ms
コンパイル使用メモリ	237,788 KB
最終ジャッジ日時	2025-01-20 23:18:54
ジャッジサーバーID （参考情報）	judge4 / judge4
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ファイルパターン	結果
sample	AC * 5
other	AC * 35
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ソースコード

raw source code
#include <bits/stdc++.h> 
using namespace std; 
using int128  = __int128_t; 
using int64   = long long; 
using int32   = int; 
using uint128 = __uint128_t; 
using uint64  = unsigned long long; 
using uint32  = unsigned int; 

#define ALL(obj) (obj).begin(),(obj).end() 
template<class T> using priority_queue_reverse = priority_queue<T,vector<T>,greater<T>>; 

constexpr int64 MOD = 1'000'000'000LL + 7; //' 
constexpr int64 MOD2 = 998244353; 
constexpr int64 HIGHINF = 1'000'000'000'000'000'000LL; 
constexpr int64 LOWINF = 1'000'000'000'000'000LL; //' 
constexpr long double PI = 3.1415926535897932384626433L; 

template <class T> vector<T> multivector(size_t N,T init){return vector<T>(N,init);} 
template <class... T> auto multivector(size_t N,T... t){return vector<decltype(multivector(t...))>(N,multivector(t...));} 
template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}} 
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;} 
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} 
template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} 
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;} 
template <class T>ostream &operator<<(ostream &o, const deque<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;} 
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;} 
void print(void) {cout << endl;} 
template <class Head> void print(Head&& head) {cout << head;print();} 
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);} 
template <class T> void chmax(T& a, const T b){a=max(a,b);} 
template <class T> void chmin(T& a, const T b){a=min(a,b);} 
vector<string> split(const string &str, const char delemiter) {vector<string> res;stringstream ss(str);string buffer; while( getline(ss, buffer, delemiter) ) res.push_back(buffer); return res;} 
inline constexpr int msb(int x) {return x?31-__builtin_clz(x):-1;} 
inline constexpr int64 ceil_div(const int64 a,const int64 b) {return (a+(b-1))/b;}// return ceil(a/b) 
void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;} 
void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;} 
void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;} 


/*
 * @title BinaryIndexedTree
 * @docs md/segment/BinaryIndexedTree.md
 */
template<class Operator> class BinaryIndexedTree {
	using TypeNode = typename Operator::TypeNode;
	size_t depth;         
	size_t length;
	size_t num;
	vector<TypeNode> node;
public:
	
	//[0,N) constructed, inplace [0,1) + [1,N+1)
	//you can ignore inplace offset
	BinaryIndexedTree(const size_t num) : num(num) {
		for (depth = 1,length = 1; length < num; depth++,length *= 2);
		node.resize(length+1, Operator::unit_node);
	}
 
	//[idx,idx+1) update 
	void update(size_t idx, TypeNode var) {
		assert(0 <= idx && idx < length);
		for (++idx; idx <= length; idx += idx & -idx) node[idx] = Operator::func_node(node[idx],var);
	}

	//[0,idx) get
	TypeNode get(size_t idx) {
		TypeNode ret = Operator::unit_node;
		for (idx = min(length,idx); idx > 0; idx -= idx & -idx) ret = Operator::func_node(ret,node[idx]);
		return ret;
	}

	//return [0,length]
	int binary_search(TypeNode var) {
		if(!Operator::func_check(node.back(),var)) return num;
		TypeNode ret = Operator::unit_node;
		size_t off = 0;
		for(size_t idx = length; idx; idx >>= 1){
			if(off + idx <= length && !Operator::func_check(Operator::func_node(ret,node[off+idx]),var)) {
				off += idx;
				ret = Operator::func_node(ret,node[off]);
			}
		}
		return min(off,num);
	}

	void print() {
		cout << "{ " << get(1);
		for(int i = 1; i < length; ++i) cout << ", " << get(i+1);
		cout << " }" << endl;
	}
};

template<class T> struct NodePrefixSumPointAdd {
	using TypeNode = T;
	inline static constexpr TypeNode unit_node = 0;
	inline static constexpr TypeNode func_node(const TypeNode& l,const TypeNode& r){return l+r;}
	// Binary Search for first index where func_check is true
	inline static constexpr bool func_check(const TypeNode nodeVal,const TypeNode& val){return val <= nodeVal;}
};

/*
 * @title RangeInversionQuery - 区間転倒数
 * @docs md/segment/RangeModeQuery.md
 */
template<class T> class RangeInversionQuery {
    vector<size_t> compressed;
    vector<long long> prefix_inv;
    vector<long long> suffix_inv;
    vector<vector<size_t>> sqrt_bucket_freq;
    vector<vector<long long>> sqrt_bucket_inv;
    vector<vector<size_t>> sqrt_bucket_sort_index;
    vector<size_t> sqrt_bucket_size;
    size_t N,B;
public:
    RangeInversionQuery(const vector<T>& ar, T pre=-1)
    : compressed(ar.size()),prefix_inv(ar.size()),suffix_inv(ar.size()) {
        N = ar.size();
        B = sqrt(N) + 1;
        //zarts
        {
            vector<pair<T,size_t>> ord(N);
            for(size_t i=0;i<N;++i) ord[i]={ar[i],i};
            sort(ord.begin(),ord.end());
            size_t inc=0;
            for(size_t i=0;i<N;++i) {
                if(pre < ord[i].first) inc++;
                compressed[ord[i].second] = inc;
                pre = ord[i].first;
            }
        }
        //freq
        {
            sqrt_bucket_freq.resize(B);
            vector<size_t> freq(N+1,0);
            for(size_t i=0;i<B;++i) {
                size_t l = i*B, r = min((i+1)*B,N);
                for(size_t j=l;j<r;++j) freq[compressed[j]]++;
                sqrt_bucket_freq[i] = freq;
                for(size_t j=1;j<=N;++j) sqrt_bucket_freq[i][j]+=sqrt_bucket_freq[i][j-1];
            }
        }
        //prefix,suffix inv
        {
            BinaryIndexedTree<NodePrefixSumPointAdd<long long>> bit(N+1);
            for(size_t i=0;i<B;++i) {
                int l = i*B, r = min((i+1)*B,N);
                //prefix
                {
                    long long inv = 0;
                    for(size_t j=l;j<r;++j) {
                        inv += bit.get(N+1)-bit.get(compressed[j]+1);
                        prefix_inv[j]=inv;
                        bit.update(compressed[j],1);
                    }
                    for(size_t j=l;j<r;++j) {
                        bit.update(compressed[j],-1);
                    }
                }
                //suffix
                {
                    long long inv = 0;
                    for(int j=r-1;l<=j;--j) {
                        inv += bit.get(compressed[j]);
                        suffix_inv[j]=inv;
                        bit.update(compressed[j],1);
                    }
                    for(size_t j=l;j<r;++j) {
                        bit.update(compressed[j],-1);
                    }
                }
            }
        }
        //sqrt bucket inv
        {
            sqrt_bucket_inv.resize(B,vector<long long>(B,0));
            for(size_t i=0;i<B;++i) {
                size_t l = i*B, r = min((i+1)*B,N);
                if(l<r) sqrt_bucket_inv[i][i] = prefix_inv[r-1];
            }
            for(size_t k=1;k<B;++k) {
                for(size_t i=0;i+k<B;++i) {
                    sqrt_bucket_inv[i][i+k] += sqrt_bucket_inv[i][i]+sqrt_bucket_inv[i+1][i+k];
                    size_t l = i*B, r = min((i+1)*B,N);
                    for(size_t j=l;j<r;++j) {
                        size_t& c = compressed[j]; 
                        sqrt_bucket_inv[i][i+k] += (sqrt_bucket_freq[i+k][c-1]-sqrt_bucket_freq[i][c-1]);
                    }
                }
            }
        }
        //sort
        {
            sqrt_bucket_sort_index.resize(B);
            sqrt_bucket_size.resize(B,0);
            size_t sz = 0;
            for(size_t i=0;i<B;++i) {
                int l = i*B, r = min((i+1)*B,N);
                sz += max(0,(r-l));
                sqrt_bucket_size[i] = sz;
                if(r-l<1) continue;
                sqrt_bucket_sort_index[i].resize(r-l);
                for(size_t j=l;j<r;++j) sqrt_bucket_sort_index[i][j-l]=j;
                sort(sqrt_bucket_sort_index[i].begin(),sqrt_bucket_sort_index[i].end(),
                [&](size_t l,size_t r){return compressed[l]==compressed[r]?l<r:compressed[l]<compressed[r];});
            }
        }
    }
    //query [l,r)
    //return {freq,mode} ({頻度,元の配列における値}) 
    long long get(int l, int r) {
        int bl = l/B + 1, br = (r-1)/B - 1;
        long long inv = 0;
        //同じbucketにl,rがあるとき
        if(bl > br + 1) {
            inv += prefix_inv[r-1];
            if(l) inv -= prefix_inv[l-1];
            bl = l / B;
            long long sum = 0;
            for(size_t i: sqrt_bucket_sort_index[bl]) {
                if(r <= i) continue;
                if(l <= i) sum++;
                else inv -= sum;
            }
        }
        else {
            if(bl<=br) inv += sqrt_bucket_inv[bl][br];
            inv += suffix_inv[l];
            inv += prefix_inv[r-1];
            size_t ml = bl*B;
            for(size_t i=l;i<ml;++i) {
                size_t& c = compressed[i];
                inv += sqrt_bucket_freq[br][c-1]-sqrt_bucket_freq[bl-1][c-1];
            }
            size_t mr = (br+1)*B;
            for(size_t i=mr;i<r;++i) {
                size_t& c = compressed[i];
                inv += (sqrt_bucket_size[br]-sqrt_bucket_freq[br][c])-(sqrt_bucket_size[bl-1]-sqrt_bucket_freq[bl-1][c]);
            }
            queue<size_t> ql,qr;
            for(size_t i: sqrt_bucket_sort_index[bl-1]) ql.push(i);
            for(size_t i: sqrt_bucket_sort_index[br+1]) qr.push(i);
            long long sum = 0;
            while(ql.size()) {
                auto xl = ql.front();
                if(xl < l) {
                    ql.pop(); 
                    continue;
                }
                if(qr.empty()) {
                    inv += sum;
                    ql.pop();
                    continue;
                }
                auto xr = qr.front();
                if(xr >= r) {
                    qr.pop();
                    continue;
                }
                if(compressed[xl] > compressed[xr]) {
                    sum++;
                    qr.pop();
                    continue;
                }
                else {
                    inv += sum;
                    ql.pop();
                    continue;
                }
            }
        }
        return inv;
    }
}; 

/** 
 * @url  
 * @est 
 */  
int main() { 
    int N; cin >> N;
    vector<int> a(N),b(N),c(N+1);
    for(int i = 0; i < N; ++i) {
        cin >> a[i];
        c[a[i]]=i;
    }	
    for(int i = 0; i < N; ++i) {
        cin >> b[i];
        b[i]=c[b[i]];
    }
    vector<int> idx(N);
    iota(ALL(idx),0);
    sort(ALL(idx),[&](int l,int r){return b[l]<b[r];});
    RangeInversionQuery<int> riq(idx);
    cout << riq.get(0,N) << endl;
    return 0;
}
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結果

ソースコード
