bzoj 2552: Zju2253 Fill the Grid 高精度+打表

题目链接：https://www.lydsy.com/JudgeOnline/problem.php?id=2552

看到数据范围，直接就想打表，先写了发dfs暴搜，结果发现连 $5$ $5$ 的点都跑到天荒地老，然后就开始dp。

dp数组一共n维，第i维表示第i行放了几个数。

如果数据范围小一点的话，就可以开一个多维的dp数组，然后大力dp了，但是这个题的数据范围显然是不允许我们这么做的，所以再大胆一点，把9个map套在一起，然后里面再套一个高精度。

代码虽然很暴力，但是打表速度还是很快的。

打表程序：

#include<bits/stdc++.h>

#define bit bitset<110>
#define ll long long

using namespace std;

inline int rd(){
    int x=0,y=1;char c=getchar();
    while(!isdigit(c)){if(c=='-')y=-y;c=getchar();}
    while(isdigit(c))x=x*10+c-'0',c=getchar();
    return x*y;
}
struct bn{
	#define MAXN 1010
	#define ll long long
	int len;
	char num[MAXN];
	bn(ll x){
		memset(num,0,sizeof(num));
		len=0;
		while(x>0){
			num[len++]=x%10;
			x/=10;
		}
	}
	bn(){memset(num,0,sizeof(num)),len=0;}
	void rd(){
		len=0;
		char c=getchar();
		while(!isdigit(c))c=getchar();
		while(isdigit(c))num[len++]=c-'0',c=getchar();
		for(int i=0; i<len/2; i++)swap(num[i],num[len-i-1]);
	}
	void out(){
		if(!len)printf("0");
		for(int i=len-1; i>=0; i--)printf("%d",num[i]);
	}
	void half(){
		for(int i=len-1; i>0; i--){
			num[i-1]+=(num[i]%2)*10;
			num[i]/=2;
		}
		num[0]/=2;
		while(len-1>=0 && !num[len-1])len--;
	}
	friend bn operator + (bn a,bn b){
		bn c;
		for(int i=0; i<a.len || i<b.len; i++){
			c.num[i]+=a.num[i]+b.num[i];
			c.num[i+1]+=c.num[i]/10;
			c.num[i]%=10;
		}
		c.len=max(a.len,b.len);
		if(c.num[c.len])c.len++;
		return c;
	}
	friend bn operator + (bn a,ll b){return a+bn(b);}
	friend bn operator + (ll a,bn b){return bn(a)+b;}
	friend bn operator - (bn a,bn b){
		bn c;
		for(int i=0; i<a.len; i++){
			c.num[i]+=a.num[i]-b.num[i];
			if(c.num[i]<0)c.num[i+1]--,c.num[i]+=10;
		}
		c.len=max(a.len,b.len);
		while(c.len-1>=0 && !c.num[c.len-1])c.len--;
		return c;
	}
	friend bn operator - (bn a,ll b){return a-bn(b);}
	friend bn operator * (bn a,bn b){
		bn c;
		for(int i=0; i<a.len; i++){
			for(int j=0; j<b.len; j++){
				c.num[i+j]+=a.num[i]*b.num[j];
				c.num[i+j+1]+=c.num[i+j]/10;
				c.num[i+j]%=10;
			}
		}
		c.len=a.len+b.len;
		while(c.len-1>=0 && !c.num[c.len-1])c.len--;
		return c;
	}
	friend bn operator * (bn a,ll b){return a*bn(b);}
	friend bn operator * (ll a,bn b){return bn(a)*b;}
	friend bool operator < (bn a,bn b){
		if(a.len!=b.len)return a.len<b.len;
		for(int i=a.len-1; i>=0; i--)if(a.num[i]!=b.num[i])return a.num[i]<b.num[i];
		return false;
	}
	friend bool operator == (bn a,bn b){
		if(a.len!=b.len)return false;
		for(int i=0; i<a.len; i++)if(a.num[i]!=b.num[i])return false;
		return true;
	}
	friend bool operator <= (bn a,bn b){
		return a<b || a==b;
	}
	friend bn operator / (bn a,bn b){
		bn c;
		bn l,r,mid;
		l=bn(0),r=a;
		while(l<=r){
			mid=l+r;
			mid.half();
			if(mid*b<=a)c=mid,l=mid+1;
			else r=mid-1;
		}
		return c;
	}
	friend bn operator % (bn a,bn b){
		return a-(b*(a/b));
	}
	friend bn operator ^ (bn x,ll y){
        bn z=1;
        while(y){
            if(y&1)z=z*x;
            x=x*x;
            y/=2;
        }
        return z;
    }
	#undef ll
	#undef MAXN
};

int n,m,ans;
int Max[11],a[11];
map<int,map<int,map<int,map<int,map<int,map<int,map<int,map<int,map<int,bn> > > > > > > > >f;

inline void init(int i,int j){
    f.clear();
    n=i,m=j;
    memset(Max,0,sizeof Max);
    for(int i=1; i<=n; i++)Max[i]=m;
}

void dfs(int deep,int num){
    if(deep==10){
        for(int i=1; i<=9; i++){
            if(a[i]){
                f[a[1]][a[2]][a[3]][a[4]][a[5]][a[6]][a[7]][a[8]][a[9]]=f[a[1]][a[2]][a[3]][a[4]][a[5]][a[6]][a[7]][a[8]][a[9]]+f[a[1]-(i==1)][a[2]-(i==2)][a[3]-(i==3)][a[4]-(i==4)][a[5]-(i==5)][a[6]-(i==6)][a[7]-(i==7)][a[8]-(i==8)][a[9]-(i==9)];
            }
        }
        return;
    }
    for(int i=0; i<=min(Max[deep],num); i++){
        a[deep]=i;
        dfs(deep+1,i);
    }
}

inline void work(){
    f[0][0][0][0][0][0][0][0][0]=1;
    dfs(1,m);
    printf("ans[%d][%d]=\"",n,m);
    f[Max[1]][Max[2]][Max[3]][Max[4]][Max[5]][Max[6]][Max[7]][Max[8]][Max[9]].out();
    cout<<"\";"<<endl;
}

int main(){
    for(int i=1; i<=9; i++){
        for(int j=1; j<=9; j++){
            init(i,j);
            if(n==0 && m==0)break;
            work();
        }
    }
    
    return 0;
}

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#include<bits/stdc++.h>

#define bit bitset<110>

#define ll long long

using namespace std;

inline int rd(){

int x=0,y=1;char c=getchar();

while(!isdigit(c)){if(c=='-')y=-y;c=getchar();}

while(isdigit(c))x=x*10+c-'0',c=getchar();

return x*y;

}

struct bn{

#define MAXN 1010

#define ll long long

int len;

char num[MAXN];

bn(ll x){

memset(num,0,sizeof(num));

len=0;

while(x>0){

num[len++]=x%10;

x/=10;

}

bn(){memset(num,0,sizeof(num)),len=0;}

void rd(){

len=0;

char c=getchar();

while(!isdigit(c))c=getchar();

while(isdigit(c))num[len++]=c-'0',c=getchar();

for(int i=0; i<len/2; i++)swap(num[i],num[len-i-1]);

}

void out(){

if(!len)printf("0");

for(int i=len-1; i>=0; i--)printf("%d",num[i]);

}

void half(){

for(int i=len-1; i>0; i--){

num[i-1]+=(num[i]%2)*10;

num[i]/=2;

}

num[0]/=2;

while(len-1>=0 && !num[len-1])len--;

}

friend bn operator + (bn a,bn b){

bn c;

for(int i=0; i<a.len || i<b.len; i++){

c.num[i]+=a.num[i]+b.num[i];

c.num[i+1]+=c.num[i]/10;

c.num[i]%=10;

}

c.len=max(a.len,b.len);

if(c.num[c.len])c.len++;

return c;

}

friend bn operator + (bn a,ll b){return a+bn(b);}

friend bn operator + (ll a,bn b){return bn(a)+b;}

friend bn operator - (bn a,bn b){

bn c;

for(int i=0; i<a.len; i++){

c.num[i]+=a.num[i]-b.num[i];

if(c.num[i]<0)c.num[i+1]--,c.num[i]+=10;

}

c.len=max(a.len,b.len);

while(c.len-1>=0 && !c.num[c.len-1])c.len--;

return c;

}

friend bn operator - (bn a,ll b){return a-bn(b);}

friend bn operator * (bn a,bn b){

bn c;

for(int i=0; i<a.len; i++){

for(int j=0; j<b.len; j++){

c.num[i+j]+=a.num[i]*b.num[j];

c.num[i+j+1]+=c.num[i+j]/10;

c.num[i+j]%=10;

}

c.len=a.len+b.len;

while(c.len-1>=0 && !c.num[c.len-1])c.len--;

return c;

}

friend bn operator * (bn a,ll b){return a*bn(b);}

friend bn operator * (ll a,bn b){return bn(a)*b;}

friend bool operator < (bn a,bn b){

if(a.len!=b.len)return a.len<b.len;

for(int i=a.len-1; i>=0; i--)if(a.num[i]!=b.num[i])return a.num[i]<b.num[i];

return false;

}

friend bool operator == (bn a,bn b){

if(a.len!=b.len)return false;

for(int i=0; i<a.len; i++)if(a.num[i]!=b.num[i])return false;

return true;

}

friend bool operator <= (bn a,bn b){

return a<b || a==b;

}

friend bn operator / (bn a,bn b){

bn c;

bn l,r,mid;

l=bn(0),r=a;

while(l<=r){

mid=l+r;

mid.half();

if(mid*b<=a)c=mid,l=mid+1;

else r=mid-1;

}

return c;

}

friend bn operator % (bn a,bn b){

return a-(b*(a/b));

}

friend bn operator ^ (bn x,ll y){

bn z=1;

while(y){

if(y&1)z=z*x;

x=x*x;

y/=2;

}

return z;

}

#undef ll

#undef MAXN

};

int n,m,ans;

int Max[11],a[11];

map<int,map<int,map<int,map<int,map<int,map<int,map<int,map<int,map<int,bn> > > > > > > > >f;

inline void init(int i,int j){

f.clear();

n=i,m=j;

memset(Max,0,sizeof Max);

for(int i=1; i<=n; i++)Max[i]=m;

}

void dfs(int deep,int num){

if(deep==10){

for(int i=1; i<=9; i++){

if(a[i]){

f[a[1]][a[2]][a[3]][a[4]][a[5]][a[6]][a[7]][a[8]][a[9]]=f[a[1]][a[2]][a[3]][a[4]][a[5]][a[6]][a[7]][a[8]][a[9]]+f[a[1]-(i==1)][a[2]-(i==2)][a[3]-(i==3)][a[4]-(i==4)][a[5]-(i==5)][a[6]-(i==6)][a[7]-(i==7)][a[8]-(i==8)][a[9]-(i==9)];

}

return;

}

for(int i=0; i<=min(Max[deep],num); i++){

a[deep]=i;

dfs(deep+1,i);

}

inline void work(){

f[0][0][0][0][0][0][0][0][0]=1;

dfs(1,m);

printf("ans[%d][%d]=\"",n,m);

f[Max[1]][Max[2]][Max[3]][Max[4]][Max[5]][Max[6]][Max[7]][Max[8]][Max[9]].out();

cout<<"\";"<<endl;

}

int main(){

for(int i=1; i<=9; i++){

for(int j=1; j<=9; j++){

init(i,j);

if(n==0 && m==0)break;

work();

}

return 0;

}

AC程序：

#include<bits/stdc++.h>

using namespace std;

inline int rd(){
    int x=0,y=1;char c=getchar();
    while(!isdigit(c)){if(c=='-')y=-y;c=getchar();}
    while(isdigit(c))x=x*10+c-'0',c=getchar();
    return x*y;
}

int n,m;
string ans[10][10];

inline void init(){
    ans[1][1]="1";
    ans[1][2]="1";
    ans[1][3]="1";
    ans[1][4]="1";
    ans[1][5]="1";
    ans[1][6]="1";
    ans[1][7]="1";
    ans[1][8]="1";
    ans[1][9]="1";
    ans[2][1]="1";
    ans[2][2]="2";
    ans[2][3]="5";
    ans[2][4]="14";
    ans[2][5]="42";
    ans[2][6]="132";
    ans[2][7]="429";
    ans[2][8]="1430";
    ans[2][9]="4862";
    ans[3][1]="1";
    ans[3][2]="5";
    ans[3][3]="42";
    ans[3][4]="462";
    ans[3][5]="6006";
    ans[3][6]="87516";
    ans[3][7]="1385670";
    ans[3][8]="23371634";
    ans[3][9]="414315330";
    ans[4][1]="1";
    ans[4][2]="14";
    ans[4][3]="462";
    ans[4][4]="24024";
    ans[4][5]="1662804";
    ans[4][6]="140229804";
    ans[4][7]="13672405890";
    ans[4][8]="1489877926680";
    ans[4][9]="177295473274920";
    ans[5][1]="1";
    ans[5][2]="42";
    ans[5][3]="6006";
    ans[5][4]="1662804";
    ans[5][5]="701149020";
    ans[5][6]="396499770810";
    ans[5][7]="278607172289160";
    ans[5][8]="231471904322784840";
    ans[5][9]="219738059326729823880";
    ans[6][1]="1";
    ans[6][2]="132";
    ans[6][3]="87516";
    ans[6][4]="140229804";
    ans[6][5]="396499770810";
    ans[6][6]="1671643033734960";
    ans[6][7]="9490348077234178440";
    ans[6][8]="67867669180627125604080";
    ans[6][9]="583692803893929928888544400";
    ans[7][1]="1";
    ans[7][2]="429";
    ans[7][3]="1385670";
    ans[7][4]="13672405890";
    ans[7][5]="278607172289160";
    ans[7][6]="9490348077234178440";
    ans[7][7]="475073684264389879228560";
    ans[7][8]="32103104214166146088869942000";
    ans[7][9]="2760171874087743799855959353857200";
    ans[8][1]="1";
    ans[8][2]="1430";
    ans[8][3]="23371634";
    ans[8][4]="1489877926680";
    ans[8][5]="231471904322784840";
    ans[8][6]="67867669180627125604080";
    ans[8][7]="32103104214166146088869942000";
    ans[8][8]="22081374992701950398847674830857600";
    ans[8][9]="20535535214275361308250745082811167425600";
    ans[9][1]="1";
    ans[9][2]="4862";
    ans[9][3]="414315330";
    ans[9][4]="177295473274920";
    ans[9][5]="219738059326729823880";
    ans[9][6]="583692803893929928888544400";
    ans[9][7]="2760171874087743799855959353857200";
    ans[9][8]="20535535214275361308250745082811167425600";
    ans[9][9]="220381378415074546123953914908618547085974856000";
}

int main(){
    init();
    while(1){
        int x=rd(),y=rd();
        if(x==0 && y==0)break;
        printf("%s\n",ans[x][y].c_str());
    }
    
    return 0;
}

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#include<bits/stdc++.h>

using namespace std;

inline int rd(){

int x=0,y=1;char c=getchar();

while(!isdigit(c)){if(c=='-')y=-y;c=getchar();}

while(isdigit(c))x=x*10+c-'0',c=getchar();

return x*y;

}

int n,m;

string ans[10][10];

inline void init(){

ans[1][1]="1";

ans[1][2]="1";

ans[1][3]="1";

ans[1][4]="1";

ans[1][5]="1";

ans[1][6]="1";

ans[1][7]="1";

ans[1][8]="1";

ans[1][9]="1";

ans[2][1]="1";

ans[2][2]="2";

ans[2][3]="5";

ans[2][4]="14";

ans[2][5]="42";

ans[2][6]="132";

ans[2][7]="429";

ans[2][8]="1430";

ans[2][9]="4862";

ans[3][1]="1";

ans[3][2]="5";

ans[3][3]="42";

ans[3][4]="462";

ans[3][5]="6006";

ans[3][6]="87516";

ans[3][7]="1385670";

ans[3][8]="23371634";

ans[3][9]="414315330";

ans[4][1]="1";

ans[4][2]="14";

ans[4][3]="462";

ans[4][4]="24024";

ans[4][5]="1662804";

ans[4][6]="140229804";

ans[4][7]="13672405890";

ans[4][8]="1489877926680";

ans[4][9]="177295473274920";

ans[5][1]="1";

ans[5][2]="42";

ans[5][3]="6006";

ans[5][4]="1662804";

ans[5][5]="701149020";

ans[5][6]="396499770810";

ans[5][7]="278607172289160";

ans[5][8]="231471904322784840";

ans[5][9]="219738059326729823880";

ans[6][1]="1";

ans[6][2]="132";

ans[6][3]="87516";

ans[6][4]="140229804";

ans[6][5]="396499770810";

ans[6][6]="1671643033734960";

ans[6][7]="9490348077234178440";

ans[6][8]="67867669180627125604080";

ans[6][9]="583692803893929928888544400";

ans[7][1]="1";

ans[7][2]="429";

ans[7][3]="1385670";

ans[7][4]="13672405890";

ans[7][5]="278607172289160";

ans[7][6]="9490348077234178440";

ans[7][7]="475073684264389879228560";

ans[7][8]="32103104214166146088869942000";

ans[7][9]="2760171874087743799855959353857200";

ans[8][1]="1";

ans[8][2]="1430";

ans[8][3]="23371634";

ans[8][4]="1489877926680";

ans[8][5]="231471904322784840";

ans[8][6]="67867669180627125604080";

ans[8][7]="32103104214166146088869942000";

ans[8][8]="22081374992701950398847674830857600";

ans[8][9]="20535535214275361308250745082811167425600";

ans[9][1]="1";

ans[9][2]="4862";

ans[9][3]="414315330";

ans[9][4]="177295473274920";

ans[9][5]="219738059326729823880";

ans[9][6]="583692803893929928888544400";

ans[9][7]="2760171874087743799855959353857200";

ans[9][8]="20535535214275361308250745082811167425600";

ans[9][9]="220381378415074546123953914908618547085974856000";

}

int main(){

init();

while(1){

int x=rd(),y=rd();

if(x==0 && y==0)break;

printf("%s\n",ans[x][y].c_str());

}

return 0;

}

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bzoj 2552: Zju2253 Fill the Grid 高精度+打表

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