Given a 2-D array of order N X M array elements, the task is to check if we can select a number from every row in such a way that xor of the selected numbers is greater than 0.
Note: There is a minimum of 2 rows.
Examples:
Input: a[][] = {{7, 7, 7}, {10, 10, 7}} Output: Yes Input: a[][] = {{1, 1, 1}, {1, 1, 1}, {1, 1, 1}, {1, 1, 1}} Output: No
Approach: Initially check if xor of first column elements of every row is 0 or not. If it is non-zero then it is possible. If it is zero, check if any of the rows has two or more distinct elements, then also it is possible. If both of the above conditions are not satisfied, then it is not possible.
Below is the implementation of the above approach:
// C++ program to implement // the above approach #include <bits/stdc++.h> using namespace std;
#define N 2 #define M 3 // Function to check if a number from every row // can be selected such that xor of the numbers // is greater than zero bool check( int mat[N][M])
{ int xorr = 0;
// Find the xor of first
// column for every row
for ( int i = 0; i < N; i++) {
xorr ^= mat[i][0];
}
// If Xorr is 0
if (xorr != 0)
return true ;
// Traverse in the matrix
for ( int i = 0; i < N; i++) {
for ( int j = 1; j < M; j++) {
// Check is atleast
// 2 distinct elements
if (mat[i][j] != mat[i][0])
return true ;
}
}
return false ;
} // Driver code int main()
{ int mat[N][M] = { { 7, 7, 7 },
{ 10, 10, 7 } };
if (check(mat))
cout << "Yes" ;
else
cout << "No" ;
return 0;
} |
// Java program to implement // the above approach import java.io.*;
class GFG
{ static int N = 2 ;
static int M = 3 ;
// Function to check if a number
// from every row can be selected
// such that xor of the numbers
// is greater than zero
static boolean check( int mat[][])
{
int xorr = 0 ;
// Find the xor of first
// column for every row
for ( int i = 0 ; i < N; i++)
{
xorr ^= mat[i] [ 0 ];
}
// If Xorr is 0
if (xorr != 0 )
return true ;
// Traverse in the matrix
for ( int i = 0 ; i < N; i++)
{
for ( int j = 1 ; j < M; j++)
{
// Check is atleast
// 2 distinct elements
if (mat[i] [j] != mat[i] [ 0 ])
return true ;
}
}
return false ;
}
// Driver code
public static void main (String[] args)
{
int mat[][] = {{ 7 , 7 , 7 },
{ 10 , 10 , 7 }};
if (check(mat))
System.out.println( "Yes" );
else
System.out.println( "No" );
}
} // This code is contributed by ajit |
# Python3 program to implement # the above approach N = 2
M = 3
# Function to check if a number from every row # can be selected such that xor of the numbers # is greater than zero def check(mat):
xorr = 0
# Find the xor of first
# column for every row
for i in range (N):
xorr ^ = mat[i][ 0 ]
# If Xorr is 0
if (xorr ! = 0 ):
return True
# Traverse in the matrix
for i in range (N):
for j in range ( 1 , M):
# Check is atleast
# 2 distinct elements
if (mat[i][j] ! = mat[i][ 0 ]):
return True
return False
# Driver code mat = [[ 7 , 7 , 7 ],
[ 10 , 10 , 7 ]]
if (check(mat)):
print ( "Yes" )
else :
print ( "No" )
# This code is contributed by mohit kumar |
// C# program to implement // the above approach using System;
class GFG
{ static int N = 2;
static int M = 3;
// Function to check if a number
// from every row can be selected
// such that xor of the numbers
// is greater than zero
static bool check( int [,]mat)
{
int xorr = 0;
// Find the xor of first
// column for every row
for ( int i = 0; i < N; i++)
{
xorr ^= mat[i, 0];
}
// If Xorr is 0
if (xorr != 0)
return true ;
// Traverse in the matrix
for ( int i = 0; i < N; i++)
{
for ( int j = 1; j < M; j++)
{
// Check is atleast
// 2 distinct elements
if (mat[i, j] != mat[i, 0])
return true ;
}
}
return false ;
}
// Driver code
static void Main()
{
int [,]mat = {{ 7, 7, 7 },
{ 10, 10, 7 }};
if (check(mat))
Console.Write( "Yes" );
else
Console.Write( "No" );
}
} // This code is contributed by mits |
<?php // PHP program to implement // the above approach $N = 2;
$M = 3;
// Function to check if a number from every row // can be selected such that xor of the numbers // is greater than zero function check( $mat )
{ global $N ;
global $M ;
$xorr = 0;
// Find the xor of first
// column for every row
for ( $i = 0; $i < $N ; $i ++)
{
$xorr = $xorr ^ $mat [ $i ][0];
}
// If Xorr is 0
if ( $xorr != 0)
return true;
// Traverse in the matrix
for ( $i = 0; $i < $N ; $i ++)
{
for ( $j = 1; $j < $M ; $j ++)
{
// Check is atleast
// 2 distinct elements
if ( $mat [ $i ][ $j ] != $mat [ $i ][0])
return true;
}
}
return false;
} // Driver code
$mat = array ( array ( 7, 7, 7 ),
array ( 10, 10, 7 ));
if (check( $mat ))
echo "Yes" ;
else
echo "No" ;
// This code is contributed by Tushil.. ?> |
<script> // Javascript program to implement // the above approach let N = 2; let M = 3; // Function to check if a number from every row // can be selected such that xor of the numbers // is greater than zero function check(mat)
{ let xorr = 0;
// Find the xor of first
// column for every row
for (let i = 0; i < N; i++) {
xorr ^= mat[i][0];
}
// If Xorr is 0
if (xorr != 0)
return true ;
// Traverse in the matrix
for (let i = 0; i < N; i++) {
for (let j = 1; j < M; j++) {
// Check is atleast
// 2 distinct elements
if (mat[i][j] != mat[i][0])
return true ;
}
}
return false ;
} // Driver code let mat = [ [ 7, 7, 7 ],
[ 10, 10, 7 ] ];
if (check(mat))
document.write( "Yes" );
else
document.write( "No" );
// This code is contributed by souravmahato348. </script> |
Yes
Time Complexity: O(N * M)
Auxiliary Space: O(1)