Python implementation: Yang Hui triangle ideas

The Yang Hui Triangle has several features:

1. Each number equals two of the sum above it.
2. Each line of numbers is symmetrical, starting from 1 to become larger.
3. The number of the nth row has n items.
4. The nth row number and 2^n-1.
5. The number of m in the nth row can be expressed as C (n-1,m-1), which is the number of combinations of m-1 elements taken from n-1 different elements.
6. The number of the nth row is equal to the number of n-m+1 and is one of the combinatorial number properties.

            1          1   1        1   2   1      1   3   3   1    1   4   6   4   1  1   5   Ten   5    1    

My idea is that the first line has only one element of 1, so the second line must be 1. So the key is to calculate the number of outputs in the next few lines, first put it into the list.

The first element of the third row table can be known as [2] is the 2nd column of the No. 0 element and the first element of the and, since the No. 0 element has been 1 without it, so there is l[a]=l[a]+l[a+1], the next line is output from the previous line, now the third line

is [to], and then the tail with a [1], you can get the third row, the list length also added one, and so on and so on [1,3,3], and then add [1], Output line fourth, the code is implemented as follows

1 def Yanghui (n): 2     l=[1,1]3      for with range (1, N):4          for inch Range (x): 5             L[a]=l[a]+l[a+1]6         L.insert (0,1)7     return l

Each line will be output in the format later,

Re-unified printing

1 x=int (input ())2 a=13 b=04print((x-a+1) *'  ', [1])5 while a<x:6     b=Yanghui (a)  7     print((x-a) *", b)8     a+=1

Better understanding than the algorithm that needs to use the generator, and some trickery, can be used as a way of thinking

Python implementation: Yang Hui triangle ideas