首页 程序设计 基础算法

# 高精度加法

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string add(string a, string b) {
    vector<int> a, b, c;

    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');
    int t = 0;
    for (int i = 0; i < max(a.size(), 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(t);

    string res = "";
    for (int i = c.size() - 1; i >= 0; i--)
        res += to_string(c[i]);
    return res;
}

# 高精度乘法

# 高精度 × 低精度

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string mul(string aa, int b) {
    vector<int> a, c;
    int t = 0;
    for (int i = aa.size() - 1; i >= 0; i--)
        a.push_back(aa[i] - '0');

    for (int i = 0; i < a.size() || t; i++) {
        if (i < a.size())
            t += a[i] * b;

        c.push_back(t % 10), t /= 10;
    }

    while (c.size() > 1 && c.back() == 0)
        c.pop_back();

    string res = "";
    for (int i = c.size() - 1; i >= 0; i--)
        res += to_string(c[i]);

    return res;
}

# 高精度 × 高精度

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string mul(string aa, string bb) {
    vector<int> a, b, c(aa.size() + bb.size(), 0);

    for (int i = aa.size() - 1; i >= 0; i--)
        a.push_back(aa[i] - '0');
    for (int i = bb.size() - 1; i >= 0; i--)
        b.push_back(bb[i] - '0');

    for (int i = 0; i < b.size(); i++)
        for (int j = 0; j < a.size(); j++)
            c[i + j] += a[j] * b[i];

    for (int i = 0; i < c.size() - 1; i++) {
        if (c[i] > 9) {
            c[i + 1] += c[i] / 10;
            c[i] %= 10;
        }
    }

    int len = c.size() - 1;
    while (len > 0 && c[len] == 0)
        len--;

    string res = "";
    for (int i = len; i >= 0; i--)
        res += to_string(c[i]);

    return res;
}

# 高精度减法

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// 比较大小
bool compare(vector<int> &a, vector<int> &b) {
    if (a.size() != b.size())
        return a.size() > b.size();
    else {
        for(int i = a.size() - 1; i >= 0; i--)
            if (a[i] != b[i])
                return a[i] > b[i];
        return 1;
    }

}

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

# 高精度除法

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