Pascal’s Triangle The first seven rows of Pascal’s triangle are 1 1 1 1 2 1 1...

Pascal’s Triangle

The first seven rows of Pascal’s triangle are

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

The first row shown has index 0, and the last row has index 6. Row 0 of the triangle consists of the single number 1. For any positive integer k, the row with index k has k + 1 numbers and starts and ends with a 1. For each position p other than the first and the last, the element at p in row k is the sum of the two elements of row (k − 1) at positions p and p − 1. Write a function

vector pascalTriangleNextRow(vector row)

that takes a row of Pascal’s triangle in the form of a vector and returns the next row in the triangle. Test your function by writing a main function that asks the user to enter an integer N and prints the first N rows of Pascal’s triangle by repeatedly calling the above function.