CSP-202305-2-矩阵运算

CSP-202305-2-矩阵运算：题目链接

知识点一：申请矩阵

1.动态分配

// 申请
int** dynamicArray = new int*[rows];
for (int i = 0; i < rows; ++i) {
	dynamicArray[i] = new int[cols];
}

// 释放
for (int i = 0; i < rows; ++i) {
	delete[] dynamicArray[i];
}
delete[] dynamicArray;

2.静态分配

const int N = 10010, D = 30;
int Array[N][D];

知识点二：矩阵乘法

void matrixMultiplication(long long** A, int rowsA, int colsA, long long** B, int rowsB, int colsB, long long** result) {
    for (int i = 0; i < rowsA; ++i) {
        for (int j = 0; j < colsB; ++j) {
            result[i][j] = 0;
            for (int k = 0; k < colsA; ++k) {
                result[i][j] += A[i][k] * B[k][j];
            }
        }
    }
}

难点

1.时间复杂度

• 若直接按照原题给出的(W⋅(Q×KT))×V计算，由于Q×KT的结果为3*3的矩阵，会显示超时，进而需要改变矩阵的计算顺序，所以要先计算KT*V（结果为2*2）的矩阵，可以通过。

2.long long替换int

• 防止由于个别数字的大小超过int的范围。

代码

#include 
using namespace std;

void matrixMultiplication(long long** A, int rowsA, int colsA, long long** B, int rowsB, int colsB, long long** result) {
    for (int i = 0; i < rowsA; ++i) {
        for (int j = 0; j < colsB; ++j) {
            result[i][j] = 0;
            for (int k = 0; k < colsA; ++k) {
                result[i][j] += A[i][k] * B[k][j];
            }
        }
    }
}

int main() {
    int row, col;
    cin >> row >> col;

    // 动态分配二维数组
    long long** Q = new long long* [row];
    long long** K_T = new long long* [col];
    long long** V = new long long* [row];
    long long** W = new long long* [1];
    for (int i = 0; i < row; i++) 
    {
        Q[i] = new long long[col];
        V[i] = new long long[col];
    }
    for (int i = 0; i < col; i++)
    {
        K_T[i] = new long long[row];
    }
    for (int i = 0; i < 1; i++)
    {
        W[i] = new long long[row];
    }

    // 输入
    for (int i = 0; i < row; i++)
    {
        for (int j = 0; j < col; j++)
        {
            cin >> Q[i][j];
        }
    }
    for (int i = 0; i < row; i++)
    {
        for (int j = 0; j < col; j++)
        {
            cin >> K_T[j][i];
        }
    }
    for (int i = 0; i < row; i++)
    {
        for (int j = 0; j < col; j++)
        {
            cin >> V[i][j];
        }
    }
    for (int i = 0; i < row; i++)
    {
        cin >> W[0][i];
    }

    // result1 = K_T * V (2*3 * 3*2 = 2*2)
    long long** result1 = new long long* [col];
    for (int i = 0; i < col; i++)
    {
        result1[i] = new long long[col];
    }
    matrixMultiplication(K_T, col, row, V, row, col, result1);

    // result2 = Q * result1
    long long** result2 = new long long* [row];
    for (int i = 0; i < row; i++)
    {
        result2[i] = new long long[col];
    }
    matrixMultiplication(Q, row, col, result1, col, col, result2);

    // result2 *= W
    for (int i = 0; i < row; i++)
    {
        for (int j = 0; j < col; j++)
        {
            result2[i][j] = W[0][i] * result2[i][j];
        }
    }

    // 输出
    for (int i = 0; i < row; i++)
    {
        for (int j = 0; j < col; j++)
        {
            cout << result2[i][j] << " ";
        }
        cout << endl;
    }

    // 释放动态分配的内存
    for (int i = 0; i < row; i++) {
        delete[] Q[i];
        delete[] V[i];
        delete[] result2[i];
    }
    for (int i = 0; i < col; i++) {
        delete[] K_T[i];
        delete[] result1[i];
    }
    delete[] Q;
    delete[] K_T;
    delete[] V;
    delete[] W[0]; 
    delete[] W;
    delete[] result2;
    delete[] result1;

    return 0;
}