UVa 10844 （大数）-白红宇

UVa 10844 （大数）

阅读量：4286 次

发布时间：2019-05-27

本文共 5409 字，大约阅读时间需要 18 分钟。

题意：给你n个木块，让你搭建筑物，可以几个木块一起搭，也可以一个成建筑物，问有多少种方法？

题解：就是斯特灵数模型求和；（即贝尔数）

/********************************************************   贝尔数模型*    *    1*    1    2*    2    3    5*    5    7    10     15*    15   20   27     37     52*    .    .     .      .      .*    .    .     .      .      .*    第1列即是贝尔数，看图找规律，祝你成功**********************************************************/#include 
   
    #include 
    
     #include 
     
      #include 
      
       using namespace std;using namespace std;const int MAXN = 1800;struct bign{    int len, num[MAXN];    bign ()    {        len = 0;        memset(num, 0, sizeof(num));    }    bign (int number)    {        *this = number;    }    bign (const char* number)    {        *this = number;    }    void DelZero ();    void Put ();    void operator = (int number);    void operator = (char* number);    bool operator <  (const bign& b) const;    bool operator >  (const bign& b) const    {        return b < *this;    }    bool operator <= (const bign& b) const    {        return !(b < *this);    }    bool operator >= (const bign& b) const    {        return !(*this < b);    }    bool operator != (const bign& b) const    {        return b < *this || *this < b;    }    bool operator == (const bign& b) const    {        return !(b != *this);    }    void operator ++ ();    void operator -- ();    bign operator + (const int& b);    bign operator + (const bign& b);    bign operator - (const int& b);    bign operator - (const bign& b);    bign operator * (const int& b);    bign operator * (const bign& b);    bign operator / (const int& b);    bign operator / (const bign& b);    int operator % (const int& b);};/*Code*/const int N = 905;int n;bign dp[2][N], ans[N];void init(){    int pre = 1, now = 0;    dp[now][1] = 1;    ans[1] = 1;    for (int i = 2; i <= 900; i++)    {        swap(now, pre);        dp[now][1] = dp[pre][i - 1];        for (int j = 2; j <= i; j++)            dp[now][j] = dp[now][j - 1] + dp[pre][j - 1];        ans[i] = dp[now][i];    }}int main(){    init();    while (~scanf("%d", &n) && n)    {        printf("%d, ", n);        ans[n].Put();        printf("\n");    }    return 0;}void bign::DelZero (){    while (len && num[len-1] == 0)    len--;    if (len == 0)    {        num[len++] = 0;    }}void bign::Put (){    printf("%d", num[len - 1]);    for (int i = len-2; i >= 0; i--)     printf("%08d", num[i]);}void bign::operator = (char* number){    len = strlen (number);    for (int i = 0; i < len; i++)    num[i] = number[len-i-1] - '0';    DelZero ();}void bign::operator = (int number){    len = 0;    while (number)    {        num[len++] = number%10;        number /= 10;    }    DelZero ();}bool bign::operator < (const bign& b) const{    if (len != b.len)    return len < b.len;    for (int i = len-1; i >= 0; i--)    if (num[i] != b.num[i])        return num[i] < b.num[i];    return false;}void bign::operator ++ (){    int s = 1;    for (int i = 0; i < len; i++)    {        s = s + num[i];        num[i] = s % 10;        s /= 10;        if (!s) break;    }    while (s)    {        num[len++] = s%10;        s /= 10;    }}void bign::operator -- (){    if (num[0] == 0 && len == 1) return;    int s = -1;    for (int i = 0; i < len; i++)    {        s = s + num[i];        num[i] = (s + 10) % 10;        if (s >= 0) break;    }    DelZero ();}bign bign::operator + (const int& b){    bign a = b;    return *this + a;}bign bign::operator + (const bign& b){    int bignSum = 0;    bign ans;    for (int i = 0; i < len || i < b.len; i++)    {        if (i < len) bignSum += num[i];        if (i < b.len) bignSum += b.num[i];        ans.num[ans.len++] = bignSum % 100000000;        bignSum /= 100000000;    }    while (bignSum)    {        ans.num[ans.len++] = bignSum % 100000000;        bignSum /= 100000000;    }    return ans;}bign bign::operator - (const int& b){    bign a = b;    return *this - a;}bign bign::operator - (const bign& b){    int bignSub = 0;    bign ans;    for (int i = 0; i < len || i < b.len; i++)    {        bignSub += num[i];        bignSub -= b.num[i];        ans.num[ans.len++] = (bignSub + 10) % 10;        if (bignSub < 0) bignSub = -1;    }    ans.DelZero ();    return ans;}bign bign::operator * (const int& b){    int bignSum = 0;    bign ans;    ans.len = len;    for (int i = 0; i < len; i++)    {        bignSum += num[i] * b;        ans.num[i] = bignSum % 10;        bignSum /= 10;    }    while (bignSum)    {        ans.num[ans.len++] = bignSum % 10;        bignSum /= 10;    }    return ans;}bign bign::operator * (const bign& b){    bign ans;    ans.len = 0;    for (int i = 0; i < len; i++)    {        int bignSum = 0;        for (int j = 0; j < b.len; j++)        {            bignSum += num[i] * b.num[j] + ans.num[i+j];            ans.num[i+j] = bignSum % 10;            bignSum /= 10;        }        ans.len = i + b.len;        while (bignSum)        {            ans.num[ans.len++] = bignSum % 10;            bignSum /= 10;        }    }    return ans;}bign bign::operator / (const int& b){    bign ans;    int s = 0;    for (int i = len-1; i >= 0; i--)    {        s = s * 10 + num[i];        ans.num[i] = s/b;        s %= b;    }    ans.len = len;    ans.DelZero ();    return ans;}int bign::operator % (const int& b){    bign ans;    int s = 0;    for (int i = len-1; i >= 0; i--)    {        s = s * 10 + num[i];        ans.num[i] = s/b;        s %= b;    }    return s;}