Given a 2D square matrix, find the sum of elements in Principal and Secondary diagonals. For example, consider the following 4 X 4 input matrix.
A00 A01 A02 A03 A10 A11 A12 A13 A20 A21 A22 A23 A30 A31 A32 A33
The primary diagonal is formed by the elements A00, A11, A22, A33.
- Condition for Principal Diagonal: The row-column condition is row = column.
The secondary diagonal is formed by the elements A03, A12, A21, A30. - Condition for Secondary Diagonal: The row-column condition is row = numberOfRows – column -1.
Examples :
Input : 4 1 2 3 4 4 3 2 1 7 8 9 6 6 5 4 3 Output : Principal Diagonal: 16 Secondary Diagonal: 20 Input : 3 1 1 1 1 1 1 1 1 1 Output : Principal Diagonal: 3 Secondary Diagonal: 3
Method 1 (O(n ^ 2) :
In this method, we use two loops i.e. a loop for columns and a loop for rows and in the inner loop we check for the condition stated above:
<?php // A simple PHP program to // find sum of diagonals $MAX = 100;
function printDiagonalSums( $mat , $n )
{ global $MAX ;
$principal = 0;
$secondary = 0;
for ( $i = 0; $i < $n ; $i ++)
{
for ( $j = 0; $j < $n ; $j ++)
{
// Condition for
// principal diagonal
if ( $i == $j )
$principal += $mat [ $i ][ $j ];
// Condition for
// secondary diagonal
if (( $i + $j ) == ( $n - 1))
$secondary += $mat [ $i ][ $j ];
}
}
echo "Principal Diagonal:" ,
$principal ,"
"; echo "Secondary Diagonal:" ,
$secondary ,"
"; } // Driver code $a = array ( array ( 1, 2, 3, 4 ),
array ( 5, 6, 7, 8 ),
array ( 1, 2, 3, 4 ),
array ( 5, 6, 7, 8 ));
printDiagonalSums( $a , 4);
// This code is contributed by ajit ?> |
Output:
Principal Diagonal:18 Secondary Diagonal:18
Time Complexity: O(N*N), as we are using a loop to traverse N*N times.
Auxiliary Space: O(1), as we are not using any extra space.
Method 2 (O(n) :
In this method we use one loop i.e. a loop for calculating sum of both the principal and secondary diagonals:
<?php // An efficient PHP program // to find sum of diagonals $MAX = 100;
function printDiagonalSums( $mat , $n )
{ global $MAX ;
$principal = 0; $secondary = 0;
for ( $i = 0; $i < $n ; $i ++)
{
$principal += $mat [ $i ][ $i ];
$secondary += $mat [ $i ][ $n - $i - 1];
}
echo "Principal Diagonal:" ,
$principal ,"
"; echo "Secondary Diagonal:" ,
$secondary ,"
"; } // Driver Code $a = array ( array (1, 2, 3, 4),
array (5, 6, 7, 8),
array (1, 2, 3, 4),
array (5, 6, 7, 8));
printDiagonalSums( $a , 4);
// This code is contributed by aj_36 ?> |
Output :
Principal Diagonal:18 Secondary Diagonal:18
Time Complexity: O(N), as we are using a loop to traverse N times.
Auxiliary Space: O(1), as we are not using any extra space.
Please refer complete article on Efficiently compute sums of diagonals of a matrix for more details!