受Raymond Chen帖子的启发,假设你有一个4x4二维数组,写一个函数使它旋转90度。Raymond链接到伪代码中的解决方案,但我想看到一些真实的东西。
[1][2][3][4]
[5][6][7][8]
[9][0][1][2]
[3][4][5][6]
就变成:
[3][9][5][1]
[4][0][6][2]
[5][1][7][3]
[6][2][8][4]
更新:Nick的答案是最直接的,但是有没有比n²更好的方法呢?如果矩阵是10000x10000呢?
受Raymond Chen帖子的启发,假设你有一个4x4二维数组,写一个函数使它旋转90度。Raymond链接到伪代码中的解决方案,但我想看到一些真实的东西。
[1][2][3][4]
[5][6][7][8]
[9][0][1][2]
[3][4][5][6]
就变成:
[3][9][5][1]
[4][0][6][2]
[5][1][7][3]
[6][2][8][4]
更新:Nick的答案是最直接的,但是有没有比n²更好的方法呢?如果矩阵是10000x10000呢?
当前回答
JavaScript解决方案旋转矩阵90度的地方:
function rotateBy90(m) {
var length = m.length;
//for each layer of the matrix
for (var first = 0; first < length >> 1; first++) {
var last = length - 1 - first;
for (var i = first; i < last; i++) {
var top = m[first][i]; //store top
m[first][i] = m[last - i][first]; //top = left
m[last - i][first] = m[last][last - i]; //left = bottom
m[last][last - i] = m[i][last]; //bottom = right
m[i][last] = top; //right = top
}
}
return m;
}
其他回答
当前所有的解决方案都有O(n^2)开销作为临时空间(这不包括那些肮脏的OOP骗子!)这里有一个内存占用为O(1)的解决方案,将矩阵原地右转90度。该死的延展性,这玩意儿跑得很快!
#include <algorithm>
#include <cstddef>
// Rotates an NxN matrix of type T 90 degrees to the right.
template <typename T, size_t N>
void rotate_matrix(T (&matrix)[N][N])
{
for(size_t i = 0; i < N; ++i)
for(size_t j = 0; j <= (N-i); ++j)
std::swap(matrix[i][j], matrix[j][i]);
}
免责声明:我实际上并没有测试这个。让我们玩打虫游戏吧!
这是一个Javascript解决方案:
const transpose = m => m[0].map((x,i) => m.map(x => x[i]));
a: // original matrix
123
456
789
transpose(a).reverse(); // rotate 90 degrees counter clockwise
369
258
147
transpose(a.slice().reverse()); // rotate 90 degrees clockwise
741
852
963
transpose(transpose(a.slice().reverse()).slice().reverse())
// rotate 180 degrees
987
654
321
为新手程序员,在纯c++。(宝蓝的东西)
#include<iostream.h>
#include<conio.h>
int main()
{
clrscr();
int arr[10][10]; // 2d array that holds input elements
int result[10][10]; //holds result
int m,n; //rows and columns of arr[][]
int x,y; //rows and columns of result[][]
int i,j; //loop variables
int t; //temporary , holds data while conversion
cout<<"Enter no. of rows and columns of array: ";
cin>>m>>n;
cout<<"\nEnter elements of array: \n\n";
for(i = 0; i < m; i++)
{
for(j = 0; j<n ; j++)
{
cin>>arr[i][j]; // input array elements from user
}
}
//rotating matrix by +90 degrees
x = n ; //for non-square matrix
y = m ;
for(i = 0; i < x; i++)
{ t = m-1; // to create required array bounds
for(j = 0; j < y; j++)
{
result[i][j] = arr[t][i];
t--;
}
}
//print result
cout<<"\nRotated matrix is: \n\n";
for(i = 0; i < x; i++)
{
for(j = 0; j < y; j++)
{
cout<<result[i][j]<<" ";
}
cout<<"\n";
}
getch();
return 0;
}
试试我图书馆的算盘——常见的:
@Test
public void test_42519() throws Exception {
final IntMatrix matrix = IntMatrix.range(0, 16).reshape(4);
N.println("======= original =======================");
matrix.println();
// print out:
// [0, 1, 2, 3]
// [4, 5, 6, 7]
// [8, 9, 10, 11]
// [12, 13, 14, 15]
N.println("======= rotate 90 ======================");
matrix.rotate90().println();
// print out:
// [12, 8, 4, 0]
// [13, 9, 5, 1]
// [14, 10, 6, 2]
// [15, 11, 7, 3]
N.println("======= rotate 180 =====================");
matrix.rotate180().println();
// print out:
// [15, 14, 13, 12]
// [11, 10, 9, 8]
// [7, 6, 5, 4]
// [3, 2, 1, 0]
N.println("======= rotate 270 ======================");
matrix.rotate270().println();
// print out:
// [3, 7, 11, 15]
// [2, 6, 10, 14]
// [1, 5, 9, 13]
// [0, 4, 8, 12]
N.println("======= transpose =======================");
matrix.transpose().println();
// print out:
// [0, 4, 8, 12]
// [1, 5, 9, 13]
// [2, 6, 10, 14]
// [3, 7, 11, 15]
final IntMatrix bigMatrix = IntMatrix.range(0, 10000_0000).reshape(10000);
// It take about 2 seconds to rotate 10000 X 10000 matrix.
Profiler.run(1, 2, 3, "sequential", () -> bigMatrix.rotate90()).printResult();
// Want faster? Go parallel. 1 second to rotate 10000 X 10000 matrix.
final int[][] a = bigMatrix.array();
final int[][] c = new int[a[0].length][a.length];
final int n = a.length;
final int threadNum = 4;
Profiler.run(1, 2, 3, "parallel", () -> {
IntStream.range(0, n).parallel(threadNum).forEach(i -> {
for (int j = 0; j < n; j++) {
c[i][j] = a[n - j - 1][i];
}
});
}).printResult();
}
Javascript解决NxN矩阵与运行时O(N^2)和内存O(1)
function rotate90(matrix){
var length = matrix.length
for(var row = 0; row < (length / 2); row++){
for(var col = row; col < ( length - 1 - row); col++){
var tmpVal = matrix[row][col];
for(var i = 0; i < 4; i++){
var rowSwap = col;
var colSwap = (length - 1) - row;
var poppedVal = matrix[rowSwap][colSwap];
matrix[rowSwap][colSwap] = tmpVal;
tmpVal = poppedVal;
col = colSwap;
row = rowSwap;
}
}
}
}