[英]Efficiency of the script (finding a pair of integers which have the same remainder)
I am trying to find a pair (x,y) in A such that xy = 0 (mod n) where inputs are a positive integer n, a set A of m nonnegative integers and m > n.我试图在 A 中找到一对 (x,y),使得 xy = 0 (mod n),其中输入为正 integer n,一组由 m 个非负整数和 m > n 组成的 A。 To run the code below I took an m and n just for the sake of running an example.为了运行下面的代码,我拿了一个 m 和 n 只是为了运行一个例子。
Below is the script I have written.下面是我写的脚本。
I wonder if there is a more efficient way to write the script我想知道是否有更有效的方法来编写脚本
import numpy as np import sys
n = 10
m = 12
def functi(n, m):
A = [0] * m
for i in range(m):
A[i] = np.random.randint(0,34)
X = [-1] * n
for i in range(len(A)-1,-1,-1) : #loop backwards
a = A[i]
A.pop(i)
r = a % n
if X[r] == -1:
X[r] = a
else:
return(X[r], a)
pair = functi(n, m)
print(pair)
Note that your function doesn't have the parameters described by the problem -- it should take n
and A
as parameters, not take an m
and generate its own A
.请注意,您的 function 没有问题描述的参数 - 它应该将n
和A
作为参数,而不是采用m
并生成自己的A
。
The problem is much easier if you look at it as simply "find a pair of numbers with the same value mod n".如果您将其简单地视为“找到一对具有相同值 mod n 的数字”,则问题会容易得多。 An simple approach to this is to bucket all of the numbers according to their value % n
, and return a bucket once it has two numbers in it.一个简单的方法是根据它们的值% n
对所有数字进行存储,并在其中包含两个数字时返回一个存储桶。 That way you don't need to compare each pair of values individually to see if they match.这样您就不需要单独比较每对值来查看它们是否匹配。
>>> import random
>>> def find_equal_pair_mod_n(n, A):
... assert len(A) > n
... mods = {}
... for i in A:
... xy = mods.setdefault(i % n, [])
... xy.append(i)
... if len(xy) > 1:
... return tuple(xy)
...
>>> find_equal_pair_mod_n(10, [random.randint(0, 34) for _ in range(12)])
(26, 6)
>>> find_equal_pair_mod_n(10, [random.randint(0, 34) for _ in range(12)])
(30, 10)
>>> find_equal_pair_mod_n(10, [random.randint(0, 34) for _ in range(12)])
(32, 32)
>>> find_equal_pair_mod_n(10, [random.randint(0, 34) for _ in range(12)])
(1, 1)
>>> find_equal_pair_mod_n(10, [random.randint(0, 34) for _ in range(12)])
(28, 8)
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