求高精度冪數

標籤：面試題

求高精度冪數

個人資訊：就讀於燕大本科軟體工程專業 目前大三;

本人部落格：google搜尋“cqs_2012”即可;

個人愛好：酷愛資料結構和演算法，希望將來從事演算法工作為人民作出自己的貢獻;

程式設計語言：C++ ;

編程壞境：Windows 7 專業版 x64;

編程工具：vs2008;

製圖工具：office 2010 powerpoint;

硬體資訊：7G-3 筆記本;

真言

去往火焰山，煉就紅色眼

題目

百鍊 1001 冪運算

網址 http://bailian.openjudge.cn/practice/1001/

解法

用字串處理。

對這個系統不是很瞭解，多次嘗試後才發現這個系統不相容很多東西，如下

system（“pause”）；

<Windows.h>

對於輸入輸出控制，不能按照給的例子指定輸入輸出的個數，而用while（cin>>）來控制是否繼續輸入。

哎，一把辛酸淚。

看題：此問題是冪操作，求高精度運算，問題不難，在於細心，考慮整形溢出即可，利用字串類比整形運算

演算法

個人演算法用C++代碼錶示如下（代碼有部分用過以前寫過的程式，所以看起來比較亂，但是純個人寫的代碼，沒有copy）

#include<iostream>#include <string>using namespace std;// 小數的冪次方string FloatPower(string a,unsigned int b);bool XiaoshuCheck(string a);bool Check_all_number(string a);// 小數乘法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);// 小數的冪次方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 ;// 找出小數點for(unsigned int i=0;i<b.length();i++)if(b[i] == '.'){xiaoshu = true;// 去掉小數點後判斷是否符合整數形式b = b.substr(0,i)+b.substr(i+1,b.length()-i-1);if(Check_all_number(b) != true)xiaoshu = false;break;}return xiaoshu ;}// 小數乘法string FloatMult(string a,string b){// 把小數擴充成整數，然後去操作// (a*b)/(小數點長度之和)// std::pair<string,int> sa = StandardXiaoshu(a);std::pair<string,int> sb = StandardXiaoshu(b);a = sa.first;b = sb.first;// a*b,得到放大結果string r = MULT_Int(a,b);// 結果是負數怎麼辦？把其變成正數bool fushu = false;if(r[0] == '-'){fushu = true;r = r.substr(1,r.length()-1);}// 結果產生很多 0，並且小數長度大於0unsigned int maxlength = sa.second + sb.second;while(r[r.length()-1] == '0' && maxlength > 0){r = r.substr(0,r.length()-1) ;maxlength -- ;}// 如果結果是小數，並且小於1，前面補0while(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// 加上小數點r = r.substr(0,r.length()-maxlength)+"."+r.substr(r.length()-maxlength,maxlength);// 如果結果是負數，怎麼辦if(fushu == true)r = '-'+r;// 返回結果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){// 資料域bool fushu = false ;string b;unsigned int i;// 檢查a是否是小數if(a[0] == '-'){fushu = true;a = a.substr(1,a.length()-1);}// a是小數if(XiaoshuCheck(a) == true){// 把小數部分的末尾0去掉while(true){if(a[a.length()-1] == '0')a = a.substr(0,a.length()-1);else break;}// 把整數部分的前面的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;// 傳回值return std::make_pair(a,i);}// a是整數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 inputif( 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 resultc = 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 numberint 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 inputif( 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 inputif(!Check_all_number(a) || !Check_all_number(b))return "exception of input MinusInt";Standardization(a);Standardization(b);// particular string of inputif(a.empty()){if(b.empty())return "0";elsereturn "-"+b;}else if(b.empty()){return a;}// normal number a < bstring 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 >= bstring::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 inputif( 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;}