利用二维数组输出杨辉三角

### 使用二维数组生成并输出杨辉三角 以下是基于多种编程语言的实现方式，展示如何使用二维数组来生成并打印杨辉三角。 #### C++ 实现 C++ 中可以借助 `std::vector` 动态分配二维数组存储杨辉三角的数据结构[^3]： ```cpp #include <iostream> #include <vector> using namespace std; vector<vector<int>> generatePascalsTriangle(int numRows) { vector<vector<int>> triangle; for (int i = 0; i < numRows; ++i) { vector<int> row(i + 1, 1); for (int j = 1; j < i; ++j) { row[j] = triangle[i - 1][j - 1] + triangle[i - 1][j]; } triangle.push_back(row); } return triangle; } void printPascalsTriangle(const vector<vector<int>>& triangle) { for (const auto& row : triangle) { for (const auto& num : row) { cout << num << " "; } cout << endl; } } int main() { int n = 10; // 输出前 10 行 vector<vector<int>> pascalsTriangle = generatePascalsTriangle(n); printPascalsTriangle(pascalsTriangle); return 0; } ``` --- #### Python 实现 Python 提供了简洁的方式来处理二维列表，适合快速生成杨辉三角[^1]： ```python def generate_pascals_triangle(num_rows): triangle = [] for i in range(num_rows): row = [1] * (i + 1) for j in range(1, i): row[j] = triangle[i - 1][j - 1] + triangle[i - 1][j] triangle.append(row) return triangle def print_pascals_triangle(triangle): for row in triangle: print(" ".join(map(str, row))) if __name__ == "__main__": n = 10 # 输出前 10 行 pascals_triangle = generate_pascals_triangle(n) print_pascals_triangle(pascals_triangle) ``` --- #### Java 实现 Java 的二维数组可以通过静态初始化完成，也可以动态扩展以适应不同需求[^5]： ```java public class PascalsTriangle { public static int[][] generatePascalsTriangle(int numRows) { int[][] triangle = new int[numRows][]; for (int i = 0; i < numRows; i++) { triangle[i] = new int[i + 1]; triangle[i][0] = 1; triangle[i][i] = 1; for (int j = 1; j < i; j++) { triangle[i][j] = triangle[i - 1][j - 1] + triangle[i - 1][j]; } } return triangle; } public static void printPascalsTriangle(int[][] triangle) { for (int[] row : triangle) { for (int num : row) { System.out.print(num + " "); } System.out.println(); } } public static void main(String[] args) { int n = 10; // 输出前 10 行 int[][] pascalsTriangle = generatePascalsTriangle(n); printPascalsTriangle(pascalsTriangle); } } ``` --- #### C 实现 在 C 中，由于缺乏内置的动态数组支持，通常需要手动管理内存分配和释放操作[^5]： ```c #include <stdio.h> #include <stdlib.h> int** generatePascalsTriangle(int numRows, int* returnSize, int** returnColumnSizes) { *returnSize = numRows; int** triangle = (int**)malloc(sizeof(int*) * numRows); *returnColumnSizes = (int*)malloc(sizeof(int) * numRows); for (int i = 0; i < numRows; i++) { triangle[i] = (int*)malloc(sizeof(int) * (i + 1)); (*returnColumnSizes)[i] = i + 1; triangle[i][0] = 1; triangle[i][i] = 1; for (int j = 1; j < i; j++) { triangle[i][j] = triangle[i - 1][j - 1] + triangle[i - 1][j]; } } return triangle; } void printPascalsTriangle(int** triangle, int numRows, int* columnSizes) { for (int i = 0; i < numRows; i++) { for (int j = 0; j < columnSizes[i]; j++) { printf("%d ", triangle[i][j]); } printf("\n"); } } int main() { int numRows = 10; int returnSize; int* returnColumnSizes; int** pascalsTriangle = generatePascalsTriangle(numRows, &returnSize, &returnColumnSizes); printPascalsTriangle(pascalsTriangle, returnSize, returnColumnSizes); // Free allocated memory for (int i = 0; i < returnSize; i++) { free(pascalsTriangle[i]); } free(pascalsTriangle); free(returnColumnSizes); return 0; } ``` --- ###

要用二维数组输出杨辉三角形，可以使用动态规划的方法来实现。首先，我们需要创建一个二维数组来存储杨辉三角形的元素。然后，通过循环遍历数组，根据杨辉三角形的规律，计算每个位置上的元素值，并将其存储在数组中。最后，按照格式输出数组的内容即可。 以下是用二维数组输出杨辉三角形的示例代码： ```python def generate_pascal_triangle(num_rows): triangle = [ * (i + 1) for i in range(num_rows)] for i in range(2, num_rows): for j in range(1, i): triangle[i][j] = triangle[i-1][j-1] + triangle[i-1][j] return triangle def print_pascal_triangle(triangle): for row in triangle: for num in row: print(num, end=' ') print() num_rows = 5 triangle = generate_pascal_triangle(num_rows) print_pascal_triangle(triangle) ``` 运行以上代码，将会输出一个5行的杨辉三角形： ``` 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 ```