用c++。1、输于两个n×n的矩阵A和B,实现乘积运算，并输出运算结果和计算时间； 2、逐渐增大矩阵A和B的规模，分析运算时间的变化。 3、用分治法的实现矩阵乘积运算，比较使用分治法前后的计算量差异。

1. 以下是C++代码实现矩阵乘积运算并输出计算时间：

#include <iostream>
#include <ctime>
using namespace std;

const int maxn = 1000;

int A[maxn][maxn], B[maxn][maxn], C[maxn][maxn];

int main() {
    int n;
    cout << "Enter the size of matrix: ";
    cin >> n;

    // input matrix A and B
    cout << "Enter the matrix A: " << endl;
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            cin >> A[i][j];
        }
    }

    cout << "Enter the matrix B: " << endl;
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            cin >> B[i][j];
        }
    }

    // calculate matrix product
    clock_t start = clock();
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            C[i][j] = 0;
            for(int k = 0; k < n; k++) {
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }
    clock_t end = clock();

    // output matrix C and calculate time
    cout << "The matrix product C = A * B is:" << endl;
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            cout << C[i][j] << " ";
        }
        cout << endl;
    }
    cout << "The time of calculation is " << (double)(end - start) / CLOCKS_PER_SEC << " seconds." << endl;

    return 0;
}

2. 逐渐增大矩阵A和B的规模，可以使用循环来多次运行上述代码，并记录每次计算的时间，最后输出时间随矩阵规模变化的曲线图。代码如下：

#include <iostream>
#include <ctime>
#include <fstream>
using namespace std;

const int maxn = 1000;

int A[maxn][maxn], B[maxn][maxn], C[maxn][maxn];

int main() {
    ofstream out("matrix_time.txt"); // 打开输出文件
    out << "n time" << endl; // 输出表头

    for(int n = 100; n <= 1000; n += 100) { // 矩阵规模从100逐步增加到1000
        // input matrix A and B
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < n; j++) {
                A[i][j] = rand() % 100; // 随机生成0到99的整数
                B[i][j] = rand() % 100;
            }
        }

        // calculate matrix product
        clock_t start = clock();
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < n; j++) {
                C[i][j] = 0;
                for(int k = 0; k < n; k++) {
                    C[i][j] += A[i][k] * B[k][j];
                }
            }
        }
        clock_t end = clock();

        // output time
        out << n << " " << (double)(end - start) / CLOCKS_PER_SEC << endl;
    }

    out.close(); // 关闭输出文件

    return 0;
}

运行结果会输出一个文件 "matrix_time.txt"，其中每行表示矩阵规模和计算时间。可以使用Matlab或Excel等工具绘制出时间随规模变化的曲线图。

3. 分治法实现矩阵乘积运算的基本思想是将矩阵A和B分成四个子矩阵，分别计算它们的乘积，然后将结果合并成一个大矩阵C。可以使用递归实现该算法。代码如下：

#include <iostream>
#include <ctime>
#include <fstream>
using namespace std;

const int maxn = 1000;

int A[maxn][maxn], B[maxn][maxn], C[maxn][maxn];

void matrix_multiply(int n, int A[][maxn], int B[][maxn], int C[][maxn]) {
    if(n == 1) { // 当矩阵规模为1时，直接计算
        C[0][0] = A[0][0] * B[0][0];
        return;
    }

    int m = n / 2; // 将矩阵分成四个子矩阵
    int A11[maxn][maxn], A12[maxn][maxn], A21[maxn][maxn], A22[maxn][maxn];
    int B11[maxn][maxn], B12[maxn][maxn], B21[maxn][maxn], B22[maxn][maxn];
    int C11[maxn][maxn], C12[maxn][maxn], C21[maxn][maxn], C22[maxn][maxn];
    for(int i = 0; i < m; i++) {
        for(int j = 0; j < m; j++) {
            A11[i][j] = A[i][j];
            A12[i][j] = A[i][j + m];
            A21[i][j] = A[i + m][j];
            A22[i][j] = A[i + m][j + m];
            B11[i][j] = B[i][j];
            B12[i][j] = B[i][j + m];
            B21[i][j] = B[i + m][j];
            B22[i][j] = B[i + m][j + m];
        }
    }

    // 递归计算四个子矩阵的乘积
    matrix_multiply(m, A11, B11, C11);
    matrix_multiply(m, A12, B21, C12);
    matrix_multiply(m, A11, B12, C21);
    matrix_multiply(m, A12, B22, C22);

    // 合并四个子矩阵的结果
    for(int i = 0; i < m; i++) {
        for(int j = 0; j < m; j++) {
            C[i][j] = C11[i][j] + C12[i][j];
            C[i][j + m] = C21[i][j] + C22[i][j];
            C[i + m][j] = C11[i + m][j] + C12[i + m][j];
            C[i + m][j + m] = C21[i + m][j] + C22[i + m][j];
        }
    }
}

int main() {
    int n;
    cout << "Enter the size of matrix: ";
    cin >> n;

    // input matrix A and B
    cout << "Enter the matrix A: " << endl;
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            cin >> A[i][j];
        }
    }

    cout << "Enter the matrix B: " << endl;
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            cin >> B[i][j];
        }
    }

    // calculate matrix product using divide and conquer
    clock_t start = clock();
    matrix_multiply(n, A, B, C);
    clock_t end = clock();

    // output matrix C and calculate time
    cout << "The matrix product C = A * B is:" << endl;
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            cout << C[i][j] << " ";
        }
        cout << endl;
    }
    cout << "The time of calculation is " << (double)(end - start) / CLOCKS_PER_SEC << " seconds." << endl;

    return 0;
}

可以将分治法的计算时间和普通算法的计算时间进行比较，观察它们之间的差异。