计算给定的行数的 杨辉三角形。

在 杨辉 三角形中, 可以看到，一个数由它头顶左右两个数相加得到的。

    1
   1 1
  1 2 1
 1 3 3 1
1 4 6 4 1
# ... etc

在数学世界的杨辉三角形http://mathworld.wolfram.com/PascalsTriangle.html

维基百科https://zh.wikipedia.org/wiki/杨辉三角形

pub struct PascalsTriangle;

impl PascalsTriangle {
   pub fn new(row_count: u32) -> Self {
       unimplemented!("create Pascal's triangle with {} rows", row_count);
   }

   pub fn rows(&self) -> Vec<Vec<u32>> {
       unimplemented!();
   }
}

# #![allow(unused_variables)]
#fn main() {
#[test]
fn no_rows() {
   let pt = PascalsTriangle::new(0);
   let expected: Vec<Vec<u32>> = Vec::new();
   assert_eq!(expected, pt.rows());
}

#[test]
//#[ignore]
fn one_row() {
   let pt = PascalsTriangle::new(1);
   let expected: Vec<Vec<u32>> = vec![vec![1]];
   assert_eq!(expected, pt.rows());
}

#[test]
//#[ignore]
fn two_rows() {
   let pt = PascalsTriangle::new(2);
   let expected: Vec<Vec<u32>> = vec![vec![1], vec![1, 1]];
   assert_eq!(expected, pt.rows());
}

#[test]
//#[ignore]
fn three_rows() {
   let pt = PascalsTriangle::new(3);
   let expected: Vec<Vec<u32>> = vec![vec![1], vec![1, 1], vec![1, 2, 1]];
   assert_eq!(expected, pt.rows());
}

#[test]
//#[ignore]
fn last_of_four_rows() {
   let pt = PascalsTriangle::new(4);
   let expected: Vec<u32> = vec![1, 3, 3, 1];
   assert_eq!(Some(expected), pt.rows().pop());
}

#[test]
//#[ignore]
fn five_rows() {
   let pt = PascalsTriangle::new(5);
   let expected: Vec<Vec<u32>> = vec![
       vec![1],
       vec![1, 1],
       vec![1, 2, 1],
       vec![1, 3, 3, 1],
       vec![1, 4, 6, 4, 1],
   ];
   assert_eq!(expected, pt.rows());
}

#[test]
//#[ignore]
fn six_rows() {
   let pt = PascalsTriangle::new(6);
   let expected: Vec<Vec<u32>> = vec![
       vec![1],
       vec![1, 1],
       vec![1, 2, 1],
       vec![1, 3, 3, 1],
       vec![1, 4, 6, 4, 1],
       vec![1, 5, 10, 10, 5, 1],
   ];
   assert_eq!(expected, pt.rows());
}

#[test]
//#[ignore]
fn seven_rows() {
   let pt = PascalsTriangle::new(7);
   let expected: Vec<Vec<u32>> = vec![
       vec![1],
       vec![1, 1],
       vec![1, 2, 1],
       vec![1, 3, 3, 1],
       vec![1, 4, 6, 4, 1],
       vec![1, 5, 10, 10, 5, 1],
       vec![1, 6, 15, 20, 15, 6, 1],
   ];
   assert_eq!(expected, pt.rows());
}

#[test]
//#[ignore]
fn ten_rows() {
   let pt = PascalsTriangle::new(10);
   let expected: Vec<Vec<u32>> = vec![
       vec![1],
       vec![1, 1],
       vec![1, 2, 1],
       vec![1, 3, 3, 1],
       vec![1, 4, 6, 4, 1],
       vec![1, 5, 10, 10, 5, 1],
       vec![1, 6, 15, 20, 15, 6, 1],
       vec![1, 7, 21, 35, 35, 21, 7, 1],
       vec![1, 8, 28, 56, 70, 56, 28, 8, 1],
       vec![1, 9, 36, 84, 126, 126, 84, 36, 9, 1],
   ];
   assert_eq!(expected, pt.rows());
}

#}

# #![allow(unused_variables)]
#fn main() {
pub struct PascalsTriangle {
   row_count: u32,
}

impl PascalsTriangle {
   pub fn new(row_count: u32) -> Self {
       PascalsTriangle {
           row_count: row_count,
       }
   }

   pub fn rows(&self) -> Vec<Vec<u32>> {
       (0..self.row_count)
           .map(|row| PascalsTriangle::row(row))
           .collect()
   }

   pub fn row(number: u32) -> Vec<u32> {
       let mut r = vec![1];

       for p in 1..(number + 1) {
           if let Some(&last) = r.last() {
               r.push((last * (number + 1 - p)) / p)
           }
       }
       r
   }
}

#}