Pascal Triangle Python

Question

所以我一直在做一个pascal三角形，但是我试图在每一行上做一些标签，比如Row=0，Row=1，Row=2，我试着把这些标签放在Pascal三角形上的每一行开始之前。有没有人能帮我在这段代码的基础上实现它？谢谢。

x = int(input("Enter the desired height. "))
list=[1]
for i in range(x):
    print(list)
    newlist=[]
    newlist.append(list[0])
    for i in range(len(list)-1):
        newlist.append(list[i]+list[i+1])
    newlist.append(list[-1])
    list=newlist

Answer 1

首先，请避免使用内置函数的名称作为变量名(在本例中为list；我已将其更改为l)。除此之外，您提到的放置标签只是简单地引用您拥有的最外层循环的迭代。以下代码的行为应该与预期一致：

x = int(input("Enter the desired height. "))
l = [1]
for i in range(x):
    # Modified v
    print("Row", i + 1, l)
    newlist = []
    newlist.append(l[0])
    for i in range(len(l) - 1):
        newlist.append(l[i] + l[i+1])
    newlist.append(l[-1])
    l = newlist

下面是一个示例运行：

Enter the desired height. 4
Row 1 [1]
Row 2 [1, 1]
Row 3 [1, 2, 1]
Row 4 [1, 3, 3, 1]

希望这能有所帮助！

Answer 2

如果你从右到左重新考虑这个问题，而不是从左到右，它会简化很多：

rows = int(input("Enter the desired height: "))

array = []

for row in range(1, rows + 1):
    array.append(1)  # both widen the row and initialize last element

    for i in range(row - 2, 0, -1):  # fill in the row, right to left
        array[i] += array[i - 1]  # current computed from previous

    print("Row", row, array)

输出

Enter the desired height: 9
Row 1 [1]
Row 2 [1, 1]
Row 3 [1, 2, 1]
Row 4 [1, 3, 3, 1]
Row 5 [1, 4, 6, 4, 1]
Row 6 [1, 5, 10, 10, 5, 1]
Row 7 [1, 6, 15, 20, 15, 6, 1]
Row 8 [1, 7, 21, 35, 35, 21, 7, 1]
Row 9 [1, 8, 28, 56, 70, 56, 28, 8, 1]

Answer 3

我认为代码是不言自明的。You can Visualise on it here.

def pascal_triangle(degree):
'''
Gives row and column wise enrtry for given degree
'''
Pascal_list =[[1]]   #FIrst entry Defined to start 
print(Pascal_list[0] ,'\n')
for i in range(1,degree+1): #+1 As we are starting from 1
    temp_list =[]
    for j in range(i+1):  #+1 As we are considering last element
        if(j==0):#First Element = 1
            temp_list.append(1)
            continue
        elif(j == i):#Last Element = 1
            temp_list.append(1)
            continue
        else:
            temp_list.append(Pascal_list[i-1][j]+Pascal_list[i-1][j-1]) # Addition of Upper Two Elements
    Pascal_list.append(temp_list)
    print(Pascal_list[i] ,'\n')

return Pascal_list

输入：

Pascal_Triangle = pascal_triangle(4)
print('Pascal_Triangle: ', Pascal_Triangle)

输出：

[1] 

[1, 1] 

[1, 2, 1] 

[1, 3, 3, 1] 

[1, 4, 6, 4, 1] 

Pascal_Triangle:  [[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1]]