Home Backend Development Python Tutorial 用Python输出一个杨辉三角的例子

用Python输出一个杨辉三角的例子

Jun 16, 2016 am 08:43 AM
erlang python

关于杨辉三角是什么东西,右转维基百科:杨辉三角

稍微看一下直观一点的图:

复制代码 代码如下:

        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


杨辉三角有以下几个特点:

每一项的值等于他左上角的数和右上角的数的和,如果左上角或者右上角没有数字,就按0计算。
第N层项数总比N-1层多1个

计算第N层的杨辉三角,必须知道N-1层的数字,然后将相邻2项的数字相加,就能得到下一层除了最边上2个1的所有数字。 听起来有点像递归的思想,我们不妨假设我们已经知道N-1层的数字,来计算一下N层的数字吧。

复制代码 代码如下:

def _yanghui_trangle(n, result):
    if n == 1:
        return [1]
    else:
        return [sum(i) for i in zip([0] + result, result + [0])]

上面代码中,result表示N-1层杨辉三角的数字。实习上,我们在列表2端各补了一个0,然后计算相邻项的和,就可以直接得到结果。

稍微完善一下代码:

复制代码 代码如下:

def yanghui_trangle(n):
    def _yanghui_trangle(n, result):
        if n == 1:
            return [1]
        else:
            return [sum(i) for i in 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可以用lambda的方式简写,但是可读性感觉会变差,所以还是保持现状好了。

tips: 上面的程序并没有考虑数据格式化的问题,也就是说输出不是完美的三角形。

鉴于最近在学习erlang,补上一个erlang版本的,性能上没有测试过,不过还是要惊叹于函数式语言的表达能力:

复制代码 代码如下:

-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].

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