Dada una array cuadrada, la tarea es que la giremos 180 grados en sentido contrario a las agujas del reloj sin usar ningún espacio extra.
Ejemplos:
Input : 1 2 3
4 5 6
7 8 9
Output : 9 8 7
6 5 4
3 2 1
Input : 1 2 3 4
5 6 7 8
9 0 1 2
3 4 5 6
Output : 6 5 4 3
2 1 0 9
8 7 6 5
4 3 2 1
Método: 1 (Solo imprime array rotada)
La solución a este problema es que para rotar una array 180 grados podemos seguir fácilmente ese paso
Matrix = a00 a01 a02
a10 a11 a12
a20 a21 a22
when we rotate it by 90 degree
then matrix is
Matrix = a02 a12 a22
a01 a11 a21
a00 a10 a20
when we rotate it by again 90
degree then matrix is
Matrix = a22 a21 a20
a12 a11 a10
a02 a01 a00
De la ilustración anterior , obtenemos que simplemente para rotar la array 180 grados, tendremos que imprimir la array dada de manera inversa.
C++
// C++ program to rotate a matrix by 180 degrees
#include <bits/stdc++.h>
#define N 3
using namespace std;
// Function to Rotate the matrix by 180 degree
void rotateMatrix(int mat[][N])
{
// Simply print from last cell to first cell.
for (int i = N - 1; i >= 0; i--) {
for (int j = N - 1; j >= 0; j--)
printf("%d ", mat[i][j]);
printf("\n");
}
}
// Driven code
int main()
{
int mat[N][N] = {
{ 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 }
};
rotateMatrix(mat);
return 0;
}
Java
// Java program to rotate a
// matrix by 180 degrees
import java.util.*;
class GFG {
static int N = 3;
// Function to Rotate the
// matrix by 180 degree
static void rotateMatrix(int mat[][])
{
// Simply print from last
// cell to first cell.
for (int i = N - 1; i >= 0; i--) {
for (int j = N - 1; j >= 0; j--)
System.out.print(mat[i][j] + " ");
System.out.println();
}
}
// Driver Code
public static void main(String[] args)
{
int[][] mat = { { 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 } };
rotateMatrix(mat);
}
}
// This code is contributed by ChitraNayal
Python3
# Python3 program to # rotate a matrix by # 180 degrees N = 3; # Function to Rotate # the matrix by 180 degree def rotateMatrix(mat): # Simply print from # last cell to first cell. i = N - 1; while(i >= 0): j = N - 1; while(j >= 0): print(mat[i][j], end = " "); j = j - 1; print(); i = i - 1; # Driven code mat = [[1, 2, 3], [ 4, 5, 6 ], [ 7, 8, 9 ]]; rotateMatrix(mat); # This code is contributed # by mits
C#
// C# program to rotate a
// matrix by 180 degrees
using System;
class GFG {
static int N = 3;
// Function to Rotate the
// matrix by 180 degree
static void rotateMatrix(int[, ] mat)
{
// Simply print from last
// cell to first cell.
for (int i = N - 1; i >= 0; i--) {
for (int j = N - 1; j >= 0; j--)
Console.Write(mat[i, j] + " ");
Console.WriteLine();
}
}
// Driver Code
static public void Main()
{
int[, ] mat = { { 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 } };
rotateMatrix(mat);
}
}
// This code is contributed by aj_36
PHP
<?php
// PHP program to rotate
// a matrix by 180 degree
$N = 3;
// Function to Rotate the
// matrix by 180 degree
function rotateMatrix($mat)
{
global $N;
// Simply print from
// last cell to first cell.
for ($i = $N - 1; $i >= 0; $i--)
{
for ($j = $N - 1; $j >= 0; $j--)
echo $mat[$i][$j], " ";
echo "\n";
}
}
// Driver Code
$mat = array(array(1, 2, 3),
array(4, 5, 6),
array(7, 8, 9));
rotateMatrix($mat);
// This code is contributed by ajit
?>
Javascript
<script>
// Javascript program to rotate a
// matrix by 180 degrees
N = 3;
// Function to Rotate the
// matrix by 180 degree
function rotateMatrix(mat)
{
// Simply print from last
// cell to first cell.
for(var i = N - 1; i >= 0; i--)
{
for(var j = N - 1; j >= 0; j--)
document.write(mat[i][j] + " ");
document.write("<br>");
}
}
// Driver Code
var mat = [ [ 1, 2, 3 ],
[ 4, 5, 6 ],
[ 7, 8, 9 ] ];
rotateMatrix(mat);
// This code is contributed by kirti
</script>
Producción :
9 8 7 6 5 4 3 2 1
Complejidad temporal: O(N*N)
Espacio auxiliar: O(1)
Método: 2 (Rotación en el lugar)
Hay cuatro pasos:
1- Encuentra la transposición de una array.
2- Columnas inversas de la transpuesta.
3- Hallar la transpuesta de una array.
4- Columnas inversas de la transpuesta
Let the given matrix be 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 First we find transpose. 1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16 Then we reverse elements of every column. 4 8 12 16 3 7 11 15 2 6 10 14 1 5 9 13 then transpose again 4 3 2 1 8 7 6 5 12 11 10 9 16 15 14 13 Then we reverse elements of every column again 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
C++
// C++ program for left rotation of matrix by 180
#include <bits/stdc++.h>
using namespace std;
#define R 4
#define C 4
// Function to rotate the matrix by 180 degree
void reverseColumns(int arr[R][C])
{
for (int i = 0; i < C; i++)
for (int j = 0, k = C - 1; j < k; j++, k--)
swap(arr[j][i], arr[k][i]);
}
// Function for transpose of matrix
void transpose(int arr[R][C])
{
for (int i = 0; i < R; i++)
for (int j = i; j < C; j++)
swap(arr[i][j], arr[j][i]);
}
// Function for display the matrix
void printMatrix(int arr[R][C])
{
for (int i = 0; i < R; i++) {
for (int j = 0; j < C; j++)
cout << arr[i][j] << " ";
cout << '\n';
}
}
// Function to anticlockwise rotate matrix
// by 180 degree
void rotate180(int arr[R][C])
{
transpose(arr);
reverseColumns(arr);
transpose(arr);
reverseColumns(arr);
}
// Driven code
int main()
{
int arr[R][C] = { { 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 },
{ 13, 14, 15, 16 } };
rotate180(arr);
printMatrix(arr);
return 0;
}
Java
// Java program for left
// rotation of matrix by 180
import java.util.*;
class GFG {
static int R = 4, C = 4, t = 0;
// Function to rotate the
// matrix by 180 degree
static void reverseColumns(int arr[][])
{
for (int i = 0; i < C; i++) {
for (int j = 0, k = C - 1; j < k; j++, k--) {
t = arr[j][i];
arr[j][i] = arr[k][i];
arr[k][i] = t;
}
}
}
// Function for transpose of matrix
static void transpose(int arr[][])
{
for (int i = 0; i < R; i++) {
for (int j = i; j < C; j++) {
t = arr[i][j];
arr[i][j] = arr[j][i];
arr[j][i] = t;
}
}
}
// Function for display the matrix
static void printMatrix(int arr[][])
{
for (int i = 0; i < R; i++) {
for (int j = 0; j < C; j++)
System.out.print(arr[i][j] + " ");
System.out.println();
}
}
// Function to anticlockwise
// rotate matrix by 180 degree
static void rotate180(int arr[][])
{
transpose(arr);
reverseColumns(arr);
transpose(arr);
reverseColumns(arr);
}
// Driver Code
public static void main(String[] args)
{
int[][] arr = { { 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 },
{ 13, 14, 15, 16 } };
rotate180(arr);
printMatrix(arr);
}
}
// This code is contributed by ChitraNayal
C#
// C# program for left
// rotation of matrix by 180
using System;
class GFG {
static int R = 4, C = 4, t = 0;
// Function to rotate the
// matrix by 180 degree
static void reverseColumns(int[, ] arr)
{
for (int i = 0; i < C; i++) {
for (int j = 0, k = C - 1;
j < k; j++, k--) {
t = arr[j, i];
arr[j, i] = arr[k, i];
arr[k, i] = t;
}
}
}
// Function for transpose of matrix
static void transpose(int[, ] arr)
{
for (int i = 0; i < R; i++) {
for (int j = i; j < C; j++) {
t = arr[i, j];
arr[i, j] = arr[j, i];
arr[j, i] = t;
}
}
}
// Function for display the matrix
static void printMatrix(int[, ] arr)
{
for (int i = 0; i < R; i++) {
for (int j = 0; j < C; j++)
Console.Write(arr[i, j] + " ");
Console.WriteLine();
}
}
// Function to anticlockwise
// rotate matrix by 180 degree
static void rotate180(int[, ] arr)
{
transpose(arr);
reverseColumns(arr);
transpose(arr);
reverseColumns(arr);
}
// Driver Code
static public void Main()
{
int[, ] arr = { { 1, 2, 3, 4 },
{ 5, 6, 7, 8 },
{ 9, 10, 11, 12 },
{ 13, 14, 15, 16 } };
rotate180(arr);
printMatrix(arr);
}
}
// This code is contributed by ajit
Python3
# Python3 program for left rotation of matrix by 180 R = 4 C = 4 # Function to rotate the matrix by 180 degree def reverseColumns(arr): for i in range(C): j = 0 k = C-1 while j < k: t = arr[j][i] arr[j][i] = arr[k][i] arr[k][i] = t j += 1 k -= 1 # Function for transpose of matrix def transpose(arr): for i in range(R): for j in range(i, C): t = arr[i][j] arr[i][j] = arr[j][i] arr[j][i] = t # Function for display the matrix def printMatrix(arr): for i in range(R): for j in range(C): print(arr[i][j], end = " "); print(); # Function to anticlockwise rotate matrix # by 180 degree def rotate180(arr): transpose(arr); reverseColumns(arr); transpose(arr); reverseColumns(arr); # Driven code arr = [ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8 ], [9, 10, 11, 12 ], [13, 14, 15, 16 ] ]; rotate180(arr); printMatrix(arr);
PHP
<?php
// PHP program for left rotation of matrix by 180
$R = 4;
$C = 4;
// Function to rotate the matrix by 180 degree
function reverseColumns(&$arr)
{
global $C;
for ($i = 0; $i < $C; $i++)
{
for ($j = 0, $k = $C - 1; $j < $k; $j++, $k--)
{
$t = $arr[$j][$i];
$arr[$j][$i] = $arr[$k][$i];
$arr[$k][$i] = $t;
}
}
}
// Function for transpose of matrix
function transpose(&$arr)
{
global $R, $C;
for ($i = 0; $i < $R; $i++)
{
for ($j = $i; $j < $C; $j++)
{
$t = $arr[$i][$j];
$arr[$i][$j] = $arr[$j][$i];
$arr[$j][$i] = $t;
}
}
}
// Function for display the matrix
function printMatrix(&$arr)
{
global $R, $C;
for ($i = 0; $i < $R; $i++) {
for ($j = 0; $j < $C; $j++)
{
echo $arr[$i][$j]." ";
}
echo "\n";
}
}
// Function to anticlockwise rotate matrix
// by 180 degree
function rotate180(&$arr)
{
transpose($arr);
reverseColumns($arr);
transpose($arr);
reverseColumns($arr);
}
// Driven code
$arr = array( array( 1, 2, 3, 4 ),
array( 5, 6, 7, 8 ),
array( 9, 10, 11, 12 ),
array( 13, 14, 15, 16 ) );
rotate180($arr);
printMatrix($arr);
return 0;
?>
Javascript
<script>
// Javascript program for left
// rotation of matrix by 180
let R = 4, C = 4, t = 0;
// Function to rotate the
// matrix by 180 degree
function reverseColumns(arr)
{
for (let i = 0; i < C; i++) {
for (let j = 0, k = C - 1; j < k; j++, k--) {
t = arr[j][i];
arr[j][i] = arr[k][i];
arr[k][i] = t;
}
}
}
// Function for transpose of matrix
function transpose(arr)
{
for (let i = 0; i < R; i++) {
for (let j = i; j < C; j++) {
t = arr[i][j];
arr[i][j] = arr[j][i];
arr[j][i] = t;
}
}
}
// Function for display the matrix
function printMatrix(arr)
{
for (let i = 0; i < R; i++) {
for (let j = 0; j < C; j++)
document.write(arr[i][j] + " ");
document.write("<br>");
}
}
// Function to anticlockwise
// rotate matrix by 180 degree
function rotate180(arr)
{
transpose(arr);
reverseColumns(arr);
transpose(arr);
reverseColumns(arr);
}
// Driver Code
let arr = [ [ 1, 2, 3, 4 ],
[ 5, 6, 7, 8 ],
[9, 10, 11, 12 ],
[13, 14, 15, 16 ] ];
rotate180(arr);
printMatrix(arr);
//This code is contributed by avanitrachhadiya2155
</script>
Producción :
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Complejidad temporal: O(R*C)
Espacio auxiliar: O(1)
En el código anterior, la transposición de la array debe encontrarse dos veces y, además, las columnas deben invertirse dos veces.
Entonces, podemos tener una mejor solución.
Método: 3 (Intercambio de posición)
Aquí, intercambiamos los valores en las posiciones respectivas.
C++
#include <bits/stdc++.h>
using namespace std;
/**
* Reverse Row at specified index in the matrix
* @param data matrix
* @param index row index
*/
void reverseRow(vector<vector<int>>& data,
int index)
{
int cols = data[index].size();
for(int i = 0; i < cols / 2; i++)
{
int temp = data[index][i];
data[index][i] = data[index][cols - i - 1];
data[index][cols - i - 1] = temp;
}
}
/**
* Print Matrix data
* @param data matrix
*/
void printMatrix(vector<vector<int>>& data)
{
for(int i = 0; i < data.size(); i++)
{
for(int j = 0; j < data[i].size(); j++)
{
cout << data[i][j] << " ";
}
cout << endl;
}
}
/**
* Rotate Matrix by 180 degrees
* @param data matrix
*/
void rotateMatrix180(vector<vector<int>>& data)
{
int rows = data.size();
int cols = data[0].size();
if (rows % 2 != 0)
{
// If N is odd reverse the middle
// row in the matrix
reverseRow(data, data.size() / 2);
}
// Swap the value of matrix [i][j] with
// [rows - i - 1][cols - j - 1] for half
// the rows size.
for(int i = 0; i <= (rows/2) - 1; i++)
{
for(int j = 0; j < cols; j++)
{
int temp = data[i][j];
data[i][j] = data[rows - i - 1][cols - j - 1];
data[rows - i - 1][cols - j - 1] = temp;
}
}
}
// Driver code
int main()
{
vector<vector<int>> data{ { 1, 2, 3, 4, 5 },
{ 6, 7, 8, 9, 10 },
{ 11, 12, 13, 14, 15 },
{ 16, 17, 18, 19, 20 },
{ 21, 22, 23, 24, 25 } };
// Rotate Matrix
rotateMatrix180(data);
// Print Matrix
printMatrix(data);
return 0;
}
// This code is contributed by divyeshrabadiya07
Java
public class GFG {
/**
* Reverse Row at specified index in the matrix
* @param data matrix
* @param index row index
*/
private static void reverseRow(int[][] data, int index) {
int cols = data[index].length;
for (int i = 0; i < cols / 2; i++) {
int temp = data[index][i];
data[index][i] = data[index][cols - i - 1];
data[index][cols - i - 1] = temp;
}
}
/**
* Print Matrix data
* @param data matrix
*/
private static void printMatrix(int[][] data) {
for (int i = 0; i < data.length; i++) {
for (int j = 0; j < data[i].length; j++) {
System.out.print(data[i][j] + " ");
}
System.out.println("");
}
}
/**
* Rotate Matrix by 180 degrees
* @param data matrix
*/
private static void rotateMatrix180(int[][] data) {
int rows = data.length;
int cols = data[0].length;
if (rows % 2 != 0) {
//If N is odd reverse the middle row in the matrix
reverseRow(data, data.length / 2);
}
//Swap the value of matrix [i][j] with [rows - i - 1][cols - j - 1] for half the rows size.
for (int i = 0; i <= (rows/2) - 1; i++) {
for (int j = 0; j < cols; j++) {
int temp = data[i][j];
data[i][j] = data[rows - i - 1][cols - j - 1];
data[rows - i - 1][cols - j - 1] = temp;
}
}
}
public static void main(String[] args) {
int[][] data = {
{1, 2, 3, 4, 5},
{6, 7, 8, 9, 10},
{11, 12, 13, 14, 15},
{16, 17, 18, 19, 20},
{21, 22, 23, 24, 25}
};
//Rotate Matrix
rotateMatrix180(data);
//Print Matrix
printMatrix(data);
}
}
Python3
# Reverse Row at specified index in the matrix def reverseRow(data, index): cols = len(data[index]) for i in range(cols // 2): temp = data[index][i] data[index][i] = data[index][cols - i - 1] data[index][cols - i - 1] = temp return data # Print Matrix data def printMatrix(data): for i in range(len(data)): for j in range(len(data[0])): print(data[i][j], end = ' ') print() # Rotate Matrix by 180 degrees def rotateMatrix(data): rows = len(data) cols = len(data[0]) if (rows % 2): # If N is odd reverse the middle # row in the matrix data = reverseRow(data, len(data) // 2) # Swap the value of matrix [i][j] with # [rows - i - 1][cols - j - 1] for half # the rows size. for i in range(rows // 2): for j in range(cols): temp = data[i][j] data[i][j] = data[rows - i - 1][cols - j - 1] data[rows - i - 1][cols - j - 1] = temp return data # Driver Code data = [ [ 1, 2, 3, 4, 5 ], [ 6, 7, 8, 9, 10 ], [ 11, 12, 13, 14, 15 ], [ 16, 17, 18, 19, 20 ], [ 21, 22, 23, 24, 25 ] ] # Rotate Matrix data = rotateMatrix(data) # Print Matrix printMatrix(data) # This code is contributed by rohitsingh07052
C#
using System;
class GFG
{
/**
* Reverse Row at specified index in the matrix
* @param data matrix
* @param index row index
*/
private static void reverseRow(int[, ] data, int index)
{
int cols = data.GetLength(1);
for (int i = 0; i < cols / 2; i++)
{
int temp = data[index, i];
data[index, i] = data[index, cols - i - 1];
data[index, cols - i - 1] = temp;
}
}
/**
* Print Matrix data
* @param data matrix
*/
private static void printMatrix(int[, ] data)
{
for (int i = 0; i < data.GetLength(0); i++)
{
for (int j = 0; j < data.GetLength(1); j++)
{
Console.Write(data[i, j] + " ");
}
Console.WriteLine();
}
}
/**
* Rotate Matrix by 180 degrees
* @param data matrix
*/
private static void rotateMatrix180(int[, ] data)
{
int rows = data.GetLength(0);
int cols = data.GetLength(1);
if (rows % 2 != 0)
{
// If N is odd reverse the middle row in the
// matrix
reverseRow(data, data.GetLength(0) / 2);
}
// Swap the value of matrix [i][j] with [rows - i -
// 1][cols - j - 1] for half the rows size.
for (int i = 0; i <= (rows / 2) - 1; i++)
{
for (int j = 0; j < cols; j++)
{
int temp = data[i, j];
data[i, j] = data[rows - i - 1, cols - j - 1];
data[rows - i - 1, cols - j - 1] = temp;
}
}
}
// Driver code
public static void Main()
{
int[, ] data = { { 1, 2, 3, 4, 5 },
{ 6, 7, 8, 9, 10 },
{ 11, 12, 13, 14, 15 },
{ 16, 17, 18, 19, 20 },
{ 21, 22, 23, 24, 25 } };
// Rotate Matrix
rotateMatrix180(data);
// Print Matrix
printMatrix(data);
}
}
// This code is contributed by subhammahato348
Javascript
<script>
// Reverse Row at specified index in the matrix
// @param data matrix
// @param index row index
function reverseRow(data,index)
{
let cols = data[index].length;
for(let i = 0; i < cols / 2; i++)
{
let temp = data[index][i];
data[index][i] = data[index][cols - i - 1];
data[index][cols - i - 1] = temp;
}
}
/**
* Print Matrix data
* @param data matrix
*/
function printMatrix(data)
{
for(let i = 0; i < data.length; i++)
{
for(let j = 0; j < data[i].length; j++)
{
document.write(data[i][j] + " ");
}
document.write("<br>");
}
}
/**
* Rotate Matrix by 180 degrees
* @param data matrix
*/
function rotateMatrix180(data)
{
let rows = data.length;
let cols = data[0].length;
if (rows % 2 != 0)
{
// If N is odd reverse the middle
// row in the matrix
reverseRow(data, Math.floor(data.length / 2));
}
// Swap the value of matrix [i][j]
// with [rows - i - 1][cols - j - 1]
// for half the rows size.
for(let i = 0; i <= (rows/2) - 1; i++)
{
for(let j = 0; j < cols; j++)
{
let temp = data[i][j];
data[i][j] = data[rows - i - 1][cols - j - 1];
data[rows - i - 1][cols - j - 1] = temp;
}
}
}
// Driver code
let data = [ [ 1, 2, 3, 4, 5 ],
[ 6, 7, 8, 9, 10 ],
[ 11, 12, 13, 14, 15 ],
[ 16, 17, 18, 19, 20 ],
[ 21, 22, 23, 24, 25 ] ];
// Rotate Matrix
rotateMatrix180(data);
// Print Matrix
printMatrix(data);
// This code is contributed by rag2127
</script>
Producción :
25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Complejidad temporal : O(R*C)
Espacio auxiliar : O(1)
Publicación traducida automáticamente
Artículo escrito por SHARIQ_JMI y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA