C++高精度算法完全入门教程#

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#include <iostream>
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#include <vector>
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#include <string>
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#include <algorithm>
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using namespace std;
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vector<int> stringToVector(string s) {
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    vector<int> num;
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    for (int i = s.length() - 1; i >= 0; i--) {
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        num.push_back(s[i] - '0');
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    }
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    return num;
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}
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string vectorToString(vector<int> num) {
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    string s = "";
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    bool started = false;
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    for (int i = num.size() - 1; i >= 0; i--) {
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        if (num[i] != 0) started = true;
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        if (started) s += (num[i] + '0');
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    }
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    return (s == "") ? "0" : s;
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}
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bool compare(vector<int> A, vector<int> B) {
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    if (A.size() != B.size()) return A.size() > B.size();
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    for (int i = A.size() - 1; i >= 0; i--) {
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        if (A[i] != B[i]) return A[i] > B[i];
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    }
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    return true;
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}
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vector<int> add(vector<int> A, vector<int> B) {
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    vector<int> C;
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    int carry = 0;
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    for (int i = 0; i < A.size() || i < B.size(); i++) {
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        int x = (i < A.size()) ? A[i] : 0;
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        int y = (i < B.size()) ? B[i] : 0;
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        int sum = x + y + carry;
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        C.push_back(sum % 10);
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        carry = sum / 10;
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    }
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    if (carry > 0) C.push_back(carry);
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    return C;
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}
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vector<int> subtract(vector<int> A, vector<int> B) {
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    vector<int> C;
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    int borrow = 0;
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    for (int i = 0; i < A.size(); i++) {
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        int x = A[i];
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        int y = (i < B.size()) ? B[i] : 0;
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        int diff = x - y - borrow;
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        if (diff < 0) {
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            diff += 10;
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            borrow = 1;
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        } else {
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            borrow = 0;
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        }
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        C.push_back(diff);
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    }
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    while (C.size() > 1 && C.back() == 0) C.pop_back();
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    return C;
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}
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vector<int> multiplyInt(vector<int> A, int b) {
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    vector<int> C;
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    int carry = 0;
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    for (int i = 0; i < A.size(); i++) {
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        int product = A[i] * b + carry;
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        C.push_back(product % 10);
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        carry = product / 10;
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    }
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    while (carry > 0) {
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        C.push_back(carry % 10);
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        carry /= 10;
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    }
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    while (C.size() > 1 && C.back() == 0) C.pop_back();
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    return C;
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}
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vector<int> multiply(vector<int> A, vector<int> B) {
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    vector<int> C(A.size() + B.size(), 0);
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    for (int i = 0; i < A.size(); i++) {
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        for (int j = 0; j < B.size(); j++) {
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            C[i + j] += A[i] * B[j];
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        }
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    }
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    for (int i = 0; i < C.size() - 1; i++) {
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        if (C[i] >= 10) {
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            C[i + 1] += C[i] / 10;
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            C[i] %= 10;
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        }
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    }
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    while (C.size() > 1 && C.back() == 0) C.pop_back();
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    return C;
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}
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vector<int> divide(vector<int> A, int b, int &r) {
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    vector<int> C;
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    r = 0;
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    for (int i = A.size() - 1; i >= 0; i--) {
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        r = r * 10 + A[i];
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        C.push_back(r / b);
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        r %= b;
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    }
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    reverse(C.begin(), C.end());
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    while (C.size() > 1 && C.back() == 0) C.pop_back();
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    return C;
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}
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int main() {
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    cout << "=== C++高精度计算器 ===" << endl;
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    cout << "1.加法 2.减法 3.乘法(×小数) 4.乘法(×大数) 5.除法" << endl;
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    int choice;
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    cin >> choice;
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    string a, b;
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    vector<int> A, B, C;
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    if (choice == 1) {
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        cin >> a >> b;
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        A = stringToVector(a);
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        B = stringToVector(b);
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        C = add(A, B);
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        cout << vectorToString(C) << endl;
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    }
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    else if (choice == 2) {
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        cin >> a >> b;
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        A = stringToVector(a);
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        B = stringToVector(b);
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        if (!compare(A, B)) {
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            swap(A, B);
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            cout << "-";
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        }
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        C = subtract(A, B);
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        cout << vectorToString(C) << endl;
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    }
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    else if (choice == 3) {
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        int num;
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        cin >> a >> num;
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        A = stringToVector(a);
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        C = multiplyInt(A, num);
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        cout << vectorToString(C) << endl;
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    }
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    else if (choice == 4) {
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        cin >> a >> b;
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        A = stringToVector(a);
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        B = stringToVector(b);
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        C = multiply(A, B);
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        cout << vectorToString(C) << endl;
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    }
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    else if (choice == 5) {
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        int num, remainder;
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        cin >> a >> num;
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        A = stringToVector(a);
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        C = divide(A, num, remainder);
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        cout << "商：" << vectorToString(C) << endl;
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        cout << "余数：" << remainder << endl;
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    }
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    return 0;
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}