Dada una array 2D, la tarea es encontrar la Traza y la Normal de la array.
La normal de una array se define como la raíz cuadrada de la suma de los cuadrados de los elementos de la array.
La traza de una array cuadrada xn es la suma de los elementos diagonales.
Ejemplos:
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)
Implementación:
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 source
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;
}
Java
// Java program to find trace and normal
// of given matrix
import java.io.*;
class GFG {
// Size of given matrix
static int MAX = 100;
// Returns Normal of a matrix of size n x n
static int findNormal(int mat[][], 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 (int)Math.sqrt(sum);
}
// Returns trace of a matrix of size n x n
static int findTrace(int mat[][], int n)
{
int sum = 0;
for (int i=0; i<n; i++)
sum += mat[i][i];
return sum;
}
// Driven source
public static void main (String[] args) {
int mat[][] = {{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},
};
System.out.println ("Trace of Matrix = "
+ findTrace(mat, 5));
System.out.println ("Normal of Matrix = "
+ findNormal(mat, 5));
}
}
// This code is contributed by vt_m.
Python3
# Python3 program to find trace and
# normal of given matrix
import math
# Size of given matrix
MAX = 100;
# Returns Normal of a matrix
# of size n x n
def findNormal(mat, n):
sum = 0;
for i in range(n):
for j in range(n):
sum += mat[i][j] * mat[i][j];
return math.floor(math.sqrt(sum));
# Returns trace of a matrix of
# size n x n
def findTrace(mat, n):
sum = 0;
for i in range(n):
sum += mat[i][i];
return sum;
# Driver Code
mat = [[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]];
print("Trace of Matrix =", findTrace(mat, 5));
print("Normal of Matrix =", findNormal(mat, 5));
# This code is contributed by mits
C#
// C# program to find trace and normal
// of given matrix
using System;
class GFG {
// Returns Normal of a matrix of
// size n x n
static int findNormal(int [,]mat, 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 (int)Math.Sqrt(sum);
}
// Returns trace of a matrix of size
// n x n
static int findTrace(int [,]mat, int n)
{
int sum = 0;
for (int i = 0; i < n; i++)
sum += mat[i,i];
return sum;
}
// Driven source
public static void Main ()
{
int [,]mat = { {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},
};
Console.Write ("Trace of Matrix = "
+ findTrace(mat, 5) + "\n");
Console.Write("Normal of Matrix = "
+ findNormal(mat, 5));
}
}
// This code is contributed by nitin mittal.
PHP
<?php
// PHP program to find trace and
// normal of given matrix
// Size of given matrix
$MAX = 100;
// Returns Normal of a
// matrix of size n x n
function findNormal($mat, $n)
{
$sum = 0;
for ( $i = 0; $i < $n; $i++)
for ( $j = 0; $j < $n; $j++)
$sum += $mat[$i][$j] *
$mat[$i][$j];
return floor(sqrt($sum));
}
// Returns trace of a
// matrix of size n x n
function findTrace( $mat, $n)
{
$sum = 0;
for ( $i = 0; $i < $n; $i++)
$sum += $mat[$i][$i];
return $sum;
}
// Driver Code
$mat = array(array(1, 1, 1, 1, 1),
array(2, 2, 2, 2, 2),
array(3, 3, 3, 3, 3),
array(4, 4, 4, 4, 4),
array(5, 5, 5, 5, 5));
echo "Trace of Matrix = ",
findTrace($mat, 5),"\n";
echo "Normal of Matrix = " ,
findNormal($mat, 5) ;
// This code is contributed by anuj_67.
?>
Javascript
<script>
// Javascript program to find trace
// and normal of given matrix
// Size of given matrix
var MAX = 100;
// Returns Normal of a matrix of size n x n
function findNormal(mat, n)
{
var sum = 0;
for(var i = 0; i < n; i++)
for(var j = 0; j < n; j++)
sum += mat[i][j] * mat[i][j];
return parseInt(Math.sqrt(sum));
}
// Returns trace of a matrix of size n x n
function findTrace(mat, n)
{
var sum = 0;
for(var i = 0; i < n; i++)
sum += mat[i][i];
return sum;
}
// Driver code
var mat = [ [ 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 ] ];
document.write("Trace of Matrix = " +
findTrace(mat, 5) + "<br>");
document.write("Normal of Matrix = " +
findNormal(mat, 5));
// This code is contributed by Kirti
</script>
Producción
Trace of Matrix = 15 Normal of Matrix = 16
Complejidad de tiempo: O(n*n)
Complejidad de espacio: O(1)
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Publicación traducida automáticamente
Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA