写一篇用矩阵快速幂加速的高精度加法c++代码

以下是使用矩阵快速幂加速的高精度加法的 C++ 代码示例：

#include <iostream>
#include <vector>

using namespace std;

const int MOD = 1000000007;
const int MAX_DIGITS = 100;

typedef vector<vector<int>> Matrix;

Matrix multiply(const Matrix& A, const Matrix& B) {
    int rowsA = A.size();
    int colsA = A[0].size();
    int colsB = B[0].size();

    Matrix C(rowsA, vector<int>(colsB, 0));

    for (int i = 0; i < rowsA; i++) {
        for (int j = 0; j < colsB; j++) {
            for (int k = 0; k < colsA; k++) {
                C[i][j] = (C[i][j] + (A[i][k] * B[k][j]) % MOD) % MOD;
            }
        }
    }

    return C;
}

Matrix matrixPow(const Matrix& A, int n) {
    if (n == 0) {
        Matrix I(A.size(), vector<int>(A[0].size(), 0));
        for (int i = 0; i < A.size(); i++) {
            I[i][i] = 1;
        }
        return I;
    }
    if (n == 1) {
        return A;
    }

    Matrix halfPower = matrixPow(A, n / 2);
    Matrix result = multiply(halfPower, halfPower);

    if (n % 2 == 1) {
        result = multiply(result, A);
    }

    return result;
}

vector<int> add(const vector<int>& a, const vector<int>& b) {
    vector<int> result(MAX_DIGITS, 0);
    int carry = 0;

    for (int i = 0; i < MAX_DIGITS; i++) {
        int sum = a[i] + b[i] + carry;
        result[i] = sum % 10;
        carry = sum / 10;
    }

    return result;
}

vector<int> matrixExponentiationAdd(const vector<int>& a, int n) {
    Matrix baseMatrix(MAX_DIGITS, vector<int>(MAX_DIGITS, 0));
    Matrix resultMatrix(MAX_DIGITS, vector<int>(MAX_DIGITS, 0));

    // Initialize baseMatrix with coefficients of 10^i
    for (int i = 0; i < MAX_DIGITS; i++) {
        baseMatrix[i][i] = 10;
    }

    // Initialize resultMatrix with identity matrix
    for (int i = 0; i < MAX_DIGITS; i++) {
        resultMatrix[i][i] = 1;
    }

    int power = n;
    int index = 0;

    while (power > 0) {
        if (power % 2 == 1) {
            resultMatrix = multiply(resultMatrix, matrixPow(baseMatrix, index));
        }
        index++;
        power = power / 2;
    }

    vector<int> result = a;

    for (int i = 0; i < MAX_DIGITS; i++) {
        result = add(result, multiply(resultMatrix[i], a));
    }

    return result;
}

int main() {
    vector<int> a(MAX_DIGITS, 0);
    vector<int> b(MAX_DIGITS, 0);

    // Input the two numbers a and b
    cout << "Enter the first number (a): ";
    string strA;
    cin >> strA;

    cout << "Enter the second number (b): ";
    string strB;
    cin >> strB;

    // Convert the input strings into vector of digits
    int lenA = strA.length();
    for (int i = lenA - 1, j = 0; i >= 0; i--, j++) {
        a[j] = strA[i] - '0';
    }

    int lenB = strB.length();
    for (int i = lenB - 1, j = 0; i >= 0; i--, j++) {
        b[j] = strB[i] - '0';
    }

    // Perform the addition
    vector<int> result = matrixExponentiationAdd(a, b[0]);

    // Remove leading zeros in the result
    int i = MAX_DIGITS - 1;
    while (result[i] == 0) {
        i--;
    }

    // Output the result
    cout << "Result: ";
    for (; i >= 0; i--) {
        cout << result[i];
    }
    cout << endl;

    return 0;
}

该代码首先定义了一个 Matrix 类型来表示矩阵。multiply 函数用于计算两个矩阵的乘积，matrixPow 函数用于计算矩阵的幂，add 函数用于执行两个高精度数的加法。matrixExponentiationAdd 函数使用矩阵快速幂加速高精度加法。在 main 函数中，用户输入两个数字，然后调用 matrixExponentiationAdd 函数执行加法，并输出结果。

请注意，该代码仅适用于两个非负整数的加法。如果需要进行减法或处理负数，请根据具体需求进行相应的修改