题目

答题思路

我这里使用的是两个多维数组，因此此段代码仅需修改输入部分既可用于多种对称矩阵的转置

第一个多维数组用于记录原始的矩阵排列，第二个多维数组用于记录转置后的矩阵排列

我的思路很简单，先将右上角的数交换到左下角（本人非数学专业，专业名词要使用错了还请包涵），再将左下角的数交换到右上角

完整的代码

#include <stdio.h>
#define Matrix_Number 3

int main(){

    int Row_Counter,Print_Counter;
    int Matrix[Matrix_Number][Matrix_Number];
    int Matrix_Switch[Matrix_Number][Matrix_Number];
    int Switch_Column_Counter;
    printf("3 X 3 Matrix:\n");

    //Input each number of ROW
    for (Row_Counter = 0;Row_Counter < Matrix_Number; Row_Counter++)
    {
        printf("ROW Number %d \n",Row_Counter + 1);

        printf("Please input Column Number : \n");
        scanf("%d,%d,%d",&Matrix[Row_Counter][0],&Matrix[Row_Counter][1],&Matrix[Row_Counter][2]);

    }

    //Print the Matrix before Switch
    printf("Before Switch :\n");
    for (Row_Counter = 0;Row_Counter < Matrix_Number; Row_Counter++)
    {
        for (Print_Counter = 0 ; Print_Counter < 2 ; Print_Counter++)
        {
            printf("%d  ",Matrix[Row_Counter][Print_Counter]);
        }
        printf("%d  \n",Matrix[Row_Counter][2]);
    }

    //Exchange the number in the upper right corner to the lower left corner
    for (int Switch_Row_Counter = 0 ; Switch_Row_Counter < Matrix_Number ; Switch_Row_Counter++)
    {
        for (Switch_Column_Counter = Switch_Row_Counter; Switch_Column_Counter < Matrix_Number ; Switch_Column_Counter++)
        {
            Matrix_Switch[Switch_Column_Counter][Switch_Row_Counter] = Matrix[Switch_Row_Counter][Switch_Column_Counter];
        }
    }

    //Exchange the number in the lower left corner to the upper right corner.
    for (int Switch_Row_Counter = 0 ; Switch_Row_Counter < Matrix_Number ; Switch_Row_Counter++)
    {
        for (Switch_Column_Counter = Switch_Row_Counter; Switch_Column_Counter < Matrix_Number ; Switch_Column_Counter++)
        {
            Matrix_Switch[Switch_Row_Counter][Switch_Column_Counter] = Matrix[Switch_Column_Counter][Switch_Row_Counter];
        }
    }

    //Print the Matrix after Switch
    printf("After Switch :\n");
    for (Row_Counter = 0;Row_Counter < Matrix_Number; Row_Counter++)
    {

        for (Print_Counter = 0 ; Print_Counter < 2 ; Print_Counter++)
        {
            printf("%d  ",Matrix_Switch[Row_Counter][Print_Counter]);
        }
        printf("%d  \n",Matrix_Switch[Row_Counter][2]);
    }
}

代码的分部讲解

交换的第一步

for (int Switch_Row_Counter = 0 ; Switch_Row_Counter < Matrix_Number ; Switch_Row_Counter++)
{
    for (Switch_Column_Counter = Switch_Row_Counter; Switch_Column_Counter < Matrix_Number ; Switch_Column_Counter++)
    {
        Matrix_Switch[Switch_Column_Counter][Switch_Row_Counter] = Matrix[Switch_Row_Counter][Switch_Column_Counter];
    }
}

最外层的循环控制器控制的是矩阵的行数，当 Switch_Row_Counter = 0 的时候，让嵌套的循环的控制器等于 0 ，嵌套的循环控制器控制的是矩阵的列，这样我们就可以读取原始的多维数组 Matrix[0] [0] 的数据了，这里对新的多维矩阵的[0] [0]进行赋值。当

Switch_Row_Counter = 1 的时候，Switch_Column_Counter = 1，这里的意思是，从矩阵的第二行的第二个开始交换，所以当第二行交换完成之后，就按照这个方法继续交换剩下的部分。

这样就将右上部分的数据交换到了新的矩阵的左下部分。

交换的第二步

for (int Switch_Row_Counter = 0 ; Switch_Row_Counter < Matrix_Number ; Switch_Row_Counter++)
{
    for (Switch_Column_Counter = Switch_Row_Counter; Switch_Column_Counter < Matrix_Number ; Switch_Column_Counter++)
    {
        Matrix_Switch[Switch_Row_Counter][Switch_Column_Counter] = Matrix[Switch_Column_Counter][Switch_Row_Counter];
    }
}