Use Python to output an example of a Yang Hui's triangle _python

About Yang Hui's triangle is something that right turn Wikipedia: Yang Hui's triangle

Take a look at a slightly more intuitive picture:

Copy Code code as follows:

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
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1

The Yang Hui's triangle has the following several characteristics:

The value of each item equals the number of the upper-left corner and the number of the upper-right corner, and if there are no digits in the upper-left corner or upper-right corner, count to 0.
The number of n-tier items is always one more than the N-1 layer

To compute the Yang Hui's triangle of the nth layer, you must know the number of the N-1 layer and then add the numbers of the adjacent 2 items to get all the numbers on the next level except for the 2 1 on the edge. Sounds a bit like a recursive thought, let's assume we already know the N-1 layer of numbers to calculate n-tier numbers.

Copy Code code as follows:

def _yanghui_trangle (n, result):
if n = 1:
return [1]
Else
return [sum (i) for I with ZIP ([0] + result, result + [0])]

In the code above, result represents the number of Yang Hui's triangles in the N-1 layer. Internship, we are in the list 2 each complement a 0, and then calculate the adjacent items and, you can directly get results.

Slightly refine the code:

Copy Code code as follows:

def yanghui_trangle (n):
def _yanghui_trangle (n, result):
if n = 1:
return [1]
Else
return [sum (i) for I with ZIP ([0] + result, result + [0])]
Pre_result = []
For I in Xrange (n):
Pre_result = _yanghui_trangle (i + 1, pre_result)
Yield Pre_result

if __name__ = = "__main__":
For line in Yanghui_trangle1 (5):
Print Line

_yanghui_trangle can be abbreviated with a lambda, but the readability will get worse, so keep the status quo good.

Tips: The above program does not consider the problem of data formatting, which means that the output is not a perfect triangle.

In view of the recent learning of Erlang, a version of Erlang has not been tested on performance, but it is still a marvel at the expressive power of functional languages:

Copy Code code as follows:

-module (Yanghui).
-author (LFYZJCK).
-export ([TRIANGLE/1]).

Triangle_next (P)->
Lists:zipwith (Fun (X, Y)-> x+y end, [0| P], p + + [0]).

Triangle (1)->
[[1]];
Triangle (N)->
L = triangle (N-1),
[H|_] = L,
[Triangle_next (H) | L].