高精度加、减、乘笔记

#include<iostream>
using namespace std;
// 高精度加法
string jia(string a, string b){
int lena = a.length();
int lenb = b.length();
int lenc = max(lena, lenb);
int aa[2005]={0},bb[2005]={0},cc[2005]={0};
string c = "";
for(int i=0;i<lena;i++) aa[i] = a[lena-i-1]-48;
for(int i=0;i<lenb;i++) bb[i] = b[lenb-i-1]-48;
int x = 0;
for(int i=0;i<lenc;i++){
cc[i] = aa[i] + bb[i] + x;
x = cc[i]/10;
cc[i] = cc[i]%10;
}
cc[lenc++] = x;
while(cc[lenc-1]==0&&lenc-1>0) lenc--;
for(int i=0;i<lenc;i++) c += char(cc[lenc-i-1]+48);
return c;
}
// 高精度数大小判断
bool max_a(string a, string b){
int lena = a.length();
int lenb = b.length();
if(lena!=lenb) return lena>lenb;
else{
for(int i=0;i<lena;i++){
if(a[i] == b[i]) continue;
return a[i]>b[i];
}
}
return true;
}
// 高精度减法
string jian(string a, string b){
string c;
if(!max_a(a,b)){
c = a;
a = b;
b = c;
c = "-";
}
int lena = a.length();
int lenb = b.length();
int lenc = max(lena, lenb);
int aa[2005]={0},bb[2005]={0},cc[2005]={0};
for(int i=0;i<lena;i++) aa[i] = a[lena-i-1]-48;
for(int i=0;i<lenb;i++) bb[i] = b[lenb-i-1]-48;
int x = 0;
for(int i=0;i<lenc;i++){
cc[i] = aa[i] - bb[i] - x;
if(cc[i]<0){
cc[i] += 10;
x = 1;
}
else x = 0;
}
cc[lenc++] = x;
while(cc[lenc-1]==0&&lenc-1>0) lenc--;
for(int i=0;i<lenc;i++) c += char(cc[lenc-i-1]+48);
return c;
}
// 高精度乘法
string cheng(string a, string b){
string s = "";
int aa[505] = {0}, bb[505] = {0}, cc[1005] = {0};
int lena = a.length();
int lenb = b.length();
int len = lena+lenb-1;
<span class="hl-keyword hl-control hl-c++">for</span><span class="hl-meta hl-group hl-c++"><span class="hl-punctuation hl-section hl-group hl-begin hl-c++">(</span><span class="hl-storage hl-type hl-c">int</span> i<span class="hl-keyword hl-operator hl-assignment hl-c">=</span><span class="hl-constant hl-numeric hl-c++">0</span><span class="hl-punctuation hl-terminator hl-c++">;</span>i<span class="hl-keyword hl-operator hl-comparison hl-c">&lt;</span>lena<span class="hl-punctuation hl-terminator hl-c++">;</span>i<span class="hl-keyword hl-operator hl-arithmetic hl-c">+</span><span class="hl-keyword hl-operator hl-arithmetic hl-c">+</span><span class="hl-punctuation hl-section hl-group hl-end hl-c++">)</span></span><span class="hl-meta hl-block hl-c++"><span class="hl-punctuation hl-section hl-block hl-begin hl-c++">{</span>
	aa<span class="hl-meta hl-brackets hl-c++"><span class="hl-punctuation hl-section hl-brackets hl-begin hl-c++">[</span>i<span class="hl-punctuation hl-section hl-brackets hl-end hl-c++">]</span></span> <span class="hl-keyword hl-operator hl-assignment hl-c">=</span> a<span class="hl-meta hl-brackets hl-c++"><span class="hl-punctuation hl-section hl-brackets hl-begin hl-c++">[</span>lena<span class="hl-keyword hl-operator hl-arithmetic hl-c">-</span><span class="hl-constant hl-numeric hl-c++">1</span><span class="hl-keyword hl-operator hl-arithmetic hl-c">-</span>i<span class="hl-punctuation hl-section hl-brackets hl-end hl-c++">]</span></span> <span class="hl-keyword hl-operator hl-arithmetic hl-c">-</span> <span class="hl-constant hl-numeric hl-c++">48</span><span class="hl-punctuation hl-terminator hl-c++">;</span>
<span class="hl-punctuation hl-section hl-block hl-end hl-c++">}</span></span>
<span class="hl-keyword hl-control hl-c++">for</span><span class="hl-meta hl-group hl-c++"><span class="hl-punctuation hl-section hl-group hl-begin hl-c++">(</span><span class="hl-storage hl-type hl-c">int</span> i<span class="hl-keyword hl-operator hl-assignment hl-c">=</span><span class="hl-constant hl-numeric hl-c++">0</span><span class="hl-punctuation hl-terminator hl-c++">;</span>i<span class="hl-keyword hl-operator hl-comparison hl-c">&lt;</span>lenb<span class="hl-punctuation hl-terminator hl-c++">;</span>i<span class="hl-keyword hl-operator hl-arithmetic hl-c">+</span><span class="hl-keyword hl-operator hl-arithmetic hl-c">+</span><span class="hl-punctuation hl-section hl-group hl-end hl-c++">)</span></span><span class="hl-meta hl-block hl-c++"><span class="hl-punctuation hl-section hl-block hl-begin hl-c++">{</span>
	bb<span class="hl-meta hl-brackets hl-c++"><span class="hl-punctuation hl-section hl-brackets hl-begin hl-c++">[</span>i<span class="hl-punctuation hl-section hl-brackets hl-end hl-c++">]</span></span> <span class="hl-keyword hl-operator hl-assignment hl-c">=</span> b<span class="hl-meta hl-brackets hl-c++"><span class="hl-punctuation hl-section hl-brackets hl-begin hl-c++">[</span>lenb<span class="hl-keyword hl-operator hl-arithmetic hl-c">-</span><span class="hl-constant hl-numeric hl-c++">1</span><span class="hl-keyword hl-operator hl-arithmetic hl-c">-</span>i<span class="hl-punctuation hl-section hl-brackets hl-end hl-c++">]</span></span> <span class="hl-keyword hl-operator hl-arithmetic hl-c">-</span> <span class="hl-constant hl-numeric hl-c++">48</span><span class="hl-punctuation hl-terminator hl-c++">;</span>
<span class="hl-punctuation hl-section hl-block hl-end hl-c++">}</span></span>
<span class="hl-comment hl-line hl-double-slash hl-c"><span class="hl-punctuation hl-definition hl-comment hl-c">//</span> 乘法核心

	for(int i=0;i<lena;i++){
for(int j=0;j<lenb;j++){
cc[i+j] += aa[i]*bb[j];
cc[i+j+1] += cc[i+j]/10;
cc[i+j] %= 10;
if(cc[len]) len++;
}
}
// 防止结果为零
	while(cc[len-1] == 0 && len-1>0) len--;
for(int i=len-1;i>=0;i--){
s += char(cc[i]+48);
}
return s;
}
int main(){
string a,b,c;
cin>>a>>b>>c;
cout<<jian(jia(a,b),c);
return 0;
}