高精度(大数)加减乘除

一般大数的运算会超过long long的长度 那我们自然就想到用到数组去存储

• 加法和减法就是按照小学的思想 一位一位的对应加减
• 乘法和除法复杂一些,但是本质上也是小学运算的思想

加法

#include<iostream>
#include<vector>
using namespace std;
vector<int> addBig(vector<int> &A,vector<int> &B){
    int t = 0;
    vector<int> C;
    for(int i=0; i < A.size() || i < B.size(); i++){
        if (i < A.size()) t+=A[i];
        if (i < B.size()) t+=B[i];
        C.push_back(t%10);
        t/=10;
    }
    if (t) C.push_back(1);
    return C;
}
int main(){
    string a,b;

    cin>>a>>b;
    vector<int> A, B;
    for(int i=a.size()-1; i>=0; i--){
        A.push_back(a[i]-'0');
    }
    for(int i=b.size()-1; i>=0; i--){
        B.push_back(b[i]-'0');
    }
    auto C = addBig(A,B);
    for(int i=C.size()-1; i>=0; i--){
        printf("%d",C[i]);
    }
}

减法

#include<iostream>
#include<vector>
using namespace std;
bool flag = true;
bool cmp(vector<int> &A, vector<int> &B){
	if (A.size() != B.size()) return A.size()>B.size();
	for (int i = A.size()-1; i>=0; i--){
		if (A[i]!=B[i]){
			return A[i]>B[i];
		}
	}
	return true;
}
vector<int> removeab(vector<int> &A, vector<int> &B){
    int t = 0;
    vector<int> C;
    for(int i = 0,t=0; i < A.size(); i++){
        t= A[i]-t;
        if(i < B.size()) t -= B[i];
        C.push_back((t+10)%10);
        if(t<0) t = 1;
		else t = 0; 
    }
    while(C.size()>1 && C.back() == 0){
        C.pop_back();
    }
    return C;
}

int main(){
    string a,b;
    vector<int> A,B;
    cin>>a>>b;
    for(int i = a.size()-1; i >= 0; i--) {
        A.push_back(a[i]-'0');
    }
    for(int i = b.size()-1; i >= 0; i--) {
        B.push_back(b[i]-'0');
    }
    
    if (cmp(A,B)){
        vector<int> C = removeab(A,B);
        for(int i = C.size()-1; i >= 0; i--){
    		printf("%d",C[i]);
    	}
    }else{
		
        vector<int> C = removeab(B,A);
        cout<<'-';
        for(int i = C.size()-1; i >= 0; i--){
    		printf("%d",C[i]);
    	}
    }
    return 0;
    
}

乘法

#include<iostream>
#include<vector>
using namespace std;
vector<int> multi(vector<int> &A,int b){
    int t = 0;
    vector<int> C;
    for(int i = 0; i < A.size() || t; i++){
        if(i<A.size()){
            t+=A[i]*b;
        }
        C.push_back(t%10);
        t=t/10;
    }
    return C;
}

int main(){
    string a;
    int b;
    vector<int> A;
    cin>>a>>b;
    for(int i = a.size()-1; i >= 0; i--) {
        A.push_back(a[i]-'0');
    }
    if(b==0||a=="0"){
        cout<<0<<endl;;
    }else{
        
    auto C = multi(A,b);
    for(int i = C.size()-1; i>=0 ; i--) {
        printf("%d", C[i]);
    }
    }
    
    
}

除法

#include<iostream>
#include<vector>
#include<algorithm>
int r;
using namespace std;
vector<int> div(vector<int> &A,int b, int &r){
    vector<int> C;
    r = 0;
    for(int i = A.size()-1;i >= 0; i--){
        r = r*10+A[i];
        C.push_back(r/b);
        r = r%b;    
    }
    reverse(C.begin(),C.end());
    while(C.size()>1 && C.back()==0) C.pop_back();

    
    return C;
}

int main(){
    string a;
    int b;
    cin>>a>>b;
    vector<int> A;
    for (int i = a.size()-1;i>=0;i--){
        A.push_back(a[i]-'0');
    }
    
    auto C = div(A,b,r);
    for(int i = C.size()-1;i >=0;i--){
        printf("%d",C[i]);
    }
    cout<<endl<<r<<endl;
    
}