给定2D矩阵,任务是查找矩阵的“迹线”和“法线”。
矩阵的法线定义为矩阵元素平方和的平方根。
轴方阵的轨迹是对角元素的总和。
例子 :
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
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; iJava
// 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; iPython3
# 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
Javascript
输出 :
Trace of matrix = 15
Normal of matrix = 16