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Given a 2D matrix, the task is to find Trace and Normal of matrix.
Normal of a matrix is defined as square root of sum of squares of matrix elements.
Trace of a n x n square matrix is sum of diagonal elements.
Examples :
Input : mat[][] = {{7, 8, 9},
{6, 1, 2},
{5, 4, 3}};
Output : Normal = 16
Trace = 11
Explanation :
Normal = sqrt(7*7+ 8*8 + 9*9 + 6*6 +
1*1 + 2*2 + 5*5 + 4*4 + 3*3)
= 16
Trace = 7+1+3 = 11
Input :mat[][] = {{1, 2, 3},
{6, 4, 5},
{2, 1, 3}};
Output : Normal = 10
Trace = 8
Explanation :
Normal = sqrt(1*1 +2*2 + 3*3 + 6*6 + 4*4 +
5*5 + 2*2 + 1*1 + 3*3)
Trace = 8(1+4+3)
Implementation:
Trace of Matrix = 15 Normal of Matrix = 16
Time Complexity : O(n*n)
Space Complexity : O(1), since no extra space has been taken.