2.2 闲话 & solution - 『听,万物复苏的声音』
一个好的闲话需要一张头图
当然我还有一张
solution - 2024初三年前集训测试2
\(189/400\), \(rk4\) ,还是太菜了,而且没打出来T3T4的暴力
垫底了
赛时
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T1『上海』
天依最开始想了一个奇怪的分解质因数解法,但会T掉😰😰😰
后来发现分解质因数的时候没有到\(\sqrt n\)截止,改完大样例就过了
点击查看代码
#include<bits/stdc++.h> inline void fire(){freopen("a.in","r",stdin);freopen("a.out","w",stdout);} namespace Fast_I {char *_Buf, *_Start_ptr, *_End_ptr;std::streambuf* inbuf;unsigned int Size;bool _Ok;struct Fast_Istream {operator bool(){return _Ok; }Fast_Istream(std::streambuf*, unsigned int);Fast_Istream(unsigned int);Fast_Istream(const char*, unsigned int);Fast_Istream& operator>>(char&);Fast_Istream& operator>>(char*);Fast_Istream& operator>>(bool&);Fast_Istream& operator>>(short&);Fast_Istream& operator>>(int&);Fast_Istream& operator>>(long&);Fast_Istream& operator>>(long long&);Fast_Istream& operator>>(unsigned short&);Fast_Istream& operator>>(unsigned int&);Fast_Istream& operator>>(unsigned long&);Fast_Istream& operator>>(unsigned long long&);Fast_Istream& operator>>(float&);Fast_Istream& operator>>(double&);Fast_Istream& operator>>(long double&);Fast_Istream& operator>>(std::string&);template <typename Typex>void operator()(Typex& _Val) { *this >> _Val; }template <typename Typex, typename... More>void operator()(Typex&, More&...);std::streambuf* rdbuf() { return inbuf; }void rdbuf(std::streambuf* _inbuf) { inbuf = _inbuf; }void rdbuf(const char*);void pop();char peek();};} namespace Fast_O {std::string buf;std::streambuf* outbuf;struct Fast_Ostream {Fast_Ostream(std::streambuf*, unsigned int);Fast_Ostream(std::streambuf* out) { outbuf = out; }Fast_Ostream(const char*, unsigned int);Fast_Ostream(unsigned int);void flush();~Fast_Ostream();void endl() { buf.push_back('\n'); }template <typename Typex>void endl(const Typex& _Val);template <typename Typex, typename... More>void endl(const Typex&, const More&...);template <typename Typex>void operator()(const Typex& _Val);template <typename Typex, typename... More>void operator()(const Typex&, const More&...);Fast_Ostream& operator<<(char);Fast_Ostream& operator<<(const char*);Fast_Ostream& operator<<(const std::string&);Fast_Ostream& operator<<(bool);Fast_Ostream& operator<<(short);Fast_Ostream& operator<<(int);Fast_Ostream& operator<<(long);Fast_Ostream& operator<<(long long);Fast_Ostream& operator<<(unsigned short);Fast_Ostream& operator<<(unsigned int);Fast_Ostream& operator<<(unsigned long);Fast_Ostream& operator<<(unsigned long long);std::streambuf* rdbuf() { return outbuf; }void rdbuf(std::streambuf* _outbuf) { outbuf = _outbuf; }void rdbuf(const char*);};} namespace Fast_IO {Fast_I::Fast_Istream fin(std::cin.rdbuf(), 1048576);Fast_O::Fast_Ostream fout(std::cout.rdbuf()); } #define cin Fast_IO::fin #define cout Fast_IO::fout namespace Fast_I {Fast_Istream::Fast_Istream(std::streambuf* in, unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;inbuf = in;_Start_ptr = _End_ptr = _Buf = new char[Sz];}Fast_Istream::Fast_Istream(const char* in, unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;rdbuf(in);_Start_ptr = _End_ptr = _Buf = new char[Sz];}Fast_Istream::Fast_Istream(unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;_Start_ptr = _End_ptr = _Buf = new char[Sz];}void Fast_Istream::rdbuf(const char* File) {static std::ifstream __In__(File);rdbuf(__In__.rdbuf());}void Get_Char(char& _Val) {if (_Start_ptr == _End_ptr) {_Start_ptr = _Buf;_End_ptr = _Buf + inbuf->sgetn(_Buf, Size);}if (_Start_ptr == _End_ptr) {_Val = -1;_Ok = 0;} else {_Val = *_Start_ptr++;}}Fast_Istream& Fast_Istream::operator>>(char& _Val) {if(_Ok){Get_Char(_Val);while (_Val == 32 || _Val == 10 || _Val == 13 || _Val == 8 || _Val == 9 || _Val == 7 || _Val == 12 || _Val == 11) {Get_Char(_Val);}}return *this;}Fast_Istream& Fast_Istream::operator>>(char* _Val) {if (_Ok) {Get_Char(*_Val);while (*_Val == 32 || *_Val == 10 || *_Val == 13 || *_Val == 8 ||*_Val == 9 || *_Val == 7 || *_Val == 12 || *_Val == 11) {Get_Char(*_Val);}while (*_Val != 32 && *_Val != 10 && *_Val && *_Val != -1 && *_Val != 9 &&*_Val != 11 && *_Val != 12) {Get_Char(*++_Val);}*_Val = 0;--_Start_ptr;}return *this;}Fast_Istream& Fast_Istream::operator>>(std::string& _Val) {if (_Ok) {char c;Get_Char(c);while (c == 32 || c == 10 || c == 13 || c == 8 || c == 9 || c == 7 ||c == 12 || c == 11) {Get_Char(c);}for (_Val.clear();c != 32 && c != 10 && c && c != -1 && c != 9 && c != 11 && c != 12;Get_Char(c)) {_Val.push_back(c);}--_Start_ptr;}return *this;}template <typename Typex>void Get_Int(Typex& _Val) {if (_Ok) {char ch;bool _F = 0;for (Get_Char(ch); (ch < 48 || ch > 57) && ch != -1; Get_Char(ch)) {_F = ch == 45;}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}if (_F) {_Val = ~_Val + 1;}--_Start_ptr;}}template <typename Typex>void Get_Unsigned(Typex& _Val) {if (_Ok) {char ch;Get_Char(ch);while ((ch < 48 || ch > 57) && ch != -1) {Get_Char(ch);}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}--_Start_ptr;}}template <typename Typex>void Get_Double(Typex& _Val) {if(_Ok){char ch;bool _F = 0;for (Get_Char(ch); (ch < 48 || ch > 57) && ch != -1; Get_Char(ch)) {_F = ch == 45;}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}if (ch == 46) {unsigned long long _Pow = 1;for (Get_Char(ch); ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val += Typex((ch ^ 48) * 1.0 / (_Pow *= 10));}}if (_F) {_Val = -_Val;}--_Start_ptr;}}Fast_Istream& Fast_Istream::operator>>(bool& _Val) {if(_Ok){char ch;Get_Char(ch);while (ch == 32 || ch == 10 || ch == 13 || ch == 8 || ch == 9 || ch == 7 ||ch == 12 || ch == 11) {Get_Char(ch);}while (ch != 32 && ch != 10 && ch && ch != -1 && ch != 9 && ch != 11 &&ch != 12) {_Val |= ch != 48;Get_Char(ch);}--_Start_ptr;}return *this;}Fast_Istream& Fast_Istream::operator>>(short& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(int& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long long& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned short& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned int& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned long& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned long long& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(float& _Val) {Get_Double(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(double& _Val) {Get_Double(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long double& _Val) {Get_Double(_Val);return *this;}template <typename Typex, typename... More>void Fast_Istream::operator()(Typex& _Val, More&... _More) {*this >> _Val;operator()(_More...);}void Fast_Istream::pop() {char ch;Get_Char(ch);}char Fast_Istream::peek() {if (_Start_ptr == _End_ptr) {_Start_ptr = _Buf;_End_ptr = _Buf + inbuf->sgetn(_Buf, Size);}if (_Start_ptr == _End_ptr) {_Ok = 0;return -1;} else {return *_Start_ptr;}}} namespace Fast_O {Fast_Ostream::Fast_Ostream(std::streambuf* out, unsigned int Size) {buf.reserve(Size);outbuf = out;}Fast_Ostream::Fast_Ostream(const char* File, unsigned int Size) {buf.reserve(Size);rdbuf(File);}void Fast_Ostream::rdbuf(const char* File) {static std::ofstream __Out__(File);rdbuf(__Out__.rdbuf());}Fast_Ostream::Fast_Ostream(unsigned int Size) {buf.reserve(Size);}void Fast_Ostream::flush() {outbuf->sputn(buf.data(), buf.size());buf.clear();}Fast_Ostream::~Fast_Ostream() {flush();}Fast_Ostream& Fast_Ostream::operator<<(char _Val) {buf.push_back(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(const char* _Val) {while (*_Val) {buf.push_back(*_Val++);}return *this;}Fast_Ostream& Fast_Ostream::operator<<(const std::string& _Val) {for (auto&& i : _Val) {buf.push_back(i);}return *this;}template <typename Typex>void Put_Unsigned(Typex _Val) {char* _Stack = (char*)malloc(sizeof(Typex) * 3);unsigned S_top = 0;while (_Val) {_Stack[++S_top] = (_Val % 10) ^ 48;_Val /= 10;}if (!S_top) {buf.push_back('0');}while (S_top) {buf.push_back(_Stack[S_top--]);}free(_Stack);}void Put_Int(long long _Val) {if (_Val < 0) {buf.push_back('-');Put_Unsigned(~_Val + 1);} else {Put_Unsigned(_Val);}}Fast_Ostream& Fast_Ostream::operator<<(bool _Val) {buf.push_back(_Val ? '1' : '0');return *this;}Fast_Ostream& Fast_Ostream::operator<<(short _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(int _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(long _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(long long _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned short _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned int _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned long _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned long long _Val) {Put_Unsigned(_Val);return *this;}template <typename Typex>void Fast_Ostream::endl(const Typex& _Val) {*this << _Val << '\n';}template <typename Typex, typename... More>void Fast_Ostream::endl(const Typex& _Val, const More&... _More) {*this << _Val;endl(_More...);}template <typename Typex>void Fast_Ostream::operator()(const Typex& _Val) {*this << _Val;}template <typename Typex, typename... More>void Fast_Ostream::operator()(const Typex& _Val, const More&... _More) {*this << _Val;operator()(_More...);}} #define ull unsigned long long #define int long long #define INF (0x66ccff0712ll) #define N (0x66ccff) #define M (0x6cf) #define MAXN (1e6+5) #define MAXM (1e5+5) #define lc (q<<1) #define rc (q<<1|1) #define cerr std::cerr #define sort std::stable_sort #define re register #define lower_bound std::lower_bound #define upper_bound std::upper_bound #define unique std::unique #define string std::string #define pair std::pair #define vector std::vector #define map std::map #define set std::set #define queue std::queue #define make_pair std::make_pair #define priority_queue std::priority_queue #define bitset std::bitset #define deque std::deque #define array std::array #define unordered_set std::unordered_set #define unordered_map std::unordered_map #define list std::list #define it map<int,int>::iterator #define min(a,b) (a)>(b)?(b):(a) #define max(a,b) (a)<(b)?(b):(a) #define PII pair<int,int> #define swap std::swap PII a[N];int tot; signed main(){ fire(); int k,n;cin(k); n=k; for(int i=2;i<=sqrt(n);i++){ if((k%i==0)){ ++tot; a[tot].second=i; while(k%i==0){ a[tot].first++; k/=i; } } if(k==1) break; } if(tot==0){ cout(-1,"\n"); } else{ int ans=1; for(int i=1;i<=tot;i++) for(int j=1;j<=(a[i].first+1)/2;j++) ans*=a[i].second; if(ans==n) cout<<-1; else cout(ans); } }
期望得分:\(100 pts\)
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T2『华二』
还是分解质因数,观察题目发现只有\(\{1 \sim 9\}\)
从\(\{1,2,3,4,5,6,7,8,9\}\)中一一分解,发现有且只有\(6\)能分解成两个质因数\(\{2,3\}\)
并且\(1,5,7\)可以放到任何位置(质数同时没有其倍数),后面再考虑
剩下的\(\{2,3,4,8,9\}\)和\(6\)的\(\gcd\)都不为\(1\),所以\(6\)不会交换出去
剩下的显而易见了吧\(\{2,4,8\}\)之间互不能交换,\(\{3,9\}\)之间互不能交换
其组合数是\(\dbinom{x}{x+y}\),其中\(x\)是\(2,4,8\)的个数,\(y\)是\(3,9\)的个数
最后的\(1,5,7\)直接插板法了
点击查看代码
#include<bits/stdc++.h> inline void fire(){freopen("b.in","r",stdin);freopen("b.out","w",stdout);} namespace Fast_I {char *_Buf, *_Start_ptr, *_End_ptr;std::streambuf* inbuf;unsigned int Size;bool _Ok;struct Fast_Istream {operator bool(){return _Ok; }Fast_Istream(std::streambuf*, unsigned int);Fast_Istream(unsigned int);Fast_Istream(const char*, unsigned int);Fast_Istream& operator>>(char&);Fast_Istream& operator>>(char*);Fast_Istream& operator>>(bool&);Fast_Istream& operator>>(short&);Fast_Istream& operator>>(int&);Fast_Istream& operator>>(long&);Fast_Istream& operator>>(long long&);Fast_Istream& operator>>(unsigned short&);Fast_Istream& operator>>(unsigned int&);Fast_Istream& operator>>(unsigned long&);Fast_Istream& operator>>(unsigned long long&);Fast_Istream& operator>>(float&);Fast_Istream& operator>>(double&);Fast_Istream& operator>>(long double&);Fast_Istream& operator>>(std::string&);template <typename Typex>void operator()(Typex& _Val) { *this >> _Val; }template <typename Typex, typename... More>void operator()(Typex&, More&...);std::streambuf* rdbuf() { return inbuf; }void rdbuf(std::streambuf* _inbuf) { inbuf = _inbuf; }void rdbuf(const char*);void pop();char peek();};} namespace Fast_O {std::string buf;std::streambuf* outbuf;struct Fast_Ostream {Fast_Ostream(std::streambuf*, unsigned int);Fast_Ostream(std::streambuf* out) { outbuf = out; }Fast_Ostream(const char*, unsigned int);Fast_Ostream(unsigned int);void flush();~Fast_Ostream();void endl() { buf.push_back('\n'); }template <typename Typex>void endl(const Typex& _Val);template <typename Typex, typename... More>void endl(const Typex&, const More&...);template <typename Typex>void operator()(const Typex& _Val);template <typename Typex, typename... More>void operator()(const Typex&, const More&...);Fast_Ostream& operator<<(char);Fast_Ostream& operator<<(const char*);Fast_Ostream& operator<<(const std::string&);Fast_Ostream& operator<<(bool);Fast_Ostream& operator<<(short);Fast_Ostream& operator<<(int);Fast_Ostream& operator<<(long);Fast_Ostream& operator<<(long long);Fast_Ostream& operator<<(unsigned short);Fast_Ostream& operator<<(unsigned int);Fast_Ostream& operator<<(unsigned long);Fast_Ostream& operator<<(unsigned long long);std::streambuf* rdbuf() { return outbuf; }void rdbuf(std::streambuf* _outbuf) { outbuf = _outbuf; }void rdbuf(const char*);};} namespace Fast_IO {Fast_I::Fast_Istream fin(std::cin.rdbuf(), 1048576);Fast_O::Fast_Ostream fout(std::cout.rdbuf()); } #define cin Fast_IO::fin #define cout Fast_IO::fout namespace Fast_I {Fast_Istream::Fast_Istream(std::streambuf* in, unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;inbuf = in;_Start_ptr = _End_ptr = _Buf = new char[Sz];}Fast_Istream::Fast_Istream(const char* in, unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;rdbuf(in);_Start_ptr = _End_ptr = _Buf = new char[Sz];}Fast_Istream::Fast_Istream(unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;_Start_ptr = _End_ptr = _Buf = new char[Sz];}void Fast_Istream::rdbuf(const char* File) {static std::ifstream __In__(File);rdbuf(__In__.rdbuf());}void Get_Char(char& _Val) {if (_Start_ptr == _End_ptr) {_Start_ptr = _Buf;_End_ptr = _Buf + inbuf->sgetn(_Buf, Size);}if (_Start_ptr == _End_ptr) {_Val = -1;_Ok = 0;} else {_Val = *_Start_ptr++;}}Fast_Istream& Fast_Istream::operator>>(char& _Val) {if(_Ok){Get_Char(_Val);while (_Val == 32 || _Val == 10 || _Val == 13 || _Val == 8 || _Val == 9 || _Val == 7 || _Val == 12 || _Val == 11) {Get_Char(_Val);}}return *this;}Fast_Istream& Fast_Istream::operator>>(char* _Val) {if (_Ok) {Get_Char(*_Val);while (*_Val == 32 || *_Val == 10 || *_Val == 13 || *_Val == 8 ||*_Val == 9 || *_Val == 7 || *_Val == 12 || *_Val == 11) {Get_Char(*_Val);}while (*_Val != 32 && *_Val != 10 && *_Val && *_Val != -1 && *_Val != 9 &&*_Val != 11 && *_Val != 12) {Get_Char(*++_Val);}*_Val = 0;--_Start_ptr;}return *this;}Fast_Istream& Fast_Istream::operator>>(std::string& _Val) {if (_Ok) {char c;Get_Char(c);while (c == 32 || c == 10 || c == 13 || c == 8 || c == 9 || c == 7 ||c == 12 || c == 11) {Get_Char(c);}for (_Val.clear();c != 32 && c != 10 && c && c != -1 && c != 9 && c != 11 && c != 12;Get_Char(c)) {_Val.push_back(c);}--_Start_ptr;}return *this;}template <typename Typex>void Get_Int(Typex& _Val) {if (_Ok) {char ch;bool _F = 0;for (Get_Char(ch); (ch < 48 || ch > 57) && ch != -1; Get_Char(ch)) {_F = ch == 45;}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}if (_F) {_Val = ~_Val + 1;}--_Start_ptr;}}template <typename Typex>void Get_Unsigned(Typex& _Val) {if (_Ok) {char ch;Get_Char(ch);while ((ch < 48 || ch > 57) && ch != -1) {Get_Char(ch);}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}--_Start_ptr;}}template <typename Typex>void Get_Double(Typex& _Val) {if(_Ok){char ch;bool _F = 0;for (Get_Char(ch); (ch < 48 || ch > 57) && ch != -1; Get_Char(ch)) {_F = ch == 45;}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}if (ch == 46) {unsigned long long _Pow = 1;for (Get_Char(ch); ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val += Typex((ch ^ 48) * 1.0 / (_Pow *= 10));}}if (_F) {_Val = -_Val;}--_Start_ptr;}}Fast_Istream& Fast_Istream::operator>>(bool& _Val) {if(_Ok){char ch;Get_Char(ch);while (ch == 32 || ch == 10 || ch == 13 || ch == 8 || ch == 9 || ch == 7 ||ch == 12 || ch == 11) {Get_Char(ch);}while (ch != 32 && ch != 10 && ch && ch != -1 && ch != 9 && ch != 11 &&ch != 12) {_Val |= ch != 48;Get_Char(ch);}--_Start_ptr;}return *this;}Fast_Istream& Fast_Istream::operator>>(short& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(int& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long long& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned short& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned int& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned long& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned long long& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(float& _Val) {Get_Double(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(double& _Val) {Get_Double(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long double& _Val) {Get_Double(_Val);return *this;}template <typename Typex, typename... More>void Fast_Istream::operator()(Typex& _Val, More&... _More) {*this >> _Val;operator()(_More...);}void Fast_Istream::pop() {char ch;Get_Char(ch);}char Fast_Istream::peek() {if (_Start_ptr == _End_ptr) {_Start_ptr = _Buf;_End_ptr = _Buf + inbuf->sgetn(_Buf, Size);}if (_Start_ptr == _End_ptr) {_Ok = 0;return -1;} else {return *_Start_ptr;}}} namespace Fast_O {Fast_Ostream::Fast_Ostream(std::streambuf* out, unsigned int Size) {buf.reserve(Size);outbuf = out;}Fast_Ostream::Fast_Ostream(const char* File, unsigned int Size) {buf.reserve(Size);rdbuf(File);}void Fast_Ostream::rdbuf(const char* File) {static std::ofstream __Out__(File);rdbuf(__Out__.rdbuf());}Fast_Ostream::Fast_Ostream(unsigned int Size) {buf.reserve(Size);}void Fast_Ostream::flush() {outbuf->sputn(buf.data(), buf.size());buf.clear();}Fast_Ostream::~Fast_Ostream() {flush();}Fast_Ostream& Fast_Ostream::operator<<(char _Val) {buf.push_back(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(const char* _Val) {while (*_Val) {buf.push_back(*_Val++);}return *this;}Fast_Ostream& Fast_Ostream::operator<<(const std::string& _Val) {for (auto&& i : _Val) {buf.push_back(i);}return *this;}template <typename Typex>void Put_Unsigned(Typex _Val) {char* _Stack = (char*)malloc(sizeof(Typex) * 3);unsigned S_top = 0;while (_Val) {_Stack[++S_top] = (_Val % 10) ^ 48;_Val /= 10;}if (!S_top) {buf.push_back('0');}while (S_top) {buf.push_back(_Stack[S_top--]);}free(_Stack);}void Put_Int(long long _Val) {if (_Val < 0) {buf.push_back('-');Put_Unsigned(~_Val + 1);} else {Put_Unsigned(_Val);}}Fast_Ostream& Fast_Ostream::operator<<(bool _Val) {buf.push_back(_Val ? '1' : '0');return *this;}Fast_Ostream& Fast_Ostream::operator<<(short _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(int _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(long _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(long long _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned short _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned int _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned long _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned long long _Val) {Put_Unsigned(_Val);return *this;}template <typename Typex>void Fast_Ostream::endl(const Typex& _Val) {*this << _Val << '\n';}template <typename Typex, typename... More>void Fast_Ostream::endl(const Typex& _Val, const More&... _More) {*this << _Val;endl(_More...);}template <typename Typex>void Fast_Ostream::operator()(const Typex& _Val) {*this << _Val;}template <typename Typex, typename... More>void Fast_Ostream::operator()(const Typex& _Val, const More&... _More) {*this << _Val;operator()(_More...);}} #define ull unsigned long long #define int long long #define INF (0x66ccff0712ll) #define N (0x66ccff) #define M (0x6cf) #define MAXN (1e6+5) #define MAXM (1e5+5) #define lc (q<<1) #define rc (q<<1|1) #define cerr std::cerr #define sort std::stable_sort #define re register #define lower_bound std::lower_bound #define upper_bound std::upper_bound #define unique std::unique #define string std::string #define pair std::pair #define vector std::vector #define map std::map #define set std::set #define queue std::queue #define make_pair std::make_pair #define priority_queue std::priority_queue #define bitset std::bitset #define deque std::deque #define array std::array #define unordered_set std::unordered_set #define unordered_map std::unordered_map #define list std::list #define it map<int,int>::iterator #define min(a,b) (a)>(b)?(b):(a) #define max(a,b) (a)<(b)?(b):(a) #define PII pair<int,int> #define swap std::swap #define gcd std::__gcd #define lcm(a,b) ((a*b)/gcd(a,b)) const int MOD=998244353; int n,a[N],tot[N]; int ans=1,fac[N],inv[N]; inline int qpow(int a,int b){ int ans=1; while(b){ if(b&1) ans=ans*a%MOD; a=a*a%MOD,b>>=1; } return ans; } inline int Comb(int n,int m){ if(n<m) return 0; return fac[n]*inv[m]%MOD*inv[n-m]%MOD; } signed main(){ fire(); cin(n); fac[0]=1; for(int i=1;i<=n;++i) fac[i]=fac[i-1]*i%MOD; inv[n]=qpow(fac[n],MOD-2); for(int i=n-1;i>=0;--i) inv[i]=inv[i+1]*(i+1)%MOD; for(int i=1;i<=n;i++) cin(a[i]); for(int i=1;i<=n;++i){ if(a[i]==2)tot[1]++; if(a[i]==4)tot[1]++; if(a[i]==8)tot[1]++; if(a[i]==3)tot[2]++; if(a[i]==9)tot[2]++; if(a[i]==1)tot[3]++; if(a[i]==5)tot[4]++; if(a[i]==7)tot[5]++; if(a[i]==6||(i==n)){ ans=ans*Comb(tot[1]+tot[2],tot[1])%MOD; tot[1]=tot[2]=0; } } cout(ans*Comb(n-tot[4]-tot[5],tot[3])%MOD*Comb(n-tot[5],tot[4])%MOD*Comb(n,tot[5])%MOD,'\n'); }
期望得分:\(100pts\)
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T3『高爸』
你好,我非常喜欢暴力数据结构,所以我使用了分块
你好,我分块打假了,\(0pts\)
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T4『金牌』
天依是奔着 \(50pts\) 去打的,想到一半然后突然发现只有\(20\)分,原地破防了,再次仔细思考之后发现\(20\)分都没有\((┭┮﹏┭┮)\)
思路大概就是树剖,然后快速幂暴力维护
首先求出树上这两点之间的距离,然后在两侧枚举其子树
这样可以\(O(n^3 \log^2 n)\),发现 \(20pts\) 都没有,更破防了
想了一下可能要分类讨论
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\(x\)和\(y\)中有一个是另一个的
LCA
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\(x\)和\(y\)没太大关系
但是没想出来怎么讨论\(\text{T_T}\),所以\(0pts\)
HS_xh的奇妙树剖赛时只关了同步流导致没过UU的数据,赛后用Fastio就A掉了这道题\(Σ(ŎдŎ|||)ノノ\)
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赛后改题
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T1『上海』
分解质因数不彻底被Hack掉11分,实际得分89pts
最后需要乘上分解后的\(k\)
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T2『华二』
这题A了
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T3『高爸』
赛时完全没向值域线段树上面想,思路是分块+二分,复杂度过不去
还能用平衡树做...这个有点抽象的,不过仔细想想确实,我为啥考场想不到啊...哎呀我恼了
讲的是权值线段树写法,看起来很简单,考场都没想到
似乎有比较好的解法
每新加一条龙进去新的决策只会在排序后上只龙左右移动一条
移动决策的代价只和左右有多少只龙乘上对应的 \(a\) 或 \(b\) 有关
点击查看代码
#include<bits/stdc++.h> inline void fire(){freopen("c.in","r",stdin);freopen("c.out","w",stdout);} namespace Fast_I {char *_Buf, *_Start_ptr, *_End_ptr;std::streambuf* inbuf;unsigned int Size;bool _Ok;struct Fast_Istream {operator bool(){return _Ok; }Fast_Istream(std::streambuf*, unsigned int);Fast_Istream(unsigned int);Fast_Istream(const char*, unsigned int);Fast_Istream& operator>>(char&);Fast_Istream& operator>>(char*);Fast_Istream& operator>>(bool&);Fast_Istream& operator>>(short&);Fast_Istream& operator>>(int&);Fast_Istream& operator>>(long&);Fast_Istream& operator>>(long long&);Fast_Istream& operator>>(unsigned short&);Fast_Istream& operator>>(unsigned int&);Fast_Istream& operator>>(unsigned long&);Fast_Istream& operator>>(unsigned long long&);Fast_Istream& operator>>(float&);Fast_Istream& operator>>(double&);Fast_Istream& operator>>(long double&);Fast_Istream& operator>>(std::string&);template <typename Typex>void operator()(Typex& _Val) { *this >> _Val; }template <typename Typex, typename... More>void operator()(Typex&, More&...);std::streambuf* rdbuf() { return inbuf; }void rdbuf(std::streambuf* _inbuf) { inbuf = _inbuf; }void rdbuf(const char*);void pop();char peek();};} namespace Fast_O {std::string buf;std::streambuf* outbuf;struct Fast_Ostream {Fast_Ostream(std::streambuf*, unsigned int);Fast_Ostream(std::streambuf* out) { outbuf = out; }Fast_Ostream(const char*, unsigned int);Fast_Ostream(unsigned int);void flush();~Fast_Ostream();void endl() { buf.push_back('\n'); }template <typename Typex>void endl(const Typex& _Val);template <typename Typex, typename... More>void endl(const Typex&, const More&...);template <typename Typex>void operator()(const Typex& _Val);template <typename Typex, typename... More>void operator()(const Typex&, const More&...);Fast_Ostream& operator<<(char);Fast_Ostream& operator<<(const char*);Fast_Ostream& operator<<(const std::string&);Fast_Ostream& operator<<(bool);Fast_Ostream& operator<<(short);Fast_Ostream& operator<<(int);Fast_Ostream& operator<<(long);Fast_Ostream& operator<<(long long);Fast_Ostream& operator<<(unsigned short);Fast_Ostream& operator<<(unsigned int);Fast_Ostream& operator<<(unsigned long);Fast_Ostream& operator<<(unsigned long long);std::streambuf* rdbuf() { return outbuf; }void rdbuf(std::streambuf* _outbuf) { outbuf = _outbuf; }void rdbuf(const char*);};} namespace Fast_IO {Fast_I::Fast_Istream fin(std::cin.rdbuf(), 1048576);Fast_O::Fast_Ostream fout(std::cout.rdbuf()); } #define cin Fast_IO::fin #define cout Fast_IO::fout namespace Fast_I {Fast_Istream::Fast_Istream(std::streambuf* in, unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;inbuf = in;_Start_ptr = _End_ptr = _Buf = new char[Sz];}Fast_Istream::Fast_Istream(const char* in, unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;rdbuf(in);_Start_ptr = _End_ptr = _Buf = new char[Sz];}Fast_Istream::Fast_Istream(unsigned int Sz) {_Ok = 1;Fast_I::Size = Sz;_Start_ptr = _End_ptr = _Buf = new char[Sz];}void Fast_Istream::rdbuf(const char* File) {static std::ifstream __In__(File);rdbuf(__In__.rdbuf());}void Get_Char(char& _Val) {if (_Start_ptr == _End_ptr) {_Start_ptr = _Buf;_End_ptr = _Buf + inbuf->sgetn(_Buf, Size);}if (_Start_ptr == _End_ptr) {_Val = -1;_Ok = 0;} else {_Val = *_Start_ptr++;}}Fast_Istream& Fast_Istream::operator>>(char& _Val) {if(_Ok){Get_Char(_Val);while (_Val == 32 || _Val == 10 || _Val == 13 || _Val == 8 || _Val == 9 || _Val == 7 || _Val == 12 || _Val == 11) {Get_Char(_Val);}}return *this;}Fast_Istream& Fast_Istream::operator>>(char* _Val) {if (_Ok) {Get_Char(*_Val);while (*_Val == 32 || *_Val == 10 || *_Val == 13 || *_Val == 8 ||*_Val == 9 || *_Val == 7 || *_Val == 12 || *_Val == 11) {Get_Char(*_Val);}while (*_Val != 32 && *_Val != 10 && *_Val && *_Val != -1 && *_Val != 9 &&*_Val != 11 && *_Val != 12) {Get_Char(*++_Val);}*_Val = 0;--_Start_ptr;}return *this;}Fast_Istream& Fast_Istream::operator>>(std::string& _Val) {if (_Ok) {char c;Get_Char(c);while (c == 32 || c == 10 || c == 13 || c == 8 || c == 9 || c == 7 ||c == 12 || c == 11) {Get_Char(c);}for (_Val.clear();c != 32 && c != 10 && c && c != -1 && c != 9 && c != 11 && c != 12;Get_Char(c)) {_Val.push_back(c);}--_Start_ptr;}return *this;}template <typename Typex>void Get_Int(Typex& _Val) {if (_Ok) {char ch;bool _F = 0;for (Get_Char(ch); (ch < 48 || ch > 57) && ch != -1; Get_Char(ch)) {_F = ch == 45;}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}if (_F) {_Val = ~_Val + 1;}--_Start_ptr;}}template <typename Typex>void Get_Unsigned(Typex& _Val) {if (_Ok) {char ch;Get_Char(ch);while ((ch < 48 || ch > 57) && ch != -1) {Get_Char(ch);}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}--_Start_ptr;}}template <typename Typex>void Get_Double(Typex& _Val) {if(_Ok){char ch;bool _F = 0;for (Get_Char(ch); (ch < 48 || ch > 57) && ch != -1; Get_Char(ch)) {_F = ch == 45;}for (_Val = 0; ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val = _Val * 10 + (ch ^ 48);}if (ch == 46) {unsigned long long _Pow = 1;for (Get_Char(ch); ch > 47 && ch < 58 && ch != -1; Get_Char(ch)) {_Val += Typex((ch ^ 48) * 1.0 / (_Pow *= 10));}}if (_F) {_Val = -_Val;}--_Start_ptr;}}Fast_Istream& Fast_Istream::operator>>(bool& _Val) {if(_Ok){char ch;Get_Char(ch);while (ch == 32 || ch == 10 || ch == 13 || ch == 8 || ch == 9 || ch == 7 ||ch == 12 || ch == 11) {Get_Char(ch);}while (ch != 32 && ch != 10 && ch && ch != -1 && ch != 9 && ch != 11 &&ch != 12) {_Val |= ch != 48;Get_Char(ch);}--_Start_ptr;}return *this;}Fast_Istream& Fast_Istream::operator>>(short& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(int& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long long& _Val) {Get_Int(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned short& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned int& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned long& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(unsigned long long& _Val) {Get_Unsigned(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(float& _Val) {Get_Double(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(double& _Val) {Get_Double(_Val);return *this;}Fast_Istream& Fast_Istream::operator>>(long double& _Val) {Get_Double(_Val);return *this;}template <typename Typex, typename... More>void Fast_Istream::operator()(Typex& _Val, More&... _More) {*this >> _Val;operator()(_More...);}void Fast_Istream::pop() {char ch;Get_Char(ch);}char Fast_Istream::peek() {if (_Start_ptr == _End_ptr) {_Start_ptr = _Buf;_End_ptr = _Buf + inbuf->sgetn(_Buf, Size);}if (_Start_ptr == _End_ptr) {_Ok = 0;return -1;} else {return *_Start_ptr;}}} namespace Fast_O {Fast_Ostream::Fast_Ostream(std::streambuf* out, unsigned int Size) {buf.reserve(Size);outbuf = out;}Fast_Ostream::Fast_Ostream(const char* File, unsigned int Size) {buf.reserve(Size);rdbuf(File);}void Fast_Ostream::rdbuf(const char* File) {static std::ofstream __Out__(File);rdbuf(__Out__.rdbuf());}Fast_Ostream::Fast_Ostream(unsigned int Size) {buf.reserve(Size);}void Fast_Ostream::flush() {outbuf->sputn(buf.data(), buf.size());buf.clear();}Fast_Ostream::~Fast_Ostream() {flush();}Fast_Ostream& Fast_Ostream::operator<<(char _Val) {buf.push_back(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(const char* _Val) {while (*_Val) {buf.push_back(*_Val++);}return *this;}Fast_Ostream& Fast_Ostream::operator<<(const std::string& _Val) {for (auto&& i : _Val) {buf.push_back(i);}return *this;}template <typename Typex>void Put_Unsigned(Typex _Val) {char* _Stack = (char*)malloc(sizeof(Typex) * 3);unsigned S_top = 0;while (_Val) {_Stack[++S_top] = (_Val % 10) ^ 48;_Val /= 10;}if (!S_top) {buf.push_back('0');}while (S_top) {buf.push_back(_Stack[S_top--]);}free(_Stack);}void Put_Int(long long _Val) {if (_Val < 0) {buf.push_back('-');Put_Unsigned(~_Val + 1);} else {Put_Unsigned(_Val);}}Fast_Ostream& Fast_Ostream::operator<<(bool _Val) {buf.push_back(_Val ? '1' : '0');return *this;}Fast_Ostream& Fast_Ostream::operator<<(short _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(int _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(long _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(long long _Val) {Put_Int(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned short _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned int _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned long _Val) {Put_Unsigned(_Val);return *this;}Fast_Ostream& Fast_Ostream::operator<<(unsigned long long _Val) {Put_Unsigned(_Val);return *this;}template <typename Typex>void Fast_Ostream::endl(const Typex& _Val) {*this << _Val << '\n';}template <typename Typex, typename... More>void Fast_Ostream::endl(const Typex& _Val, const More&... _More) {*this << _Val;endl(_More...);}template <typename Typex>void Fast_Ostream::operator()(const Typex& _Val) {*this << _Val;}template <typename Typex, typename... More>void Fast_Ostream::operator()(const Typex& _Val, const More&... _More) {*this << _Val;operator()(_More...);}} #define qwq Vsinger_LuoTianYi #define ull unsigned long long #define int long long #define INF (0x66ccff0712ll) #define N (0x66ccff) #define M (0x6cf) #define MAXN (1e6+5) #define MAXM (1e5+5) #define lc ls(q) #define rc rs(q) #define mid ((l+r)>>1) #define cerr std::cerr #define sort std::stable_sort #define re register #define lower_bound std::lower_bound #define upper_bound std::upper_bound #define unique std::unique #define string std::string #define pair std::pair #define vector std::vector #define map std::map #define set std::set #define queue std::queue #define make_pair std::make_pair #define priority_queue std::priority_queue #define bitset std::bitset #define deque std::deque #define array std::array #define unordered_set std::unordered_set #define unordered_map std::unordered_map #define list std::list #define it map<int,int>::iterator #define min(a,b) (a)>(b)?(b):(a) #define max(a,b) (a)<(b)?(b):(a) #define PII pair<int,int> #define swap std::swap int tot; int n,a,b,cnt=1; int suma,sumb,cnta,cntb; struct tree{ int sum,cnt,ls,rs; }t[N<<2]; inline int ls(int q){ if(!t[q].ls) t[q].ls=++cnt; return t[q].ls; } inline int rs(int q){ if(!t[q].rs) t[q].rs=++cnt; return t[q].rs; } inline void change(int l,int r,int q,int x){ if(l==r){ t[q].sum+=x,t[q].cnt++; return; } if(x<=mid) change(l,mid,lc,x); else change(mid+1,r,rc,x); t[q].sum=t[t[q].ls].sum+t[t[q].rs].sum; t[q].cnt=t[t[q].ls].cnt+t[t[q].rs].cnt; } inline int qwq(int x){ return (cnta*x-suma)*a+(sumb-cntb*x)*b; } inline void ask(int l,int r,int q){ if(l==r){ suma+=t[q].sum; cnta+=t[q].cnt; cout(qwq(l),'\n'); return; } suma+=t[t[q].ls].sum; sumb+=t[t[q].rs].sum; cnta+=t[t[q].ls].cnt; cntb+=t[t[q].rs].cnt; if(qwq(mid)<qwq(mid+1)){ suma-=t[t[q].ls].sum, cnta-=t[t[q].ls].cnt; ask(l,mid,lc); return; } else{ sumb-=t[t[q].rs].sum, cntb-=t[t[q].rs].cnt; ask(mid+1,r,rc); return; } } signed main(){ fire(); cin(n,a,b); for(int i=1,x;i<=n;++i){ cin(x); change(0,INF,1,x); suma=sumb=0; cnta=cntb=0; ask(0,INF,1); } }
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T4『金牌』
赛时的思路是正确的,但是没有讨论出来证明了天依还是太菜了...
赛后不想改,真的不想改啊...
重新看题面,\(2^q\)...用快速幂吧
树上两点简单路径....树剖吗,或者 tarjan 来\(O(1)\)求...
还是分讨吧...
所以求出每个点 \(x\) 本身及其子树中的点到它的权值和 \(f_x\) 与所有点到它的权值和 \(d_x\)
大概有点思路...赛时降智了
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若\(x\)或\(y=\text{lca}(x,y)\),钦定\(x.dep<y.dep\)
\[(f_x-2d_{dep_x-dep_y-1})\times d_y\times 2^{{dis}(x,y)} \] -
否则
\[d_x\times d_y\times 2^{dis(x,y)} \]
代码...不想写了...
模拟赛改的好累...
update:代码写完了
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总结:
\(189pts\),天依还是太菜了啊,而且思路太窄了,太窄了,代码能力太不行了,赛时思路没问题的情况下 T3 的代码没打出来
足够简单的题能想出来...也就只有足够简单的了
T3的分块代码没打出来,大样例过不去没敢交
考场T4写破防了,暴力没打
赛时\(rk4\)应该是别人挂的分比较高吧,毕竟自己还是没实力的,哎
太菜了,还是太菜了啊
补充了一下图床...多放几张图吧