高精度算法

题目一 高精度加法

代码实现

#include<iostream>
#include<vector>
#include<algorithm>

using namespace std;

vector<int>a,b;

vector<int>add(vector<int>&a,vector<int>&b)
{
    int t=0,plus=0,i=0;
    vector<int>c;
    for(i;i<a.size()&&i<b.size();i++)
    {
        plus=a[i]+b[i]+t;
        c.push_back(plus%10);
        t=plus/10;
    }
    while(i<a.size())//a比较大时
    {
        plus=a[i++]+t;
        c.push_back(plus%10);
        t=plus/10;
    }
    while(i<b.size())//b比较大时
    {
        plus=b[i++]+t;
        c.push_back(plus%10);
        t=plus/10;
    }
    if(t)//最后一次加法若有进位则末尾+1
    {
        c.push_back(1);
    }
    return c;
}

int main()
{
    string A,B;
    cin>>A>>B;
    for(int i=A.size()-1;i>=0;i--)//倒序存储
    {
        a.push_back(A[i]-'0');
    }
    for(int i=B.size()-1;i>=0;i--)
    {
        b.push_back(B[i]-'0');
    }
    vector<int>c=add(a,b);
    for(int i=c.size()-1;i>=0;i--)//倒序输出
    {
        printf("%d",c[i]);
    }
    return 0;
}

题目二 高精度减法

代码实现

#include<iostream>
#include<algorithm>

using namespace std;

vector<int> a, b;

bool check(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>sub (vector<int> &a, vector<int> &b)
{
    int t = 0, i = 0, sub = 0;
    vector<int> c;
    for (i; i < a.size(); i ++)
    {
        if (i < b.size())
        {
            sub = a[i] - b[i] - t;
        }
        else
        {
            sub = a[i] - t;
        }
        
        if (sub < 0)
        {
            t = 1;
            sub += 10;
        }
        else
        {
            t = 0;
        }
        
        c.push_back(sub % 10);
    }
    
    while (c.back() == 0 && c.size() > 1)
    {
        c.pop_back();
    }
    
    return c;
}

int main()
{
    string 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');
    }
    
    vector<int> c;
    if (!check(a, b))
    {
        cout << -1;
        c = sub(b, a);
    }
    else
    {
        c = sub(a, b);
    }
    
    for (int i = c.size() - 1; i >= 0; i --)
    {
        printf("%d", c[i]);
    }
    return 0;
}

题目三 高精度乘法

代码实现

#include<iostream>
#include<algorithm>

using namespace std;

vector<int> a;

vector<int> mul(vector<int> &a, int b)
{
    vector<int>c;
    int mul = 0, t = 0, i = 0;
    
    while(i < a.size())
    {
        mul = a[i] * b + t;
        c.push_back(mul % 10);
        t = mul / 10;
        i ++;
    }
    
    if (t)
    {
        c.push_back(t);
    }
    
    while (c.back() == 0 && c.size() > 1)
    {
        c.pop_back();
    }
    return c;
}

int main()
{
    string A;
    int B;
    cin >> A >> B;
    
    for (int i = A.size() - 1; i >= 0; i --)
    {
        a.push_back(A[i] - '0');
    }
    
    vector<int> c = mul(a, B);
    
    for (int i = c.size() - 1; i >= 0; i --)
    {
        printf("%d", c[i]);
    }
    return 0;
}

题目四 高精度除法

代码实现

#include<iostream>
#include<algorithm>

using namespace std;

vector<int> a;

void div(vector<int> &a, int b)
{
    vector<int> c;
    int i = a.size() - 1, mul = 0, res = 0;
    
    while (i >= 0)
    {
        mul = (res * 10 + a[i]) / b;
        c.push_back(mul);
        res = (res * 10 + a[i]) % b;
        i --;
    }
    
    reverse(c.begin(), c.end());
    
    while (c.back() == 0 && c.size() > 1)
    {
        c.pop_back();
    }
    
    for (int i = c.size() - 1; i >= 0; i --)
    {
        printf("%d", c[i]);
    }
    
    cout << endl << res;
}

int main()
{
    string A;
    int B;
    cin >> A >> B;
    
    for (int i = A.size() - 1; i >= 0; i --)
    {
        a.push_back(A[i] - '0');
    }
    
    div(a, B);
    return 0;
}