二维数组定义和声明

• 示例

#include <iostream>
using namespace std;
int main()
{
    // 二维数组的定义和初始化
    int a[3][4] = {{1, 2, 3, 4}, {5, 6, 7, 8}, { 9, 10, 11, 12}};
    for (int i = 0; i < 3 ; i++) {
        for (int j = 0; j < 4 ; j++) {
            cout<< a[i][j]<< "  ";
        }
        cout<<endl;
    }
}

几种二维数组初始化的方式

1. 分行赋初始值

int a[3][4] = {{1, 2, 3, 4}, {5, 6, 7, 8}, { 9, 10, 11, 12}};

2. 写到一个花括号中

int a[3][4] = {1, 2, 3, 4, 5, 6, 7, 8,  9, 10, 11, 12};

上面要注意元素对应的关系和个数

3. 部分赋值, 没赋值的是0

int a[3][4] = {{1, 4}, {3}, {5}};

4. 指定列数(必须), 不指定行数

int a[][4] = {1, 2, 3, 4, 5, 6, 7, 8,  9, 10, 11, 12};

统计两个二维数组中元素相等的个数

#include <iostream>
using namespace std;
bool  isEqual(int x, int y){
    return x == y? true: false;
}
int main()
{
    int a[3][4]={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12},
    b[3][4]={12, 2, 3, 4, 10, 6, 7, 11, 9, 5, 8, 1};
    int count = 0 ;
    for (int i = 0; i < 3; ++i) {
        for (int j = 0; j < 4 ; ++j) {
            if (isEqual(a[i][j], b[i][j])){
                count++;
            }
        }
    }
    cout<< "equals numbers ="<< count<<endl;
}

示例2

//有一个3×4的二维数组，
// 要求编程序求出其中值最小的那个元素，以及其所在的行号和列号
#include <iostream>
using namespace std;
int min_value(int a[][4], int &row, int &col){
    int min = a[0][0];
    for (int i = 0; i <3 ; ++i) {
        for (int j = 0; j < 4 ; ++j) {
            if (a[i][j] < min){
                min = a[i][j];
                row = i;
                col = j;
            }
        }
    }
    return min;
}
int main()
{
    int row = 0, col = 0;
    int a[3][4]= {{1, 2, 3, 4}, {-9, 8, 7, 6}, {10, 5, 2, -5}};
    // 二维数组名作为函数的参数
    cout<< "min_value = "<<min_value(a, row, col)<<endl;
    cout<< "row = "<<row<<endl;
    cout<< "col = "<<col<<endl;

}

实现矩阵的转置

// 矩阵转置
#include <iostream>
using namespace std;
void transpose(int a[][4], int b[][4]){
    for (int i = 0; i < 4 ; ++i) {
        for (int j = 0; j < 4 ; ++j) {
            // 交换值
            b[j][i] =  a[i][j] ;
        }
    }
}
int main(){
    // 将a 转置的结果 赋值给b
    int a[4][4]={{1, 2, 3, 4}, { 5, 6, 7, 8,}, {9, 10, 11, 12}, {13, 14, 15, 16}};
    int b[4][4];
    cout<< "matrix a"<< endl;
    for (int i = 0; i < 4 ; ++i) {
        for (int j = 0; j < 4 ; ++j) {
            cout<< a[i][j]<<"  ";
        }
        cout<< endl;
    }
    // 调用
    transpose(a, b);
    cout<< "matrix b"<< endl;
    for (int i = 0; i < 4 ; ++i) {
        for (int j = 0; j < 4 ; ++j) {
            cout<< b[i][j]<<"  ";
        }
        cout<< endl;
    }

}

第二种方式

// 矩阵转置  原地操作不增加变量的定义
#include <iostream>
using namespace std;
void transpose(int a[][4]){
    for (int i = 0; i < 4 ; ++i) {
        for (int j = i + 1; j < 4 ; ++j) {
            // 注意j 可以从 i开始； 如果从 i+1开始 省略计算了主对角线
            int temp = a[i][j];
            a[i][j] = a[j][i];
            a[j][i] = temp;
        }
    }
}
int main(){
    int a[4][4]={{1, 2, 3, 4}, { 5, 6, 7, 8,}, {9, 10, 11, 12}, {13, 14, 15, 16}};
    cout<< "matrix a  before = "<< endl;
    for (int i = 0; i < 4 ; ++i) {
        for (int j = 0; j < 4 ; ++j) {
            cout<< a[i][j]<<"  ";
        }
        cout<< endl;
    }
    // 调用
    transpose(a);
    cout<< "matrix a  transposed = "<< endl;
    for (int i = 0; i < 4 ; ++i) {
        for (int j = 0; j < 4 ; ++j) {
            cout<< a[i][j]<<"  ";
        }
        cout<< endl;
    }

}

矩阵相乘

// 矩阵乘法运算
#include <iostream>
#define M 4
#define N 3
#define P 5
using namespace std;
// a 是左矩阵 b 是右矩阵, c是结果矩阵
void dot(int a[][3], int b[][5], int c[][5]){
    //  因为我们 的结果矩阵c是 4行 5列的
    //  我们要将每一个值都算出来, 所以才会有这个2层(i,j)循环
    // a.shape = (4, 3)  b.shape = (3, 5)  c = (4, 5)
    for (int i = 0; i < M ; ++i) {
        for (int j = 0; j < P ; ++j) {
            c[i][j] = 0 ; // 这代表结果矩阵c的第i行第j列的值
            // N 是行乘以列 的时候每个行列元素的个数, 是 (m,k)(k,n)z中的k
            for (int k = 0; k < N ; ++k) {
                c[i][j] =  c[i][j] +  a[i][k]*b[k][j];
            }
        }
    }

}

int main(){
    int a[M][N]={{1, 3, 5}, {2, 4, 6}, {15, 7, 4}, {-2, 8, 9}},
    b[N][P]={{3, 6, 2, 1, 7}, {9, 1, 3, -1, 5}, {2, 5, 8, 1, 9}}, c[M][P];
    //    a.dot(b) = c
    // a.shape = (4, 3)  b.shape = (3, 5)  c = (4, 5)
    cout<< "matrix a   = "<< endl;
    for (int i = 0; i < 4 ; ++i) {
        for (int j = 0; j < 3 ; ++j) {
            cout<< a[i][j]<<"  ";
        }
        cout<< endl;
    }
    cout<< "matrix b   = "<< endl;
    for (int i = 0; i < 3 ; ++i) {
        for (int j = 0; j < 5 ; ++j) {
            cout<< b[i][j]<<"  ";
        }
        cout<< endl;
    }
    // 调用相乘函数
    dot(a, b, c);
    cout<< "matrix c   = "<< endl;
    for (int i = 0; i < 4 ; ++i) {
        for (int j = 0; j < 5 ; ++j) {
            cout<< c[i][j]<<"  ";
        }
        cout<< endl;
    }
}