檢查對角矩陣和標量矩陣的程序 · GeeksForGeeks 中文系列教程

# 檢查對角矩陣和標量矩陣的程序 > 原文： [https://www.geeksforgeeks.org/program-check-diagonal-matrix-scalar-matrix/](https://www.geeksforgeeks.org/program-check-diagonal-matrix-scalar-matrix/) [**對角矩陣：**](https://en.wikipedia.org/wiki/Diagonal_matrix) 如果矩陣的除主對角線以外的元素為零，則稱方陣為對角線矩陣。平方零矩陣也是主要對角元素為零的對角矩陣。 **示例**： ``` Input : Mat[4][0] = {{4, 0, 0, 0}, {0, 5, 0, 0}, {0, 0, 2, 0}, {0, 0, 0, 1}} Output : Yes Mat[4][0] = {{6, 10, 12, 0}, {0, 5, 0, 0}, {0, 0, 9, 0}, {0, 0, 0, 1}} Output : No ``` ## CPP ``` // Program to check matrix is diagonal matrix or not. #include <bits/stdc++.h> #define N 4 using namespace std; // Function to check matrix is diagonal matrix // or not. bool isDiagonalMatrix(int mat[N][N]) { ????for (int i = 0; i < N; i++) ????????for (int j = 0; j < N; j++) ????????????// condition to check other elements? ????????????// except main diagonal are zero or not. ????????????if ((i != j) && (mat[i][j] != 0)) ????????????????return false; ????return true; } // Driver function int main() { ????int mat[N][N] = { { 4, 0, 0, 0 }, ??????????????????????{ 0, 7, 0, 0 }, ??????????????????????{ 0, 0, 5, 0 }, ??????????????????????{ 0, 0, 0, 1 } }; ????if (isDiagonalMatrix(mat)) ????????cout << "Yes" << endl; ????else ????????cout << "No" << endl; ????return 0; } ``` ## Java ```java // Program to check matrix is // diagonal matrix or not. import java.io.*; class GFG { ????static int N = 4; ????// Function to check matrix ????// is diagonal matrix ????// or not. ????static boolean isDiagonalMatrix(int mat[][]) ????{ ????????for (int i = 0; i < N; i++) ????????????for (int j = 0; j < N; j++) ????????????????// condition to check ????????????????// other elements? ????????????????// except main diagonal? ????????????????// are zero or not. ????????????????if ((i != j) && ???????????????????(mat[i][j] != 0)) ????????????????????return false; ????????return true; ????} ????// Driver function ????public static void main(String args[]) ????{ ????????int mat[][] = { { 4, 0, 0, 0 }, ??????????????????????????{ 0, 7, 0, 0 }, ??????????????????????????{ 0, 0, 5, 0 }, ??????????????????????????{ 0, 0, 0, 1 } }; ????????if (isDiagonalMatrix(mat)) ????????????System.out.println("Yes"); ????????else ????????????System.out.println("No" ); ????} } // This code is contributed by // Nikita Tiwari. ``` ## Python3 ```py # Python3 Program to check if matrix # is diagonal matrix or not. N = 4 # Function to check matrix # is diagonal matrix # or not.??? def isDiagonalMatrix(mat) : ????for i in range(0, N): ????????for j in range(0, N) : ????????????# condition to check ????????????# other elements? ????????????# except main diagonal ????????????# are zero or not. ????????????if ((i != j) and ?????????????(mat[i][j] != 0)) : ????????????????return False ????return True # Driver function mat = [[ 4, 0, 0, 0 ], ???????[ 0, 7, 0, 0 ], ???????[ 0, 0, 5, 0 ], ???????[ 0, 0, 0, 1 ]] if (isDiagonalMatrix(mat)) : ????print("Yes") else : ????print("No") # This code is contributed by Nikita Tiwari. ``` ## C# ```cs // Program to check matrix is // diagonal matrix or not. using System; class GFG { ????static int N = 4; ????// Function to check matrix ????// is diagonal matrix ????// or not. ????static bool isDiagonalMatrix(int [,]mat) ????{ ????????for (int i = 0; i < N; i++) ????????????for (int j = 0; j < N; j++) ????????????????// condition to check ????????????????// other elements? ????????????????// except main diagonal? ????????????????// are zero or not. ????????????????if ((i != j) &&??? (mat[i,j] != 0)) ????????????????????return false; ????????return true; ????} ????// Driver function ????public static void Main() ????{ ????????int [,]mat = { { 4, 0, 0, 0 }, ????????????????????????{ 0, 7, 0, 0 }, ????????????????????????{ 0, 0, 5, 0 }, ????????????????????????{ 0, 0, 0, 1 } }; ????????if (isDiagonalMatrix(mat)) ????????????Console.WriteLine("Yes"); ????????else ????????????Console.WriteLine("No" ); ????} } // This code is contributed by // vt_m. ``` ## PHP ```php <?php // Program to check matrix is // diagonal matrix or not. $N= 4; // Function to check matrix is // diagonal matrix or not. function isDiagonalMatrix($mat) { ????global $N; ????for ($i = 0; $i < $N; $i++) ????????for ($j = 0; $j < $N; $j++) ????????????// condition to check ????????????// other elements? ????????????// except main diagonal ????????????// are zero or not. ????????????if (($i != $j) &&? ????????????????($mat[$i][$j] != 0)) ????????????????return false; ????return true; } ????// Driver Code ????$mat = array(array(4, 0, 0, 0), ?????????????????array(0, 7, 0, 0), ?????????????????array(0, 0, 5, 0), ?????????????????array(0, 0, 0, 1)); ????if (isDiagonalMatrix($mat)) ????????echo "Yes" ,"\n"; ????else ????????echo "No","\n"; // This code is contributed by jit_t ?> ``` Output: ``` Yes ``` [**標量矩陣**](https://en.wikipedia.org/wiki/Diagonal_matrix#Scalar_matrix)：如果所有主要對角線元素相等且除主要對角線以外的其他元素均為零，則稱方陣為標量矩陣。標量矩陣也可以 n * I 的形式編寫，其中 n 是任何實數，而 I 是單位矩陣。示例： ``` Input : Mat[4][4] = {{4, 0, 0, 0}, {0, 4, 0, 0}, {0, 0, 4, 0}, {0, 0, 0, 4}} Output : Yes Mat[4][4] = {{4, 0, 0, 0}, {0, 4, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 4}} Output : No ``` ## CPP ``` // Program to check matrix is scalar matrix or not. #include <bits/stdc++.h> #define N 4 using namespace std; // Function to check matrix is scalar matrix or not. bool isScalarMatrix(int mat[N][N]) { ????// Check all elements except main diagonal are ????// zero or not. ????for (int i = 0; i < N; i++) ????????for (int j = 0; j < N; j++) ????????????if ((i != j) && (mat[i][j] != 0)) ????????????????return false; ????// Check all diagonal elements are same or not. ????for (int i = 0; i < N - 1; i++) ????????if (mat[i][i] != mat[i + 1][i + 1]) ????????????return false; ????return true; } // Driver function int main() { ????int mat[N][N] = { { 2, 0, 0, 0 }, ??????????????????????{ 0, 2, 0, 0 }, ??????????????????????{ 0, 0, 2, 0 }, ??????????????????????{ 0, 0, 0, 2 } }; ????// Function call ????if (isScalarMatrix(mat)) ????????cout << "Yes" << endl; ????else ????????cout << "No" << endl; ????return 0; } ``` ## Java ```java // Program to check matrix // is scalar matrix or not. import java.io.*; class GFG { ????static int N = 4; ????// Function to check matrix ????// is scalar matrix or not. ????static boolean isScalarMatrix(int mat[][]) ????{ ????????// Check all elements ????????// except main diagonal are ????????// zero or not. ????????for (int i = 0; i < N; i++) ????????????for (int j = 0; j < N; j++) ????????????????if ((i != j) ??????????????????&& (mat[i][j] != 0)) ????????????????????return false; ????????// Check all diagonal elements ????????// are same or not. ????????for (int i = 0; i < N - 1; i++) ????????????if (mat[i][i] != mat[i + 1][i + 1]) ????????????????return false; ????????return true; ????} ????// Driver function ????public static void main(String args[]) ????{ ????????int mat[ ][ ] = { { 2, 0, 0, 0 }, ??????????????????????????{ 0, 2, 0, 0 }, ??????????????????????????{ 0, 0, 2, 0 }, ??????????????????????????{ 0, 0, 0, 2 } }; ????????// Function call ????????if (isScalarMatrix(mat)) ????????????System.out.println("Yes"); ????????else ????????????System.out.println("No"); ????} } // This code is contributed // by Nikita tiwari. ``` ## Python3 ```py # Program to check matrix # is scalar matrix or not. N = 4 # Function to check matrix is # scalar matrix or not. def isScalarMatrix(mat) : ????# Check all elements? ????# except main diagonal are ????# zero or not. ????for i in range(0,N) : ????????for j in range(0,N) : ????????????if ((i != j)? ???????????????and (mat[i][j] != 0)) : ????????????????return False ????# Check all diagonal ????# elements are same or not. ????for i in range(0,N-1) : ????????if (mat[i][i] != ???????????mat[i + 1][i + 1]) : ????????????return False ????return True # Driver function mat = [[ 2, 0, 0, 0 ], ???????[ 0, 2, 0, 0 ], ???????[ 0, 0, 2, 0 ], ???????[ 0, 0, 0, 2 ]] # Function call if (isScalarMatrix(mat)): ????print("Yes") else : ????print("No") # This code is contributed by # Nikita tiwari. ``` ## C# ``` // Program to check matrix // is scalar matrix or not. using System; class GFG { ????static int N = 4; ????// Function to check matrix ????// is scalar matrix or not. ????static bool isScalarMatrix(int [,]mat) ????{ ????????// Check all elements ????????// except main diagonal are ????????// zero or not. ????????for (int i = 0; i < N; i++) ????????????for (int j = 0; j < N; j++) ????????????????if ((i != j) && (mat[i,j] != 0)) ????????????????????return false; ????????// Check all diagonal elements ????????// are same or not. ????????for (int i = 0; i < N - 1; i++) ????????????if (mat[i, i] != mat[i + 1, i + 1]) ????????????????return false; ????????return true; ????} ????// Driver function ????public static void Main() ????{ ????????int [,]mat = { { 2, 0, 0, 0 }, ????????????????????????{ 0, 2, 0, 0 }, ????????????????????????{ 0, 0, 2, 0 }, ????????????????????????{ 0, 0, 0, 2 } }; ????????// Function call ????????if (isScalarMatrix(mat)) ????????????Console.WriteLine("Yes"); ????????else ????????????Console.WriteLine("No"); ????} } // This code is contributed // by vt_m. ``` ## PHP ```php <?php // Program to check matrix // is scalar matrix or not. $N = 4; // Function to check matrix? // is scalar matrix or not. function isScalarMatrix($mat) { ????global $N; ????// Check all elements except? ????// main diagonal are zero or not. ????for ($i = 0; $i < $N; $i++) ????????for ($j = 0; $j < $N; $j++) ????????????if (($i != $j) && ????????????????($mat[$i][$j] != 0)) ????????????????return false; ????// Check all diagonal elements? ????// are same or not. ????for ($i = 0; $i < $N - 1; $i++) ????????if ($mat[$i][$i] != $mat[$i + 1][$i + 1]) ????????????return false; ????return true; } // Driver Code $mat = array(array(2, 0, 0, 0), ?????????????array(0, 2, 0, 0), ?????????????array(0, 0, 2, 0), ?????????????array(0, 0, 0, 2)); // Function call if (isScalarMatrix($mat)) ????echo "Yes"; else ????echo "No" ; // This code is contributed by mits ?> ``` **輸出**： ``` Yes ``` * * * * * *