HDOJ 1134 数学+大数

这个题是卡特兰数的公式题

不需要讲太多的东西，关键是贴个大数的模板

bin神的模板改造过来

bin神的思路是一个int值保存一个整数的4个数位

其实在模拟题中，如果内存够的话，保存1个数位是更好处理的，因为可以更好的判断首位和末位的情况

改动如下：

把private的a数组和len值改为public的（不然在BigNum的定义外面没有访问的权限）

把DLEN改为1

把MAXN改为9

然后注意，istream和ostream其实可以不需要（因为可以先读取字符串，然后在转化成BigNum）

在print（）函数中

要把%04d改为%0d，因为现在一位中只有一个数字了

#include<bits/stdc++.h>
using namespace std;

#define MAXN 9
#define MAXSIZE 1010
#define DLEN 1

class BigNum{
public:
    int a[MAXSIZE];
    int len;
    BigNum(){len=1;memset(a,0,sizeof(a));}
    BigNum(const int);
    BigNum(const char *);
    BigNum(const BigNum &);
    BigNum & operator = (const BigNum &);
    friend istream & operator >> (istream &,BigNum &);
    friend ostream & operator << (ostream &,BigNum &);
    BigNum operator + (const BigNum &) const;
    BigNum operator - (const BigNum &) const;
    BigNum operator * (const BigNum &) const;
    BigNum operator / (const int &) const;
    BigNum operator ^ (const int &) const;
    int operator % (const int &) const;
    bool operator > (const BigNum &T) const;
    bool operator > (const int &t) const;
    void print();
};

BigNum::BigNum(const int b){
    int c,d=b;
    len=0;
    memset(a,0,sizeof(a));
    while(d>MAXN){
        c=d-(d/(MAXN+1))*(MAXN+1);
        d=d/(MAXN+1);
        a[len++]=c;
    }
    a[len++]=d;
}

BigNum::BigNum(const char *s){
    int t,k,index,L,i;
    memset(a,0,sizeof(a));
    L=strlen(s);
    len=L/DLEN;
    if (L%DLEN) len++;
    index=0;
    for(i=L-1;i>=0;i-=DLEN){
        t=0;
        k=i-DLEN+1;
        if (k<0) k=0;
        for(int j=k;j<=i;j++)
            t=t*10+s[j]-'0';
        a[index++]=t;
    }
}

BigNum::BigNum(const BigNum &T):len(T.len){
    memset(a,0,sizeof(a));
    for(int i=0;i<len;i++) a[i]=T.a[i];
}

BigNum & BigNum::operator = (const BigNum &n){
    len=n.len;
    memset(a,0,sizeof(a));
    for(int i=0;i<len;i++) a[i]=n.a[i];
    return *this;
}

BigNum BigNum::operator + (const BigNum &T) const{
    BigNum t(*this);
    int i,big;
    big=T.len>len?T.len:len;
    for(i=0;i<big;i++){
        t.a[i]+=T.a[i];
        if (t.a[i]>MAXN){
            t.a[i+1]++;
            t.a[i]-=MAXN+1;
        }
    }
    if (t.a[big]!=0) t.len=big+1;
    else t.len=big;
    return t;
}

BigNum BigNum::operator - (const BigNum &T) const{
    int i,j,big;
    bool flag;
    BigNum t1,t2;
    if (*this>T){
        t1=*this;
        t2=T;
        flag=0;
    }
    else{
        t1=T;
        t2=*this;
        flag=1;
    }
    big=t1.len;
    for(i=0;i<big;i++){
        if (t1.a[i]<t2.a[i]){
            j=i+1;
            while(t1.a[j]==0) j++;
            t1.a[j--]--;
            while(j>i) t1.a[j--]+=MAXN;
            t1.a[i]+=MAXN+1-t2.a[i];
        }
        else t1.a[i]-=t2.a[i];
    }
    t1.len=big;
    while(t1.a[t1.len-1]==0&&t1.len>1){
        t1.len--;
        big--;
    }
    if (flag)
        t1.a[big-1]=0-t1.a[big-1];
    return t1;
}

BigNum BigNum::operator * (const BigNum &T) const{
    BigNum ret;
    int i,j,up;
    int temp,temp1;
    for(i=0;i<len;i++){
        up=0;
        for(j=0;j<T.len;j++){
            temp=a[i]*T.a[j]+ret.a[i+j]+up;
            if (temp>=MAXN){
                temp1=temp-temp/(MAXN+1)*(MAXN+1);
                up=temp/(MAXN+1);
                ret.a[i+j]=temp1;
            }
            else{
                up=0;
                ret.a[i+j]=temp;
            }
        }
        if (up) ret.a[i+j]=up;
    }
    ret.len=i+j;
    while(ret.a[ret.len-1]==0&&ret.len>1) ret.len--;
    return ret;
}

BigNum BigNum::operator / (const int &b) const{
    BigNum ret;
    int i,down=0;
    for(i=len-1;i>=0;i--){
        ret.a[i]=(a[i]+down*(MAXN+1))/b;
        down=a[i]+down*(MAXN+1)-ret.a[i]*b;
    }
    ret.len=len;
    while(ret.a[ret.len-1]==0&&ret.len>1) ret.len--;
    return ret;
}

int BigNum::operator % (const int &b) const{
    int i,d=0;
    for(i=len-1;i>=0;i--)
        d=((d*(MAXN+1))%b+a[i])%b;
    return d;
}

BigNum BigNum::operator ^ (const int &n) const{
    BigNum t,ret(1);
    int i;
    if (n<0) exit(-1);
    if (n==0) return 1;
    if (n==1) return *this;
    int m=n;
    while(m>1){
        t=*this;
        for(i=1;(i<<1)<=m;i<<=1) t=t*t;
        m-=i;
        ret=ret*t;
        if (m==1) ret=ret*(*this);
    }
    return ret;
}

bool BigNum::operator > (const BigNum &T) const{
    int ln;
    if (len>T.len) return true;
    else if (len==T.len){
        ln=len-1;
        while(a[ln]==T.a[ln]&&ln>=0) ln--;
        if (ln>=0&&a[ln]>T.a[ln]) return true;
        else return false;
    }
    else return false;
}

bool BigNum::operator > (const int &t) const{
    BigNum b(t);
    return *this>b;
}

void BigNum::print(){
    printf("%d",a[len-1]);
    for(int i=len-2;i>=0;i--) printf("%0d",a[i]);
    printf("\n");
}

BigNum x,y,z;
char s[MAXSIZE];
BigNum ans[150];
int main(){
    /*
    freopen("input.txt","r",stdin);
    scanf("%s",s);
    x=BigNum(s);
    scanf("%s",s);
    y=BigNum(s);
    y.print();
    z=x^3;
    z.print();
    z=x+y;
    z.print();
    z=x-y;
    z.print();
    z=x*y;
    z.print();
    printf("%d\n",x%100);
    z=y/100;
    z.print();
    if (x>y) printf("x>y\n");
    else printf("x<y\n");
    */
    int n;
    ans[0]=1;
    for(int i=1;i<=100;i++)
        ans[i]=ans[i-1]*(4*i-2)/(i+1);
    while(scanf("%d",&n)!=EOF){
        if (n==-1) break;
        ans[n].print();
    }
    return 0;
}