Given a matrix of n X n. The task is to calculate the absolute difference between the sums of its diagonal.
Examples:
Input : mat[][] = 11 2 4
4 5 6
10 8 -12
Output : 15
Sum of primary diagonal = 11 + 5 + (-12) = 4.
Sum of primary diagonal = 4 + 5 + 10 = 19.
Difference = |19 - 4| = 15.
Input : mat[][] = 10 2
4 5
Output : 7
Calculate the sums across the two diagonals of a square matrix. Along the first diagonal of the matrix, row index = column index i.e mat[i][j] lies on the first diagonal if i = j. Along the other diagonal, row index = n – 1 – column index i.e mat[i][j] lies on the second diagonal if i = n-1-j. By using two loops we traverse the entire matrix and calculate the sum across the diagonals of the matrix.
Below is the implementation of this approach:
PHP
<?php// PHP program to find the difference// between the sum of diagonal.function difference($arr, $n){ // Initialize sums of diagonals $d1 = 0; $d2 = 0; for ($i = 0; $i < $n; $i++) { for ($j = 0; $j < $n; $j++) { // finding sum of // primary diagonal if ($i == $j) $d1 += $arr[$i][$j]; // finding sum of // secondary diagonal if ($i == $n - $j - 1) $d2 += $arr[$i][$j]; } } // Absolute difference of the sums // across the diagonals return abs($d1 - $d2);}// Driver Code{ $n = 3; $arr = array(array(11, 2, 4), array(4 , 5, 6), array(10, 8, -12)); echo difference($arr, $n); return 0;}// This code is contributed by nitin mittal.?> |
Output:
15
Time Complexity: O(N*N), as we are using a loop to traverse N times.
Auxiliary Space: O(1), as we are not using any extra space.
We can optimize above solution to work in O(n) using the patterns present in indexes of cells.
PHP
<?php// PHP program to find the difference// between the sum of diagonal.function difference($arr, $n){ // Initialize sums of diagonals $d1 = 0; $d2 = 0; for ($i = 0; $i < $n; $i++) { $d1 += $arr[$i][$i]; $d2 += $arr[$i][$n-$i-1]; } // Absolute difference of the sums // across the diagonals return abs($d1 - $d2);}// Driver Code{ $n = 3; $arr =array(array(11, 2, 4), array(4, 5, 6), array(10, 8, -12)); echo difference($arr, $n); return 0;}// This code is contributed by nitin mittal.?> |
Output:
15
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 Find difference between sums of two diagonals for more details!
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