程序打印數組的下三角和上三角矩陣 · GeeksForGeeks 中文系列教程

# 程序打印數組的下三角和上三角矩陣 > 原文： [https://www.geeksforgeeks.org/program-print-lower-triangular-upper-triangular-matrix-array/](https://www.geeksforgeeks.org/program-print-lower-triangular-upper-triangular-matrix-array/) 先決條件– [C/C++ 中的多維數組](https://www.geeksforgeeks.org/multidimensional-arrays-c-cpp/) 給定一個二維數組，編寫一個程序以打印下三角矩陣和上三角矩陣。 * 下三角矩陣是一個矩陣，其中包含在原理對角線以下的元素（包括原理對角線元素），其余元素為 0。 * 上三角矩陣是一個矩陣，其中包含在原則對角線上的元素（包括原則對角元素），其余元素為 0。 **下三角**： ![{\displaystyle \begin{bmatrix} A_{00} & 0 & 0 & ... & 0\\ A_{10} & A_{11} & 0 & ... & 0\\ A_{20} & A_{21} & A_{22} & ... & 0\\ . & . & . & . & .\\ . & & & & \\ . & & & & \\ . & & & & \\ . & & & & \\ . & & & & \\ A_{row0} & A_{row1} & A_{row2} & ... & A_{rowcol} \end{bmatrix}}](https://img.kancloud.cn/b3/47/b3471785243620f8950804e21f70876f_416x319.png "Rendered by QuickLaTeX.com") **上矩形**： ![{\displaystyle \begin{bmatrix} A_{00} & A_{01} & A_{02} & ... & A_{0col}\\ 0 & A_{11} & A_{22} & ... & A_{1col}\\ 0 & 0 & A_{22} & ... & A_{2col}\\ . & . & . & . & .\\ . & & & & \\ . & & & & \\ . & & & & \\ . & & & & \\ . & & & & \\ 0 & 0 & 0 & ... & A_{rowcol} \end{bmatrix}}](https://img.kancloud.cn/67/48/6748227b69b8c57e692e39498959d288_342x319.png "Rendered by QuickLaTeX.com") **示例**： ``` Input : matrix[3][3] = {1 2 3 4 5 6 7 8 9} Output : Lower : 1 0 0 Upper : 1 2 3 4 5 0 0 5 6 7 8 9 0 0 9 Input : matrix[3][3] = {7 8 9 3 2 1 6 5 4} Output : Lower : 7 0 0 Upper : 7 8 9 3 2 0 0 2 1 6 5 4 0 0 4 ``` **步驟**： 1. 對于下三角矩陣，我們分別檢查索引位置 i 和 j，即行和列。如果列位置大于行位置，我們只需將該位置設為 0。 2. 對于上三角矩陣，我們分別檢查索引位置 i 和 j，即行和列。如果列位置小于行位置，我們只需將該位置設為 0。 ## C++ ```cpp // C++ program to print Lower? // triangular and Upper triangular // matrix of an array #include<iostream> using namespace std; // Function to form? // lower triangular matrix void lower(int matrix[3][3], int row, int col) { ????int i, j; ????for (i = 0; i < row; i++) ????{ ????????for (j = 0; j < col; j++) ????????{ ????????????if (i < j) ????????????{ ????????????????cout << "0" << " "; ????????????} ????????????else ????????????cout << matrix[i][j] << " "; ????????} ????????cout << endl; ????} } // Function to form upper triangular marix void upper(int matrix[3][3], int row, int col) { ????int i, j; ????for (i = 0; i < row; i++) ????{ ????????for (j = 0; j < col; j++) ????????{ ????????????if (i > j) ????????????{ ????????????????cout << "0" << " "; ????????????} ????????????else ????????????cout << matrix[i][j] << " "; ????????} ????????cout << endl; ????} } // Driver Code int main() { ????int matrix[3][3] = {{1, 2, 3},? ????????????????????????{4, 5, 6},? ????????????????????????{7, 8, 9}}; ????int row = 3, col = 3; ????cout << "Lower triangular matrix: \n"; ????lower(matrix, row, col); ????cout << "Upper triangular matrix: \n"; ????upper(matrix, row, col); ????return 0; } ``` ## Java ```java // Java program to print Lower? // triangular and Upper triangular // matrix of an array class GFG { ????// method to form lower? ????// triangular matrix ????static void lower(int matrix[][],? ??????????????????????int row, int col) ????{ ????????int i, j; ????????for (i = 0; i < row; i++) ????????{ ????????????for (j = 0; j < col; j++) ????????????{ ????????????????if (i < j) ????????????????{ ????????????????????System.out.print("0" + " "); ????????????????} ????????????????else ????????????????System.out.print(matrix[i][j] + " "); ????????????} ????????????System.out.println(); ????????} ????} ????// Method to form upper ????// triangular matrix ????static void upper(int matrix[][],? ??????????????????????int row, int col) ????{ ????????int i, j; ????????for (i = 0; i < row; i++) ????????{ ????????????for (j = 0; j < col; j++) ????????????{ ????????????????if (i > j) ????????????????{ ????????????????????System.out.print("0" + " "); ????????????????} ????????????????else ????????????????System.out.print(matrix[i][j] + " "); ????????????} ????????????System.out.println(); ????????} ????} ????// Driver Code ????public static void main(String args[]) ????{ ????????int matrix[][] = {{1, 2, 3},? ??????????????????????????{4, 5, 6},? ??????????????????????????{7, 8, 9}}; ????????int row = 3, col = 3; ????????System.out.println("Lower triangular matrix: "); ????????lower(matrix, row, col); ????????System.out.println("Upper triangular matrix: "); ????????upper(matrix, row, col); ????} } ``` ## Python3 ```py # Python3 program to print Lower? # triangular and Upper triangular # matrix of an array # Function to form lower triangular? # matrix def lower(matrix, row, col): ????for i in range(0, row): ????????for j in range(0, col): ????????????if (i < j): ????????????????print("0", end = " "); ????????????else: ????????????????print(matrix[i][j],? ???????????????????????end = " " ); ????????print(" "); # Function to form upper triangular marix def upper(matrix, row, col): ????for i in range(0, row): ????????for j in range(0, col): ????????????if (i > j): ????????????????print("0", end = " "); ????????????else: ????????????????print(matrix[i][j],? ???????????????????????end = " " ); ????????print(" "); # Driver Code matrix = [[1, 2, 3],? ??????????[4, 5, 6],? ??????????[7, 8, 9]]; row = 3; col = 3; print("Lower triangular matrix: "); lower(matrix, row, col); print("Upper triangular matrix: "); upper(matrix, row, col); # This code is contributed by # Shivi_Aggarwal? ``` ## C# ```cs // C# program to print?? // Lower triangular and // Upper triangular // matrix of an array using System; class GFG { ????// method to form lower? ????// triangular matrix ????static void lower(int [,]matrix,? ??????????????????????int row, int col) ????{ ????????int i, j; ????????for (i = 0; i < row; i++) ????????{ ????????????for (j = 0; j < col; j++) ????????????{ ????????????????if (i < j) ????????????????{ ????????????????????Console.Write("0" + " "); ????????????????} ????????????????else ????????????????Console.Write(matrix[i, j] + " "); ????????????} ????????????Console.WriteLine(); ????????} ????} ????// Method to form upper ????// triangular matrix ????static void upper(int [,]matrix,? ??????????????????????int row, int col) ????{ ????????int i, j; ????????for (i = 0; i < row; i++) ????????{ ????????????for (j = 0; j < col; j++) ????????????{ ????????????????if (i > j) ????????????????{ ????????????????????Console.Write("0" + " "); ????????????????} ????????????????else ????????????????Console.Write(matrix[i, j] + " "); ????????????} ????????Console.WriteLine(); ????????} ????} ????// Driver Code ????static public void Main () ????{ ????????int [,]matrix = {{1, 2, 3},? ????????????????????????{4, 5, 6},? ????????????????????????{7, 8, 9}}; ????????int row = 3, col = 3; ????????Console.WriteLine("Lower triangular matrix: "); ????????lower(matrix, row, col); ????????Console.WriteLine("Upper triangular matrix: "); ????????upper(matrix, row, col); ????} } // This code is contributed by ajit? ``` ## PHP ```php <?php // PHP program to print Lower? // triangular and Upper triangular // matrix of an array // Function to form? // lower triangular matrix function lower($matrix, $row, $col) { ????$i; $j; ????for ($i = 0; $i < $row; $i++) ????{ ????????for ($j = 0; $j < $col; $j++) ????????{ ????????????if ($i < $j) ????????????{ ????????????????echo "0" , " "; ????????????} ????????????else ????????????echo $matrix[$i][$j] , " "; ????????} ????????echo "\n"; ????} } // Function to form // upper triangular marix function upper($matrix, $row, $col) { ????$i; $j; ????for ($i = 0; $i < $row; $i++) ????{ ????????for ($j = 0; $j < $col; $j++) ????????{ ????????????if ($i > $j) ????????????{ ????????????????echo "0" , " "; ????????????} ????????????else ????????????echo $matrix[$i][$j] ," "; ????????} ????echo "\n"; ????} } // Driver Code $matrix = array (array (1, 2, 3), ??????????????????array (4, 5, 6), ?????????????????array (7, 8, 9)); $row = 3; $col = 3; echo "Lower triangular matrix: \n"; lower($matrix, $row, $col); echo "Upper triangular matrix: \n"; upper($matrix, $row, $col); // This code is contributed by jit_t ?> ``` **輸出**： ``` Lower triangular matrix: 1 0 0 4 5 0 7 8 9 Upper triangular matrix: 1 2 3 0 5 6 0 0 9 ```