问题描述

旋转是图像处理的基本操作，在这个问题中，你需要将一个图像逆时针旋转90度。

计算机中的图像表示可以用一个矩阵来表示，为了旋转一个图像，只需要将对应的矩阵旋转即可。

输入格式

输入的第一行包含两个整数n, m，分别表示图像矩阵的行数和列数。

接下来n行每行包含m个整数，表示输入的图像。

输出格式

输出m行，每行包含n个整数，表示原始矩阵逆时针旋转90度后的矩阵。

样例输入

2 3
1 5 3
3 2 4

样例输出

3 4
5 2
1 3

评测用例规模与约定

1 ≤ n, m ≤ 1,000，矩阵中的数都是不超过1000的非负整数。

编程语言：Python

解题思想：

1.找出矩阵转换的规律：转换前矩阵行的第i个元素是转换后矩阵的列的第（列数-i）个元素。

2.为了减少使用的空间，在输入时就进行转换，而不是重开一个嵌套for循环进行转换。

本题最开始使用Java解题的时候，只拿了90分，就是因为内存超限，使用Python，因为代码简洁，解题思路也就清晰一些，所以用了尽量少的代码。

时间复杂度：O(n^2)

IDE代码如下：

Row, Column = map(int, input().split())  # 输入矩阵的行和列
Matrix = [[0 for i in range(Column)] for j in range(Row)]  # 初始化矩阵
ConvertMatrix = [[0 for i in range(Row)] for j in range(Column)]  # 初始化旋转后的矩阵
 
for i in range(Row):
    Matrix[i] = [int(n) for n in input().split()]  # 循环输入矩阵元素的值
    for j in range(Column):
        ConvertMatrix[j][i] = Matrix[i][Column - j - 1]
 
# 按格式要求输出旋转后的矩阵
for i in range(Column):
    for j in range(Row):
        if j == Row - 1:
            print(ConvertMatrix[i][j])  # 每行最后一个元素输出并换行
        else:
            print(ConvertMatrix[i][j], end=" ")  # 每行其它元素输出并空格

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CCF-CSP_20150301:图像旋转