大数运算和大数类
2016-08-09 22:14
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1、首先看一个小问题:
整型数组、字符型数组、vector在未初始化的情况下:
vs测试结果:
(1)整型数组在未初始化时,内存中是乱码;
(2)字符型数组在未初始化时,内存中是乱码;
(3)vector指定容量,int型时,初始化为0;
(4)vector指定容量,char型时,初始化为可打印的空白字符;
(5)vector不指定容量,默认0;
2、简单的大数相加:
3、大数类:
转自:http://blog.csdn.net/hackbuteer1/article/details/6595881
附录:
#include <iostream>
#include <string>
using namespace std;
int compare(string str1, string str2)
{
//相等返回0,大于返回1,小于返回-1
if (str1.size()>str2.size()) return 1; //长度长的整数大于长度小的整数
else if (str1.size()<str2.size()) return -1;
else return str1.compare(str2); //若长度相等,则头到尾按位比较
}
string SUB_INT(string str1, string str2);
string ADD_INT(string str1, string str2) {//高精度加法
int sign = 1; //sign 为符号位
string str;
if (str1[0] == '-') {
if (str2[0] == '-') {
sign = -1;
str = ADD_INT(str1.erase(0, 1), str2.erase(0, 1));
}
else {
str = SUB_INT(str2, str1.erase(0, 1));
}
}
else {
if (str2[0] == '-') {
str = SUB_INT(str1, str2.erase(0, 1));
}
else { //把两个整数对齐,短整数前面加0补齐
string::size_type L1, L2;
int i;
L1 = str1.size();
L2 = str2.size();
if (L1<L2) {
for (i = 1; i <= L2 - L1; i++) str1 = "0" + str1;
}
else {
for (i = 1; i <= L1 - L2; i++) str2 = "0" + str2;
}
int int1 = 0, int2 = 0; //int2 记录进位
for (i = str1.size() - 1; i >= 0; i--) {
int1 = (int(str1[i]) - '0' + int(str2[i]) - '0' + int2) % 10;
int2 = (int(str1[i]) - '0' + int(str2[i]) - '0' + int2) / 10;
str = char(int1 + '0') + str;
}
if (int2 != 0) str = char(int2 + '0') + str;
}
}
//运算后处理符号位
if ((sign == -1) && (str[0] != '0')) str = "-" + str;
return str;
}
string SUB_INT(string str1, string str2) {//高精度减法
int sign = 1; //sign 为符号位
string str;
int i, j;
if (str2[0] == '-') {
str = ADD_INT(str1, str2.erase(0, 1));
}
else {
int res = compare(str1, str2);
if (res == 0) return "0";
if (res<0) {
sign = -1;
string temp = str1;
str1 = str2;
str2 = temp;
}
string::size_type tempint;
tempint = str1.size() - str2.size();
for (i = str2.size() - 1; i >= 0; i--) {
if (str1[i + tempint]<str2[i]) {
j = 1;
while (1) {//zhao4zhong1添加
if (str1[i + tempint - j] == '0') {
str1[i + tempint - j] = '9';
j++;
}
else {
str1[i + tempint - j] = char(int(str1[i + tempint - j]) - 1);
break;
}
}
str = char(str1[i + tempint] - str2[i] + ':') + str;
}
else {
str = char(str1[i + tempint] - str2[i] + '0') + str;
}
}
for (i = tempint - 1; i >= 0; i--) str = str1[i] + str;
}
//去除结果中多余的前导0
str.erase(0, str.find_first_not_of('0'));
if (str.empty()) str = "0";
if ((sign == -1) && (str[0] != '0')) str = "-" + str;
return str;
}
string MUL_INT(string str1, string str2) { //高精度乘法
int sign = 1; //sign 为符号位
string str;
if (str1[0] == '-') {
sign *= -1;
str1 = str1.erase(0, 1);
}
if (str2[0] == '-') {
sign *= -1;
str2 = str2.erase(0, 1);
}
int i, j;
string::size_type L1, L2;
L1 = str1.size();
L2 = str2.size();
for (i = L2 - 1; i >= 0; i--)
{
//模拟手工乘法竖式
string tempstr;
int int1 = 0, int2 = 0, int3 = int(str2[i]) - '0';
if (int3 != 0)
{
for (j = 1; j <= (int)(L2 - 1 - i); j++)
tempstr = "0" + tempstr;
for (j = L1 - 1; j >= 0; j--)
{
int1 = (int3*(int(str1[j]) - '0') + int2) % 10;
int2 = (int3*(int(str1[j]) - '0') + int2) / 10;
tempstr = char(int1 + '0') + tempstr;
}
if (int2 != 0) tempstr = char(int2 + '0') + tempstr;
}
str = ADD_INT(str, tempstr);
}
//去除结果中的前导0
str.erase(0, str.find_first_not_of('0'));
if (str.empty()) str = "0";
if ((sign == -1) && (str[0] != '0'))
str = "-" + str;
return str;
}
string DIVIDE_INT(string str1, string str2, int flag) { //高精度除法。flag==1时,返回商; flag==0时,返回余数
string quotient, residue; //定义商和余数
int sign1 = 1, sign2 = 1;
if (str2 == "0") { //判断除数是否为0
quotient = "ERROR!";
residue = "ERROR!";
if (flag == 1) return quotient;
else return residue;
}
if (str1 == "0") { //判断被除数是否为0
quotient = "0";
residue = "0";
}
if (str1[0] == '-') {
str1 = str1.erase(0, 1);
sign1 *= -1;
sign2 = -1;
}
if (str2[0] == '-') {
str2 = str2.erase(0, 1);
sign1 *= -1;
}
int res = compare(str1, str2);
if (res<0) {
quotient = "0";
residue = str1;
}
else if (res == 0) {
quotient = "1";
residue = "0";
}
else {
string::size_type L1, L2;
L1 = str1.size();
L2 = str2.size();
string tempstr;
tempstr.append(str1, 0, L2 - 1);
for (int i = L2 - 1; i<L1; i++) { //模拟手工除法竖式
tempstr = tempstr + str1[i];
tempstr.erase(0, tempstr.find_first_not_of('0'));//zhao4zhong1添加
if (tempstr.empty()) tempstr = "0";//zhao4zhong1添加
for (char ch = '9'; ch >= '0'; ch--) { //试商
string str;
str = str + ch;
if (compare(MUL_INT(str2, str), tempstr) <= 0) {
quotient = quotient + ch;
tempstr = SUB_INT(tempstr, MUL_INT(str2, str));
break;
}
}
}
residue = tempstr;
}
//去除结果中的前导0
quotient.erase(0, quotient.find_first_not_of('0'));
if (quotient.empty()) quotient = "0";
if ((sign1 == -1) && (quotient[0] != '0')) quotient = "-" + quotient;
if ((sign2 == -1) && (residue[0] != '0')) residue = "-" + residue;
if (flag == 1) return quotient;
else return residue;
}
string DIV_INT(string str1, string str2) {//高精度除法,返回商
return DIVIDE_INT(str1, str2, 1);
}
string MOD_INT(string str1, string str2) {//高精度除法,返回余数
return DIVIDE_INT(str1, str2, 0);
}
int main()
{
/*char ch;
string s1, s2, res;
while (cin >> s1 >> ch >> s2) {
switch (ch) {
case '+':res = ADD_INT(s1, s2); break;
case '-':res = SUB_INT(s1, s2); break;
case '*':res = MUL_INT(s1, s2); break;
case '/':res = DIV_INT(s1, s2); break;
case '%':res = MOD_INT(s1, s2); break;
default: break;
}
cout << res << endl;
}
return(0);*/
string s11, s22, res1;
s11 = "1";
s22 = "2";
for (int i = 1; i <= 1000; i++)
{
res1 = MUL_INT(s11, s22); //利用乘法做幂次运算!
s11 = res1;
}
cout << res1 << endl;
return(0);
}
整型数组、字符型数组、vector在未初始化的情况下:
int main() { int data[5]; char c[5]; vector<int> v(5); vector<char> v1(5); vector<int> v2; cout << "int[]: "; for (int i = 0; i < 5; i++) { cout << data[i] << " "; } cout << endl << endl; cout << "char[]: "; for (int i = 0; i < 5; i++) { cout << c[i] << ","; } cout << endl << endl; cout << "vector(int): "; for (int i : v) { cout << i << " "; } cout << endl << endl; cout << "vector(char): "; for (auto i : v1) { cout << i << ","; } cout << endl << endl; cout << "vector: "; for (int i : v2) { cout << i << ","; } cout << endl << endl; return 0; }
vs测试结果:
(1)整型数组在未初始化时,内存中是乱码;
(2)字符型数组在未初始化时,内存中是乱码;
(3)vector指定容量,int型时,初始化为0;
(4)vector指定容量,char型时,初始化为可打印的空白字符;
(5)vector不指定容量,默认0;
2、简单的大数相加:
#include<iostream> #include<string> #include<algorithm> using namespace std; #define N 500 //25369874522455633 + 68452156965 void bigNumAdd(string a, string b) { int carry = 0; //表示进位 //字符串反转(真正的数字位数 和 字符串下标 刚好是相反的,加法应该从数字低位算起) 且 字符串变数字 int m = { 0 }; int n = { 0 }; int len1 = a.length(), len2 = b.length(); for (int i = 0; i < len1; i++) { m[i] = a[len1 - i - 1] - '0'; //加法应该从数字低位算起 } for (int i = 0; i < len2; i++) { n[i] = b[len2 - i - 1] - '0'; //加法应该从数字低位算起 } //位运算————加法应该从数字低位算起 int len = len1>len2 ? len1 + 1 : len2 + 1; string sum(len, 0); int k; for (k = 0; k < len1 || k < len2; k++) { sum[k] = (m[k] + n[k] + carry) % 10 + '0'; carry = (m[k] + n[k] + carry) / 10; } //处理最高位进位 if (carry) { sum[k] = carry + '0'; } //结果字符串反转 并 输出 reverse(sum.begin(), sum.end()); cout << sum << endl; } int main() { string a, b; cin >> a >> b; bigNumAdd(a, b); return 0; }
3、大数类:
转自:http://blog.csdn.net/hackbuteer1/article/details/6595881
#include<iostream> #include<string> #include<iomanip> #include<algorithm> using namespace std; #define MAXN 9999 #define MAXSIZE 10 #define DLEN 4 class BigNum { private: int a[500]; //可以控制大数的位数 int len; //大数长度 public: BigNum(){ len = 1;memset(a,0,sizeof(a)); } //构造函数 BigNum(const int); //将一个int类型的变量转化为大数 BigNum(const char*); //将一个字符串类型的变量转化为大数 BigNum(const BigNum &); //拷贝构造函数 BigNum &operator=(const BigNum &); //重载赋值运算符,大数之间进行赋值运算 friend istream& operator>>(istream&, BigNum&); //重载输入运算符 friend ostream& operator<<(ostream&, BigNum&); //重载输出运算符 BigNum operator+(const BigNum &) const; //重载加法运算符,两个大数之间的相加运算 BigNum operator-(const BigNum &) const; //重载减法运算符,两个大数之间的相减运算 BigNum operator*(const BigNum &) const; //重载乘法运算符,两个大数之间的相乘运算 BigNum operator/(const int &) const; //重载除法运算符,大数对一个整数进行相除运算 BigNum operator^(const int &) const; //大数的n次方运算 int operator%(const int &) const; //大数对一个int类型的变量进行取模运算 bool operator>(const BigNum & T)const; //大数和另一个大数的大小比较 bool operator>(const int & t)const; //大数和一个int类型的变量的大小比较 void print(); //输出大数 }; BigNum::BigNum(const int b) //将一个int类型的变量转化为大数 { 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) //将一个字符串类型的变量转化为大数 { 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) //拷贝构造函数 { int i; memset(a,0,sizeof(a)); for(i = 0 ; i < len ; i++) a[i] = T.a[i]; } BigNum & BigNum::operator=(const BigNum & n) //重载赋值运算符,大数之间进行赋值运算 { int i; len = n.len; memset(a,0,sizeof(a)); for(i = 0 ; i < len ; i++) a[i] = n.a[i]; return *this; } istream& operator>>(istream & in, BigNum & b) //重载输入运算符 { char ch[MAXSIZE*4]; int i = -1; in>>ch; int l=strlen(ch); int count=0,sum=0; for(i=l-1;i>=0;) { sum = 0; int t=1; for(int j=0;j<4&&i>=0;j++,i--,t*=10) { sum+=(ch[i]-'0')*t; } b.a[count]=sum; count++; } b.len =count++; return in; } ostream& operator<<(ostream& out, BigNum& b) //重载输出运算符 { int i; cout << b.a[b.len - 1]; for(i = b.len - 2 ; i >= 0 ; i--) { cout.width(DLEN); cout.fill('0'); cout << b.a[i]; } return out; } BigNum BigNum::operator+(const BigNum & T) const //两个大数之间的相加运算 { BigNum t(*this); int i,big; //位数 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 //两个大数之间的相减运算 { 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 //两个大数之间的相乘运算 { 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 != 0) 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 //大数对一个整数进行相除运算 { 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 //大数对一个int类型的变量进行取模运算 { 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 //大数的n次方运算 { 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 //大数和另一个大数的大小比较 { 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 //大数和一个int类型的变量的大小比较 { BigNum b(t); return *this>b; } void BigNum::print() //输出大数 { int i; cout << a[len - 1]; for(i = len - 2 ; i >= 0 ; i--) { cout.width(DLEN); cout.fill('0'); cout << a[i]; } cout << endl; } int main(void) { int i,n; BigNum x[101]; //定义大数的对象数组 x[0]=1; for(i=1;i<101;i++) x[i]=x[i-1]*(4*i-2)/(i+1); while(scanf("%d",&n)==1 && n!=-1) { x .print(); } }
附录:
#include <iostream>
#include <string>
using namespace std;
int compare(string str1, string str2)
{
//相等返回0,大于返回1,小于返回-1
if (str1.size()>str2.size()) return 1; //长度长的整数大于长度小的整数
else if (str1.size()<str2.size()) return -1;
else return str1.compare(str2); //若长度相等,则头到尾按位比较
}
string SUB_INT(string str1, string str2);
string ADD_INT(string str1, string str2) {//高精度加法
int sign = 1; //sign 为符号位
string str;
if (str1[0] == '-') {
if (str2[0] == '-') {
sign = -1;
str = ADD_INT(str1.erase(0, 1), str2.erase(0, 1));
}
else {
str = SUB_INT(str2, str1.erase(0, 1));
}
}
else {
if (str2[0] == '-') {
str = SUB_INT(str1, str2.erase(0, 1));
}
else { //把两个整数对齐,短整数前面加0补齐
string::size_type L1, L2;
int i;
L1 = str1.size();
L2 = str2.size();
if (L1<L2) {
for (i = 1; i <= L2 - L1; i++) str1 = "0" + str1;
}
else {
for (i = 1; i <= L1 - L2; i++) str2 = "0" + str2;
}
int int1 = 0, int2 = 0; //int2 记录进位
for (i = str1.size() - 1; i >= 0; i--) {
int1 = (int(str1[i]) - '0' + int(str2[i]) - '0' + int2) % 10;
int2 = (int(str1[i]) - '0' + int(str2[i]) - '0' + int2) / 10;
str = char(int1 + '0') + str;
}
if (int2 != 0) str = char(int2 + '0') + str;
}
}
//运算后处理符号位
if ((sign == -1) && (str[0] != '0')) str = "-" + str;
return str;
}
string SUB_INT(string str1, string str2) {//高精度减法
int sign = 1; //sign 为符号位
string str;
int i, j;
if (str2[0] == '-') {
str = ADD_INT(str1, str2.erase(0, 1));
}
else {
int res = compare(str1, str2);
if (res == 0) return "0";
if (res<0) {
sign = -1;
string temp = str1;
str1 = str2;
str2 = temp;
}
string::size_type tempint;
tempint = str1.size() - str2.size();
for (i = str2.size() - 1; i >= 0; i--) {
if (str1[i + tempint]<str2[i]) {
j = 1;
while (1) {//zhao4zhong1添加
if (str1[i + tempint - j] == '0') {
str1[i + tempint - j] = '9';
j++;
}
else {
str1[i + tempint - j] = char(int(str1[i + tempint - j]) - 1);
break;
}
}
str = char(str1[i + tempint] - str2[i] + ':') + str;
}
else {
str = char(str1[i + tempint] - str2[i] + '0') + str;
}
}
for (i = tempint - 1; i >= 0; i--) str = str1[i] + str;
}
//去除结果中多余的前导0
str.erase(0, str.find_first_not_of('0'));
if (str.empty()) str = "0";
if ((sign == -1) && (str[0] != '0')) str = "-" + str;
return str;
}
string MUL_INT(string str1, string str2) { //高精度乘法
int sign = 1; //sign 为符号位
string str;
if (str1[0] == '-') {
sign *= -1;
str1 = str1.erase(0, 1);
}
if (str2[0] == '-') {
sign *= -1;
str2 = str2.erase(0, 1);
}
int i, j;
string::size_type L1, L2;
L1 = str1.size();
L2 = str2.size();
for (i = L2 - 1; i >= 0; i--)
{
//模拟手工乘法竖式
string tempstr;
int int1 = 0, int2 = 0, int3 = int(str2[i]) - '0';
if (int3 != 0)
{
for (j = 1; j <= (int)(L2 - 1 - i); j++)
tempstr = "0" + tempstr;
for (j = L1 - 1; j >= 0; j--)
{
int1 = (int3*(int(str1[j]) - '0') + int2) % 10;
int2 = (int3*(int(str1[j]) - '0') + int2) / 10;
tempstr = char(int1 + '0') + tempstr;
}
if (int2 != 0) tempstr = char(int2 + '0') + tempstr;
}
str = ADD_INT(str, tempstr);
}
//去除结果中的前导0
str.erase(0, str.find_first_not_of('0'));
if (str.empty()) str = "0";
if ((sign == -1) && (str[0] != '0'))
str = "-" + str;
return str;
}
string DIVIDE_INT(string str1, string str2, int flag) { //高精度除法。flag==1时,返回商; flag==0时,返回余数
string quotient, residue; //定义商和余数
int sign1 = 1, sign2 = 1;
if (str2 == "0") { //判断除数是否为0
quotient = "ERROR!";
residue = "ERROR!";
if (flag == 1) return quotient;
else return residue;
}
if (str1 == "0") { //判断被除数是否为0
quotient = "0";
residue = "0";
}
if (str1[0] == '-') {
str1 = str1.erase(0, 1);
sign1 *= -1;
sign2 = -1;
}
if (str2[0] == '-') {
str2 = str2.erase(0, 1);
sign1 *= -1;
}
int res = compare(str1, str2);
if (res<0) {
quotient = "0";
residue = str1;
}
else if (res == 0) {
quotient = "1";
residue = "0";
}
else {
string::size_type L1, L2;
L1 = str1.size();
L2 = str2.size();
string tempstr;
tempstr.append(str1, 0, L2 - 1);
for (int i = L2 - 1; i<L1; i++) { //模拟手工除法竖式
tempstr = tempstr + str1[i];
tempstr.erase(0, tempstr.find_first_not_of('0'));//zhao4zhong1添加
if (tempstr.empty()) tempstr = "0";//zhao4zhong1添加
for (char ch = '9'; ch >= '0'; ch--) { //试商
string str;
str = str + ch;
if (compare(MUL_INT(str2, str), tempstr) <= 0) {
quotient = quotient + ch;
tempstr = SUB_INT(tempstr, MUL_INT(str2, str));
break;
}
}
}
residue = tempstr;
}
//去除结果中的前导0
quotient.erase(0, quotient.find_first_not_of('0'));
if (quotient.empty()) quotient = "0";
if ((sign1 == -1) && (quotient[0] != '0')) quotient = "-" + quotient;
if ((sign2 == -1) && (residue[0] != '0')) residue = "-" + residue;
if (flag == 1) return quotient;
else return residue;
}
string DIV_INT(string str1, string str2) {//高精度除法,返回商
return DIVIDE_INT(str1, str2, 1);
}
string MOD_INT(string str1, string str2) {//高精度除法,返回余数
return DIVIDE_INT(str1, str2, 0);
}
int main()
{
/*char ch;
string s1, s2, res;
while (cin >> s1 >> ch >> s2) {
switch (ch) {
case '+':res = ADD_INT(s1, s2); break;
case '-':res = SUB_INT(s1, s2); break;
case '*':res = MUL_INT(s1, s2); break;
case '/':res = DIV_INT(s1, s2); break;
case '%':res = MOD_INT(s1, s2); break;
default: break;
}
cout << res << endl;
}
return(0);*/
string s11, s22, res1;
s11 = "1";
s22 = "2";
for (int i = 1; i <= 1000; i++)
{
res1 = MUL_INT(s11, s22); //利用乘法做幂次运算!
s11 = res1;
}
cout << res1 << endl;
return(0);
}
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