【基础算法篇】高精度运算

算法基础笔记

发布日期: 2022-05-18

文章字数: 686

阅读时长: 4 分

阅读次数:

高精度加法

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

vector<int> add(vector<int> &A, vector<int> &B)
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    vector<int> C;
    int t = 0;
    for(int i = 0; i < A.size() || i < B.size(); i ++)
    &#123;
        if(i < A.size()) t += A[i];
        if(i < B.size()) t += B[i];
        C.push_back(t % 10);
        t /= 10;
    &#125;
    if(t) C.push_back(1);
    return C;
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int main()
&#123;
    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');

    auto C = add(A, B);
    for(int i = C.size() - 1; i >= 0; i --) cout << C[i];


    return 0;
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高精度减法

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

bool cmp(vector<int> &A, vector<int> &B)
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    if(A.size() != B.size()) return A.size() > B.size();
    for(int i = A.size() - 1; i >= 0; i --)
    &#123;
        if(A[i] != B[i]) return A[i] > B[i];
    &#125;
    return true;
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vector<int> sub(vector<int> &A, vector<int> &B)
&#123;
    vector<int> C;
    int t = 0;
    for(int i = 0; i < A.size(); i ++)
    &#123;
        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;
    &#125;

    // 不输出0
    while(C.size() > 1 && C.back() == 0) C.pop_back();

    return C;
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int main()
&#123;
    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))
    &#123;
        auto C = sub(A, B);
        for(int i = C.size() - 1; i >= 0; i --) cout << C[i];
    &#125;
    else
    &#123;
        auto C = sub(B, A);
        cout << "-";
        for(int i = C.size() - 1; i >= 0; i --) cout << C[i];
    &#125;

    return 0;
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高精度乘法

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

vector<int> mul(vector<int> &A, int b)
&#123;
    vector<int> C;
    int t = 0;
    for(int i = 0; i < A.size() || t; i ++)
    &#123;
        if(i < A.size()) t += A[i] * b;
        C.push_back(t % 10);
        t /= 10;
    &#125;

    while(C.size() > 1 && C.back() == 0) C.pop_back();
    return C;
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int main()
&#123;
    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');

    auto C = mul(A, b);
    for(int i = C.size() - 1; i >= 0; i --) cout << C[i];


    return 0;
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高精度除法

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

vector<int> div(vector<int> &A, int b, int &r)
&#123;
    vector<int> C;
    r = 0;
    for(int i = A.size() - 1; i >= 0; i --)
    &#123;
        r = r * 10 + A[i];
        C.push_back(r / b);
        r = r % b;
    &#125;

    reverse(C.begin(), C.end());

    while(C.size() > 1 && C.back() == 0) C.pop_back();
    return C;
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int main()
&#123;
    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');

    int r = 0; // 余数
    auto C = div(A, b, r);
    for(int i = C.size() - 1; i >= 0; i --) cout << C[i];
    cout << endl << r;
    return 0;
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