五大常用算法（一） 分治算法(2) 大整数乘法

普通算法：参考自：http://wangxiaosu0501.blog.163.com/blog/static/11565259920110495415730/

 

#include <iostream>
#include <string>
#include <vector>
using namespace std;

vector<int> multiply(vector<int> v1,vector<int> v2);
int main(){
vector<int> v1;
vector<int> v2;
string str1;
string str2;
cout<<"type in 2 bigNumber:"<<endl;
cin >> str1 >> str2;
for(int i = str1.size()-1;i>=0; i--)
v1.push_back(str1[i] - '0');
for(int i = str2.size()-1;i>=0; i--)
v2.push_back(str2[i]-'0');

vector<int> v = multiply(v1,v2);
for(int i = v.size()-1;i>=0;--i)
cout<<v[i];
cout<<endl;
return 0;
}

vector<int> multiply(vector<int> v1,vector<int> v2){
int m = v1.size();
int n = v2.size();
vector<int> v(m*n+2,0);//Constructor!
for(int i = 0; i != v2.size(); i++){
int k = i;
for(int j = 0;j != v1.size(); j++)
v[k++] += v2[i]*v1[j];
}
for(vector<int>::iterator i = v.begin(); i!=v.end();i++)
if(*i>9){
(*(i+1)) += (*i)/10;
(*i) %= 10;
}
vector<int>::iterator i = (--v.end());
while(*i == 0){
v.pop_back();
i = (--v.end());
}
return v;
}

以下代码参考自：http://blog.csdn.net/sophie_wise8/article/details/7669116

#include <iostream>
#include <sstream>
#include <string>
using namespace std;
int string_to_num(string k){
int back;
stringstream instr(k);
instr>>back;
return back;
}
string num_to_string(int intValue){
string result;
stringstream stream;
stream<<intValue;
stream>>result;
return result;
}
string stringBeforeZero(string str,int s){
for(int i = 0; i < s; i++){
str.insert(0,"0");
}
return str;
}
string stringAddstring(string str1,string str2){
if(str1.size() > str2.size()){
str2 = stringBeforeZero(str2,str1.size()-str2.size());
}else if(str1.size() < str2.size()){
str1 = stringBeforeZero(str1,str2.size()-str1.size());
}
string result;
int flag = 0;
for(int i = str1.size()-1; i >= 0; i--){
int c = (str1[i]-'0')+(str2[i]-'0')+flag;
flag = c/10;
c %= 10;
result.insert(0,num_to_string(c));
}
if(0!=flag){
result.insert(0,num_to_string(flag));
}
return result;
}
string stringSubtractstring(string str1,string str2){
while('0' == str1[0] && str1.size() > 1){
str1 = str1.substr(1,str1.size()-1);
}
while('0' == str2[0]&&str2.size() > 1){
str2 = str2.substr(1,str2.size()-1);
}
if(str1.size() > str2.size()){
str2 = stringBeforeZero(str2,str1.size()-str2.size());
}
string result;
for(int i = str1.size() - 1;i >= 0;i--){
int c= (str1[i] - '0')-(str2[i] - '0');
if(c < 0){
c += 10;
int prePos = i - 1;
char preChar = str1[prePos];
while('0' == preChar){
str1[prePos]='9';
prePos -= 1;
preChar = str1[prePos];
}
str1[prePos] -= 1;
}
result.insert(0,num_to_string(c));
}
return result;
}
string stringFollowZero(string str,int s){
for(int i = 0; i < s; i++)
str.insert(str.size(),"0");
return str;
}
string IntMult(string x,string y){
while('0' == x[0] && x.size() > 1){
x = x.substr(1,x.size()-1);
}
while('0' == y[0]&&y.size() > 1){
y = y.substr(1,y.size()-1);
}
int f = 4;
if(x.size() > 2 || y.size() > 2){
if(x.size() >= y.size()){
while(x.size() > f){
f *= 2;
}
if(x.size() != f){
x = stringBeforeZero(x,f-x.size());
y = stringBeforeZero(y,f-y.size());
}
}else{
while(y.size() > f){
f *= 2;
}
if(y.size() != f){
x = stringBeforeZero(x,f-x.size());
y = stringBeforeZero(y,f-y.size());
}
}
}
if(1 == x.size()){
x = stringBeforeZero(x,1);
}
if(1 == y.size()){
y = stringBeforeZero(y,1);
}
if(x.size() > y.size()){
y = stringBeforeZero(y,x.size()-y.size());
}
if(x.size() < y.size()){
x = stringBeforeZero(x,y.size() - x.size());
}
int s = x.size();
string a1,a0,b1,b0;
if(s > 1){
a1 = x.substr(0,s/2);
a0 = x.substr(s/2,s-1);
b1 = y.substr(0,s/2);
b0 = y.substr(s/2,s-1);
}
string result;
if(s == 2){
int na = string_to_num(a1);
int nb = string_to_num(a0);
int nc = string_to_num(b1);
int nd = string_to_num(b0);
result = num_to_string((na*10+nb)*(nc*10+nd));
}
else{
string c2 = IntMult(a1,b1);
string c0 = IntMult(a0,b0);
string c1_1 = stringAddstring(a1,a0);
string c1_2 = stringAddstring(b1,b0);
string c1_3 = IntMult(c1_1,c1_2);
string c1_4 = stringAddstring(c2,c0);
string c1 = stringSubtractstring(c1_3,c1_4);
string s1 = stringFollowZero(c1,s/2);
string s2 = stringFollowZero(c2,s);
result = stringAddstring(stringAddstring(s2,s1),c0);
}
return result;
}
int main(){
int f = 1;
while(1 == f){
string A,B,C,D;
string num1,num2;
string r;
cout<<"大整数乘法运算（分治法):"<<endl;
cout<<"输入第一个大整数:";
cin >> num1;
int i = 0;
for(i = 0; i < num1.size(); i++){
if(num1[i] < '0' || num1[i] > '9'){
cout << "您输入的数据不合法，请重新输入：";
cin >> num1;
i = -1;
}
}
cout << "请输入第二个大整数：";
cin >> num2;
for(i = 0; i < num2.size(); i++){
if(num2[i] < '0' || num2[i] > '9'){
cout << "您输入的数据不合法，请重新输入：";
cin >> num2;
i = -1;
}
}
r = IntMult(num1,num2);
while('0' == r[0] && r.size() > 1){
r = r.substr(1,r.size() - 1);
}
cout << "结果："<<endl;
cout << r << endl;
}
}