Lecture 32 - Pascal's Triangle Pattern

Pascal's Triangle is a triangular array of numbers named after the mathematician Blaise Pascal. It is constructed in such a way that each number is the sum of the two numbers directly above it. The first and last numbers in each row are always 1. Pascal's Triangle is symmetric about the center column.

Here's an example of Pascal's Triangle with 5 rows:

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        1      1   1    1   2   1  1   3   3   1 1   4   6   4   1

Let's write a C++ program to generate Pascal's Triangle based on the number of rows specified by the user:

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#include <iostream> int main() {    int rows;    std::cout << "Enter the number of rows: ";    std::cin >> rows;    for (int i = 0; i < rows; i++) {        int number = 1;        // Print spaces before the numbers        for (int space = 1; space <= rows - i; space++) {            std::cout << "  ";        }        // Print numbers in the row        for (int j = 0; j <= i; j++) {            std::cout << number << "   ";            number = number * (i - j) / (j + 1);        }        std::cout << std::endl;    }    return 0; }

Example output for rows = 5:

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        1        1   1      1   2   1    1   3   3   1   1   4   6   4   1  

In the code above, we use two nested loops. The outer loop i controls the number of rows, and the inner loop j calculates and prints the numbers in each row based on the combination formula (i choose j) which is used to calculate the numbers in Pascal's Triangle.

Feel free to experiment with different values of rows to generate Pascal's Triangle of different sizes.