Sponsored
Sponsored
This approach involves generating Pascal's Triangle row by row using an iterative method. The first row is initialized with [1], and for each subsequent row, the first and last element are always 1. The intermediate elements are calculated as sums of appropriate elements from the previous row.
Time Complexity: O(numRows^2) due to the nested loop structure.
Space Complexity: O(numRows^2) as we store all elements of the triangle.
1#include <stdio.h>
2#include <stdlib.h>
3
4int** generate(int numRows, int* returnSize, int** returnColumnSizes) {
5 *returnSize = numRows;
6 *returnColumnSizes = (int*)malloc(numRows * sizeof(int));
7 int** triangle = (int**)malloc(numRows * sizeof(int*));
8 for (int i = 0; i < numRows; i++) {
9 triangle[i] = (int*)malloc((i + 1) * sizeof(int));
10 (*returnColumnSizes)[i] = i + 1;
11 triangle[i][0] = 1;
12 triangle[i][i] = 1;
13 for (int j = 1; j < i; j++) {
14 triangle[i][j] = triangle[i - 1][j - 1] + triangle[i - 1][j];
15 }
16 }
17 return triangle;
18}
19
20int main() {
21 int returnSize;
22 int* returnColumnSizes;
23 int numRows = 5;
24 int** result = generate(numRows, &returnSize, &returnColumnSizes);
25 for (int i = 0; i < returnSize; i++) {
26 for (int j = 0; j < returnColumnSizes[i]; j++) {
27 printf("%d ", result[i][j]);
28 }
29 printf("\n");
30 free(result[i]);
31 }
32 free(result);
33 free(returnColumnSizes);
34 return 0;
35}
36In this C implementation, we allocate a 2D array to hold the triangle's content. We initialize the first and last entries of each row to 1. For each intermediate row entry, we compute its value as the sum of the two appropriate values from the preceding row, incrementally building each row from top to bottom.
This approach constructs Pascal's Triangle using recursion by calculating each value based on the combination formula. The values on the edges are always 1, and other values are calculated as combinatorial numbers derived recursively.
Time Complexity: O(numRows^3) due to recursive calls, not optimal.
Space Complexity: O(numRows^2) for storing the triangle.
1function
This JavaScript function recursively computes each element in Pascal's Triangle based on combinatorial numbers. Recursion simplifies accessing required values for constructing each new row without explicit iteration.