17.10.05

Posted 2020-10-09 *ZJ

• 上午
• 模拟考试
  • Prob.1（AC）一道简单的博弈题，找到必胜态，反推普遍情况是否可以达到必胜态即可。
  • Prob.2（AC）做到原题了呢。入门OJ 2092: [Noip模拟题]舞会
  • Prob.3（WA了3个点）一道高精度的dp题，为减少状态，我把数据按某一权值分为了两类，对于一类反着dp，状态很少，只用到高精度加法。对于另一类（30分），要用到高精度乘法，然后进位时少打了一个+号，然后就没有然后了……
• 然后整理了三个模板，贴上！

//maybe have no mistakes,^_^

//1.Big_Int
//only support + , * , = , < , <= , > , >= between Big_Int and Big_Int as well as Big_Int and int 
#define MAXN 1000
struct Big_Int{
	int len,a[30];
	Big_Int(){len=1; memset(a,0,sizeof(a));}
	void operator =(int val){
		len=0;
		do{
			a[++len]=val%MAXN;
			val/=MAXN;
		}while(val);
	}
	Big_Int operator +(const Big_Int &rtm) const{
		Big_Int now; int l=max(len,rtm.len);
		for(int i=1;i<=l;i++){
			now.a[i]+=a[i]+rtm.a[i];
			now.a[i+1]=now.a[i]/MAXN;
			now.a[i]%=MAXN;
		}
		if(now.a[l+1]) l++; now.len=l;
		return now;
	}
	Big_Int operator +(const int &val) const{
		Big_Int now,rtm;
		rtm=val; now=(*this)+rtm;
		return now;
	}
	Big_Int operator *(const Big_Int &rtm) const{
		Big_Int now; int l=len+rtm.len;
		for(int i=1;i<=len;i++)
			for(int j=1;j<=rtm.len;j++){
				now.a[i+j-1]+=a[i]*rtm.a[j];
				now.a[i+j]+=now.a[i+j-1]/MAXN;
				now.a[i+j-1]%=MAXN;
			}
		while(!now.a[l]) l--; now.len=l;
		return now;
	}
	Big_Int operator *(const int &val) const {
		Big_Int now,rtm;
		rtm=val; now=(*this)*rtm;
		return now;
	}
	bool operator ==(const Big_Int & rtm) const{
		if(len!=rtm.len) return 0;
		for(int i=len;i>=1;i--) if(a[i]!=rtm.a[i]) return 0;
		return 1;
	}
	bool operator <(const Big_Int &rtm) const{
		if(len!=rtm.len) return len<rtm.len;
		for(int i=len;i>=1;i--) if(a[i]!=rtm.a[i]) return a[i]<rtm.a[i];
		return 0;
	}
	bool operator >(const Big_Int &rtm) const{
		return rtm<(*this);
	}
	bool operator <=(const Big_Int &rtm) const{
		return (*this)<rtm||(*this)==rtm;
	}
	bool operator >=(const Big_Int &rtm) const{
		return (*this)>rtm||(*this)==rtm;
	}
	bool operator ==(const int &val) const{
		Big_Int rtm; rtm=val;
		return (*this)==rtm;
	}
	bool operator <(const int &val) const{
		Big_Int rtm; rtm=val;
		return (*this)<rtm;
	}
	bool operator >(const int &val) const{
		Big_Int rtm; rtm=val;
		return (*this)<rtm;
	}
	bool operator <=(const int &val) const{
		Big_Int rtm; rtm=val;
		return (*this)<=rtm;
	}
	bool operator >=(const int &val) const{
		Big_Int rtm; rtm=val;
		return (*this)>=rtm;
	}
	void print(){
		printf("%d",a[len]);
		for(int i=len-1;i>=1;i--){
			printf("%03d",a[i]);
		}
	}
};

//2.Fraction
//only support + , * and  reduction for fraction
struct Fraction{
	ll Numerator,Denominator;
	ll Gcd(ll a,ll b){
		while(a^=b^=a^=b%=a);
		return b;
	}
	bool Zero(){
		return Numerator==0;
	}
	void Clear(){
		Numerator=Denominator=0;
	}
	void Reduction(){
		ll g=Gcd(Numerator,Denominator);
		Numerator/=g;
		Denominator/=g;
	}
	Fraction operator +(Fraction &rtm){
		Fraction New;
		if(!Numerator&&!Denominator) 
			New.Numerator=rtm.Numerator,New.Denominator=rtm.Denominator;
		else{
			ll g=Gcd(Denominator,rtm.Denominator);
			ll a=Denominator/g,b=rtm.Denominator/g;
			New.Denominator=a*b*g;
			New.Numerator=Numerator*b+rtm.Numerator*a;
		}
		New.Reduction();
		return New;
	}
	Fraction operator *(Fraction &rtm){
		Fraction New;
		New.Denominator=Denominator*rtm.Denominator;
		New.Numerator=Numerator*rtm.Numerator;
		New.Reduction();
		return New;
	}
	void Read(){
		cin>>Numerator;
		Denominator=1;
	}
	void Write(){
		cout<<Numerator;
		if(Denominator!=1&&Denominator!=0) cout<<"/"<<Denominator<<endl;
	}
}

//3.Maxtrix
//noly supprt * , ^(quick pow) for Maxtrix
struct Maxtrix{
	int r,c;
	int val[75][75];
	Maxtrix(){
		r=c=0;
		memset(val,0,sizeof(val));
	}
	void identity(int l){
		r=c=l;
		for(int i=1;i<=l;i++) val[i][i]=1;
	}
	Maxtrix operator * (Maxtrix const b){  // c==b.r
		Maxtrix now; now.r=r; now.c=b.c;
		for(int i=1;i<=r;i++)
			for(int j=1;j<=b.c;j++)
				for(int k=1;k<=c;k++)
					now.val[i][j]=(now.val[i][j]+val[i][k]*b.val[k][j])%mod; 
		return now;
	} 
	Maxtrix operator ^ (int b){
		Maxtrix base,now; base=*this;
		now.identity(this->r); 
		while(b){
			if(b&1) now=now*base;
			base=base*base;
			b>>=1; 
		}
		return now;
	}
}

//____________________________________________________________________by *ZJ

 

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