AcWing 791. 高精度加法    原题链接    简单

作者： 作者的头像   匆匆_7 ,  2022-05-04 15:57:40 ,  所有人可见 ,  阅读 178

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题目描述

include[HTML_REMOVED]

include[HTML_REMOVED]

using namespace std;

vector[HTML_REMOVED] c;

vector[HTML_REMOVED] add(vector[HTML_REMOVED] &A,vector[HTML_REMOVED] &B)
{

int t=0;
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[HTML_REMOVED]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’);
c=add(A,B);
for(int i=c.size()-1;i>=0;i–)
cout<<c[i];
return 0;
}

样例

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

 vector<int> c;

vector<int> add(vector<int> &A,vector<int> &B)
{

    int t=0;
    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');
    c=add(A,B);
    for(int i=c.size()-1;i>=0;i--)
    cout<<c[i];
    return 0;
}

算法1

(暴力枚举) $O(n^2)$

include[HTML_REMOVED]

include[HTML_REMOVED]

using namespace std;

vector[HTML_REMOVED] c;

vector[HTML_REMOVED] add(vector[HTML_REMOVED] &A,vector[HTML_REMOVED] &B)
{

int t=0;
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[HTML_REMOVED]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’);
c=add(A,B);
for(int i=c.size()-1;i>=0;i–)
cout<<c[i];
return 0;
}

时间复杂度

参考文献

C++ 代码

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

 vector<int> c;

vector<int> add(vector<int> &A,vector<int> &B)
{

    int t=0;
    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');
    c=add(A,B);
    for(int i=c.size()-1;i>=0;i--)
    cout<<c[i];
    return 0;
}

算法2

(暴力枚举) $O(n^2)$

include[HTML_REMOVED]

include[HTML_REMOVED]

using namespace std;

vector[HTML_REMOVED] c;

vector[HTML_REMOVED] add(vector[HTML_REMOVED] &A,vector[HTML_REMOVED] &B)
{

int t=0;
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[HTML_REMOVED]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’);
c=add(A,B);
for(int i=c.size()-1;i>=0;i–)
cout<<c[i];
return 0;
}

时间复杂度

参考文献

C++ 代码

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

 vector<int> c;

vector<int> add(vector<int> &A,vector<int> &B)
{

    int t=0;
    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');
    c=add(A,B);
    for(int i=c.size()-1;i>=0;i--)
    cout<<c[i];
    return 0;
}

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