Programa para comprobar si una array es simétrica

Se dice que una array cuadrada es una array simétrica si la transpuesta de la array es la misma que la array dada. La array simétrica se puede obtener cambiando fila a columna y columna a fila.

Ejemplos: 

Input : 1 2 3
        2 1 4
        3 4 3
Output : Yes

Input : 3 5 8
        3 4 7
        8 5 3
Output : No

Una solución simple es hacer lo siguiente. 

1. Crear transposición de array dada. 
2. Compruebe si las arrays transpuestas y dadas son iguales o no,  

Implementación:

// Simple c++ code for check a matrix is
// symmetric or not.
#include <iostream>
using namespace std;
 
const int MAX = 100;
 
// Fills transpose of mat[N][N] in tr[N][N]
void transpose(int mat[][MAX], int tr[][MAX], int N)
{
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            tr[i][j] = mat[j][i];
}
 
// Returns true if mat[N][N] is symmetric, else false
bool isSymmetric(int mat[][MAX], int N)
{
    int tr[N][MAX];
    transpose(mat, tr, N);
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            if (mat[i][j] != tr[i][j])
                return false;
    return true;
}
 
// Driver code
int main()
{
    int mat[][MAX] = { { 1, 3, 5 },
                       { 3, 2, 4 },
                       { 5, 4, 1 } };
 
    if (isSymmetric(mat, 3))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}

// Simple java code for check a matrix is
// symmetric or not.
 
import java.io.*;
 
class GFG {
     
 
 
 static int  MAX = 100;
 
// Fills transpose of mat[N][N] in tr[N][N]
 static void transpose(int mat[][], int tr[][], int N)
{
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            tr[i][j] = mat[j][i];
}
 
// Returns true if mat[N][N] is symmetric, else false
 static boolean isSymmetric(int mat[][], int N)
{
    int tr[][] = new int[N][MAX];
    transpose(mat, tr, N);
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            if (mat[i][j] != tr[i][j])
                return false;
    return true;
}
 
// Driver code
    public static void main (String[] args)
 {
         
        int mat[][] = { { 1, 3, 5 },
                    { 3, 2, 4 },
                    { 5, 4, 1 } };
 
    if (isSymmetric(mat, 3))
        System.out.println( "Yes");
    else
        System.out.println ( "No");
     
    }
}

# Simple Python code for check a matrix is
# symmetric or not.
  
# Fills transpose of mat[N][N] in tr[N][N]
def transpose(mat, tr, N):
    for i in range(N):
        for j in range(N):
            tr[i][j] = mat[j][i]
  
# Returns true if mat[N][N] is symmetric, else false
def isSymmetric(mat, N):
     
    tr = [ [0 for j in range(len(mat[0])) ] for i in range(len(mat)) ]
    transpose(mat, tr, N)
    for i in range(N):
        for j in range(N):
            if (mat[i][j] != tr[i][j]):
                return False
    return True
  
# Driver code
mat = [ [ 1, 3, 5 ], [ 3, 2, 4 ], [ 5, 4, 1 ] ]
if (isSymmetric(mat, 3)):
    print "Yes"
else:
    print "No"
 
# This code is contributed by Sachin Bisht

// Simple C# code for check a matrix is
// symmetric or not.
 
using System;
 
class GFG {
     
    static int MAX = 100;
     
    // Fills transpose of mat[N][N] in tr[N][N]
    static void transpose(int [,]mat, int [,]tr, int N)
    {
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                tr[i,j] = mat[j,i];
    }
     
    // Returns true if mat[N][N] is symmetric, else false
    static bool isSymmetric(int [,]mat, int N)
    {
        int [,]tr = new int[N,MAX];
        transpose(mat, tr, N);
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                if (mat[i,j] != tr[i,j])
                    return false;
        return true;
    }
     
    // Driver code
    public static void Main ()
    {
             
        int [,]mat = { { 1, 3, 5 },
                        { 3, 2, 4 },
                        { 5, 4, 1 } };
     
        if (isSymmetric(mat, 3))
            Console.WriteLine( "Yes");
        else
            Console.WriteLine( "No");
         
      }
}
 
// This code is contributed by vt_m.

<?php
// Simple PHP code for check a matrix is
// symmetric or not.
 
// Returns true if mat[N][N] is
// symmetric, else false
function isSymmetric($mat, $N)
{
    $tr = array(array());
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
            $tr[$i][$j] = $mat[$j][$i];
     
    // Fills transpose of
    // mat[N][N] in tr[N][N]
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
            if ($mat[$i][$j] != $tr[$i][$j])
                return false;
    return true;
}
 
    // Driver code
    $mat= array(array(1, 3, 5),
                array(3, 2, 4),
                array(5, 4, 1));
                 
    if (isSymmetric($mat, 3))
        echo "Yes";
    else
        echo "No";
 
// This code is contributed by Sam007
?>

<script>
 
// Simple javascript code for check
// a matrix is symmetric or not.
let  MAX = 100;
 
// Fills transpose of mat[N][N] in tr[N][N]
function transpose(mat, tr, N)
{
    for(let i = 0; i < N; i++)
        for(let j = 0; j < N; j++)
            tr[i][j] = mat[j][i];
}
 
// Returns true if mat[N][N] is
// symmetric, else false
function isSymmetric(mat, N)
{
    let tr = new Array(N);
    for(let i = 0; i < N; i++)
    {
        tr[i] = new Array(MAX);
    }
    transpose(mat, tr, N);
     
    for(let i = 0; i < N; i++)
        for(let j = 0; j < N; j++)
            if (mat[i][j] != tr[i][j])
                return false;
                 
    return true;
}
 
// Driver code
let mat = [ [ 1, 3, 5 ],
            [ 3, 2, 4 ],
            [ 5, 4, 1 ] ];
 
if (isSymmetric(mat, 3))
    document.write("Yes");
else
    document.write("No");
     
// This code is contributed by decode2207
 
</script>

Yes

Complejidad temporal: O(N x N) 
Espacio auxiliar: O(N x N)

Una solución eficiente para verificar si una array es simétrica o no es comparar los elementos de la array sin crear una transposición. Básicamente necesitamos comparar mat[i][j] con mat[j][i].  

Implementación:

// Efficient c++ code for check a matrix is
// symmetric or not.
#include <iostream>
using namespace std;
 
const int MAX = 100;
 
// Returns true if mat[N][N] is symmetric, else false
bool isSymmetric(int mat[][MAX], int N)
{
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            if (mat[i][j] != mat[j][i])
                return false;
    return true;
}
 
// Driver code
int main()
{
    int mat[][MAX] = { { 1, 3, 5 },
                       { 3, 2, 4 },
                       { 5, 4, 1 } };
 
    if (isSymmetric(mat, 3))
        cout << "Yes";
    else
        cout << "No";
    return 0;
}

// Efficient Java code for check a matrix is
// symmetric or no
 
import java.io.*;
 
class GFG {
    
 
static int MAX = 100;
 
// Returns true if mat[N][N]
// is symmetric, else false
 static boolean isSymmetric(int mat[][], int N)
{
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            if (mat[i][j] != mat[j][i])
                return false;
    return true;
}
 
// Driver code
     
    public static void main (String[] args)
 {
            int mat[][] = { { 1, 3, 5 },
                    { 3, 2, 4 },
                    { 5, 4, 1 } };
 
    if (isSymmetric(mat, 3))
        System.out.println(  "Yes");
    else
         
        System.out.println("NO");
         
    }
}
// This article is contributed by vt_m.

# Efficient Python code for check a matrix is
# symmetric or not.
 
# Returns true if mat[N][N] is symmetric, else false
def isSymmetric(mat, N):
    for i in range(N):
        for j in range(N):
            if (mat[i][j] != mat[j][i]):
                return False
    return True
  
# Driver code
mat = [ [ 1, 3, 5 ], [ 3, 2, 4 ], [ 5, 4, 1 ] ]
if (isSymmetric(mat, 3)):
    print "Yes"
else:
    print "No"
 
# This code is contributed by Sachin Bisht

// Efficient C# code for check a matrix is
// symmetric or no
 
using System;
 
class GFG
{
    //static int MAX = 100;
     
    // Returns true if mat[N][N]
    // is symmetric, else false
    static bool isSymmetric(int [,]mat, int N)
    {
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                if (mat[i, j] != mat[j, i])
                    return false;
        return true;
    }
     
    // Driver code
    public static void Main ()
    {
        int [,]mat = { { 1, 3, 5 },
                    { 3, 2, 4 },
                    { 5, 4, 1 } };
 
        if (isSymmetric(mat, 3))
            Console.WriteLine( "Yes");
        else
             
            Console.WriteLine("NO");
         
    }
}
 
// This code is contributed by vt_m.

<?php
// Efficient PHP code for
// check a matrix is
// symmetric or not.
 
$MAX = 100;
 
// Returns true if mat[N][N]
// is symmetric, else false
function isSymmetric($mat, $N)
{
    for ($i = 0; $i < $N; $i++)
        for ($j = 0; $j < $N; $j++)
            if ($mat[$i][$j] != $mat[$j][$i])
                return false;
    return true;
}
 
// Driver code
$mat = array(array(1, 3, 5),
             array(3, 2, 4),
             array(5, 4, 1));
 
if (isSymmetric($mat, 3))
    echo("Yes");
else
    echo("No");
 
// This code is contributed by Ajit.
?>

<script>
    // Efficient Javascript code for check a matrix is symmetric or no
     
    let MAX = 100;
   
    // Returns true if mat[N][N]
    // is symmetric, else false
    function isSymmetric(mat, N)
    {
        for (let i = 0; i < N; i++)
            for (let j = 0; j < N; j++)
                if (mat[i][j] != mat[j][i])
                    return false;
        return true;
    }
     
    let mat = [ [ 1, 3, 5 ],
               [ 3, 2, 4 ],
               [ 5, 4, 1 ] ];
   
    if (isSymmetric(mat, 3))
        document.write(  "Yes");
    else
           
        document.write("NO");
 
</script>

Yes

Complejidad temporal: O(N x N) 
Espacio auxiliar: O(1)

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