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)
C++
// C++ program to find trace and // normal of given matrix #include<bits/stdc++.h> using namespace std;
// Size of given matrix const int MAX = 100;
// Returns Normal of a matrix of // size n x n int findNormal( int mat[][MAX], int n)
{ int sum = 0;
for ( int i = 0; i < n; i++)
for ( int j = 0; j < n; j++)
sum += mat[i][j] * mat[i][j];
return sqrt (sum);
} // Returns trace of a matrix of // size n x n int findTrace( int mat[][MAX], int n)
{ int sum = 0;
for ( int i = 0; i < n; i++)
sum += mat[i][i];
return sum;
} // Driven code int main()
{ int mat[][MAX] = {{1, 1, 1, 1, 1},
{2, 2, 2, 2, 2},
{3, 3, 3, 3, 3},
{4, 4, 4, 4, 4},
{5, 5, 5, 5, 5}};
cout << "Trace of Matrix = " <<
findTrace(mat, 5) << endl;
cout << "Normal of Matrix = " <<
findNormal(mat, 5) << endl;
return 0;
} |
Output :
Trace of matrix = 15 Normal of matrix = 16
Time Complexity : O(n*n)
Space Complexity : O(1)