求高精度幂数
个人信息：就读于燕大本科软件工程专业 目前大三;
本人博客：google搜索“cqs_2012”即可;
个人爱好：酷爱数据结构和算法，希望将来从事算法工作为人民作出自己的贡献;
编程语言：C++ ;
编程坏境：Windows 7 专业版 x64;
编程工具：vs2008;
制图工具：office 2010 powerpoint;
硬件信息：7G-3 笔记本;
真言题目去往火焰山，炼就红色眼
解法百炼 1001 幂运算
算法用字符串处理。
对这个系统不是很了解，多次尝试后才发现这个系统不兼容很多东西，如下
system（“pause”）；
<Windows.h>
对于输入输出控制，不能按照给的例子指定输入输出的个数，而用while（cin>>）来控制是否继续输入。
哎，一把辛酸泪。
看题：此问题是幂操作，求高精度运算，问题不难，在于细心，考虑整形溢出即可，利用字符串模拟整形运算
个人算法用C++代码表示如下（代码有部分用过以前写过的程序，所以看起来比较乱，但是纯个人写的代码，没有copy）
#include<iostream> #include <string> using namespace std; // 小数的幂次方 string FloatPower(string a,unsigned int b); bool XiaoshuCheck(string a); bool Check_all_number(string a); // 小数乘法 string FloatMult(string a,string b); std::pair<string,int> StandardXiaoshu(string a); string MULT_Int(string a,string b); bool Standardization(string &a); string IntToChar(int i); int CharToNumber(char c); string ADD_Int(string a,string b); string AddInt(string a,string b); string SubInt(string a,string b); char Compare(string a,string b); char CompareXiaoshu(string a,string b); // 小数的幂次方 string FloatPower(string a,unsigned int b) { if(!a.empty() && XiaoshuCheck(a)) { string result = "1"; for(unsigned int i = b-1;i<b;i--) { result = FloatMult(a,result); } if(result[0] == '0'&&result[1] == '.') result = result.substr(1,result.length()-1); return result; } else if(!a.empty() &&! XiaoshuCheck(a)) { string result = "1"; for(unsigned int i = b-1;i<b;i--) { result = MULT_Int(a,result); } return result; } } bool XiaoshuCheck(string a) { bool xiaoshu = false ; string b = a ; // 找出小数点 for(unsigned int i=0;i<b.length();i++) if(b[i] == '.') { xiaoshu = true; // 去掉小数点后判断是否符合整数形式 b = b.substr(0,i)+b.substr(i+1,b.length()-i-1); if(Check_all_number(b) != true) xiaoshu = false; break; } return xiaoshu ; } // 小数乘法 string FloatMult(string a,string b) { // 把小数扩展成整数，然后去操作 // (a*b)/(小数点长度之和) // std::pair<string,int> sa = StandardXiaoshu(a); std::pair<string,int> sb = StandardXiaoshu(b); a = sa.first; b = sb.first; // a*b,得到放大结果 string r = MULT_Int(a,b); // 结果是负数怎么办？把其变成正数 bool fushu = false; if(r[0] == '-') { fushu = true; r = r.substr(1,r.length()-1); } // 结果产生很多 0，并且小数长度大于0 unsigned int maxlength = sa.second + sb.second; while(r[r.length()-1] == '0' && maxlength > 0) { r = r.substr(0,r.length()-1) ; maxlength -- ; } // 如果结果是小数，并且小于1，前面补0 while(r.length() <= maxlength) { r = "0" +r; } if(maxlength == 0 || Compare(r.substr(r.length()-maxlength,maxlength),"0") == '=') r = r.substr(0,r.length()-maxlength); else // 加上小数点 r = r.substr(0,r.length()-maxlength)+"."+r.substr(r.length()-maxlength,maxlength); // 如果结果是负数，怎么办 if(fushu == true) r = '-'+r; // 返回结果 return r; } bool Check_all_number(string a) { if(a.empty()) return false ; string::size_type L = a.size(),i = 0; if(a[0] == '-') i++; while( i < L ) { if( a[i] < '0' || a[i] > '9') return false; i++; } return true ; } std::pair<string,int> StandardXiaoshu(string a) { // 数据域 bool fushu = false ; string b; unsigned int i; // 检查a是否是小数 if(a[0] == '-') { fushu = true; a = a.substr(1,a.length()-1); } // a是小数 if(XiaoshuCheck(a) == true) { // 把小数部分的末尾0去掉 while(true) { if(a[a.length()-1] == '0') a = a.substr(0,a.length()-1); else break; } // 把整数部分的前面的0去掉 for(i=0;i<a.length();i++) if(a[i] == '.') { b = a.substr(0,i); a = a.substr(i+1,a.length()-i-1); break; } Standardization(b); a = b+a; i = a.length() - b.length(); if(fushu == true) a = "-"+a; // 返回值 return std::make_pair(a,i); } // a是整数 else if(Check_all_number(a) == true) { Standardization(a); if(fushu == true) a = "-"+a; return std::make_pair(a,0); } } string MULT_Int(string a,string b) { // exception of input if( a.empty() ) return b; else if( b.empty() ) return "0"; if(!Check_all_number(a) || !Check_all_number(b)) { return "exception of input Multiplies_Int"; } Standardization(a); Standardization(b); string::size_type i = a.size(),j = b.size(); string c = "0",d = ""; bool fushu = (a[0] == '-' && b[0] != '-')||(a[0] != '-' && b[0] == '-'); if(a[0] == '-') a = a.substr(1,a.size()); if(b[0] == '-') b = b.substr(1,b.size()); int jinwei = 0; for( j = b.size()-1 ; j < b.size() ;j--) { // each number of b to * a jinwei = 0; for( i = a.size()-1 ; i < a.size() ;i-- ) { d = IntToChar( ( CharToNumber(a[i]) * CharToNumber(b[j]) + jinwei ) % 10 )+ d ; jinwei = ( CharToNumber(a[i]) * CharToNumber(b[j]) + jinwei ) / 10 ; } if(jinwei) d = IntToChar(jinwei) +d; // add all number result c = ADD_Int(c,d); d = ""; unsigned int zero = 0 ; while( zero < b.size() - j ) { d = d + '0'; zero ++; } } Standardization(c); if( fushu && c != "0" ) return '-'+c; else return c; } bool Standardization(string &a) { if(!Check_all_number(a)) { cout<<a<<" exception of input Standardization"<<endl; return false; } string::size_type i = 0 ; bool fushu = false ; if( a[0] == '-' ) { fushu = true ; i = 1 ; } while(i < a.size()) { if(a[i] != '0') break; i++; } if(i == a.size()) i--; a = a.substr(i,a.size()-i) ; if( fushu && a != "0") a = '-' + a ; return true ; } string IntToChar(int i) { if( i >= 0 && i <= 9 ) { string c = ""; return c+char(i+48); } else { cout<<i<<" exception of input IntToChar"<<endl; return "e"; } } // make char to the int number int CharToNumber(char c) { if( c >= '0' && c <= '9' ) return int(c - '0'); else { cout<<c<<" exception of input CharToNumber "<<endl; return 0; } }; string ADD_Int(string a,string b) { // exception of input if( a.empty() ) return b; else if( b.empty() ) return "0"; if(!Check_all_number(a) || !Check_all_number(b)) { return "exception of input ADD_Int"; } Standardization(a); Standardization(b); if(a[0] != '-' && b[0] != '-') return AddInt(a,b); else if(a[0] != '-'&& b[0] == '-') return SubInt( a,b.substr( 1,b.size() ) ); else if(a[0] == '-'&& b[0] != '-') return SubInt(b,a.substr(1,a.size())); else return '-'+AddInt(a.substr(1,a.size()),b.substr( 1,b.size() )); }; string SubInt(string a,string b) { // exception of input if(!Check_all_number(a) || !Check_all_number(b)) return "exception of input MinusInt"; Standardization(a); Standardization(b); // particular string of input if(a.empty()) { if(b.empty()) return "0"; else return "-"+b; } else if(b.empty()) { return a; } // normal number a < b string c = ""; bool check = true ; if(Compare(a,b) == '=') return "0"; else if(Compare(a,b) == '<') { c = a ; a = b ; b = c ; c = ""; check = false ; } // normal number a >= b string::size_type i = a.size()-1, j = b.size()-1; int jiewei = 0,now; while(i < a.size() && j < b.size()) { now = CharToNumber(a[i]) - CharToNumber(b[j]) - jiewei ; if( now < 0 ) { jiewei = 1; now = 10 + now ; } else jiewei = 0; c = IntToChar(now) + c ; i--;j--; } while(i < a.size()) { now = CharToNumber(a[i]) - jiewei ; if( now < 0 ) { jiewei = 1; now = 10 + now ; } else jiewei = 0; c = IntToChar( now ) + c ; i--; } Standardization(c); if(!check) c = '-' + c; return c; }; string AddInt(string a,string b) { // exception of input if( a.empty() ) return b; else if( b.empty() ) return "0"; if(!Check_all_number(a) || !Check_all_number(b)) { return "exception of input AddInt"; } Standardization(a); Standardization(b); string::size_type i = a.size()-1 ,j = b.size()-1 , k = 0 ; string c = ""; int jinwei = 0; while( i < a.size() && j < b.size() ) { c = IntToChar( ( CharToNumber(a[i]) + CharToNumber(b[j]) + jinwei ) % 10 ) + c; jinwei = ( CharToNumber(a[i]) + CharToNumber(b[j]) + jinwei ) / 10; j--;i--; } while( j < b.size() ) { c = IntToChar( ( CharToNumber(b[j]) + jinwei ) % 10 ) + c; jinwei = ( jinwei + CharToNumber(b[j]) ) / 10; j--; } while( i < a.size() ) { c = IntToChar( ( CharToNumber(a[i]) + jinwei ) % 10 ) + c; jinwei = ( jinwei + CharToNumber(a[i]) ) / 10; i--; } if( jinwei ) c = IntToChar( jinwei ) + c; Standardization(c); return c; }; char Compare(string a,string b) { if(a.empty() || b.empty()) { cout<<"error of input compare"; return 'e'; } else { if(!Check_all_number(a) || !Check_all_number(b)) { return 'e'; } Standardization(a); Standardization(b); if(a[0] == '-' && b[0] != '-') return '<'; else if( a[0] != '-' && b[0] == '-') return '>'; bool fushu = (a[0] == '-'); if(a.size() > b.size() ) return fushu?'<':'>'; else if(a.size() == b.size()) { for(string::size_type i = 0;i < a.size(); i++) { if(a[i] > b[i]) return fushu?'<':'>'; if(a[i] < b[i]) return fushu?'>':'<'; } return '='; } return fushu?'>':'<'; } } char CompareXiaoshu(string a,string b) { if(XiaoshuCheck(a) && XiaoshuCheck(b)) { pair<string,int> sa= StandardXiaoshu(a); pair<string,int> sb= StandardXiaoshu(b); int length = sa.second - sb.second; while(length != 0) { if(length < 0) { sa.first +="0"; length++; } else if(length > 0) { sb.first +="0"; length--; } return Compare(sa.first,sb.first); } } } int main() { string a; int b; while(cin>>a>>b) cout<<FloatPower(a,b)<<endl; //system("pause"); return 0; }
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