I am working on this python problem:
A non-empty array A consisting of N integers is given. The array contains an odd number of elements, and each element of the array can be paired with another element that has the same value, except for one element that is left unpaired.
For example, in array A such that:
A[0] = 9 A[1] = 3 A[2] = 9
A[3] = 3 A[4] = 9 A[5] = 7
A[6] = 9
the elements at indexes 0 and 2 have value 9,
the elements at indexes 1 and 3 have value 3,
the elements at indexes 4 and 6 have value 9,
the element at index 5 has value 7 and is unpaired.
Write a function:
def solution(A)
that, given an array A consisting of N integers fulfilling the above conditions, returns the value of the unpaired element.
For example, given array A such that:
A[0] = 9 A[1] = 3 A[2] = 9
A[3] = 3 A[4] = 9 A[5] = 7
A[6] = 9
the function should return 7, as explained in the example above.
Write an efficient algorithm for the following assumptions:
N is an odd integer within the range [1..1,000,000];
each element of array A is an integer within the range [1..1,000,000,000];
all but one of the values in A occur an even number of times.
This is my solution:
def solution(A):
for i in A:
B = A.copy()
B.remove(i)
if i in B:
pass
else:
return i
However, when this solution was tested with larger lists (N>200) it started encountering runtime errors and timeout errors. How can I improve this function to avoid these errors?
Many thanks
This question already has answers here:
Index of duplicates items in a python list
(21 answers)
Closed 1 year ago.
nums = [11, 2,4, 2, 5]
for i in nums:
print(nums.index(i),i )
I run the above code and it uses same index for similar elements(here 2 at index 1 and 3).
I wasn't aware of this python list behavior, does it mean the use of lists can be restrictive for similar elements in same list?
The index() method returns the position at the first occurrence of the specified value.
So it returns first index of number 2.
nums = [11, 2,4, 2, 5]
You can enumerate() to get all indexes.
nums = [11, 2,4, 2, 5]
for i,n in enumerate(nums):
print(i, n)
0 11
1 2
2 4
3 2
4 5
I tried to sort an array by permuting it with itself
(the array contain all the numbers in range between 0 to its length-1)
so to test it I used random.shuffle but it had some unexpected results
a = np.array(range(10))
random.shuffle(a)
a = a[a]
a = a[a]
print(a)
# not a sorted array
# [9 5 2 3 1 7 6 8 0 4]
a = np.array([2,1,4,7,6,5,0,3,8,9])
a = a[a]
a = a[a]
print(a)
# [0 1 2 3 4 5 6 7 8 9]
so for some reason the permutation when using the second example of an unsorted array returns the sorted array as expected but the shuffled array doesn't work the same way.
Does anyone know why? Or if there is an easier way to sort using permutation or something similar it would be great.
TL;DR
There is no reason to expect a = a[a] to sort the array. In most cases it won't. In case of a coincidence it might.
What is the operation c = b[a]? or Applying a permutation
When you use an array a obtained by shuffling range(n) as a mask for an array b of same size n, you are applying a permutation, in the mathematical sense, to the elements of b. For instance:
a = [2,0,1]
b = np.array(['Alice','Bob','Charlie'])
print(b[a])
# ['Charlie' 'Alice' 'Bob']
In this example, array a represents the permutation (2 0 1), which is a cycle of length 3. Since the length of the cycle is 3, if you apply it three times, you will end up where you started:
a = [2,0,1]
b = np.array(['Alice','Bob','Charlie'])
c = b
for i in range(3):
c = c[a]
print(c)
# ['Charlie' 'Alice' 'Bob']
# ['Bob' 'Charlie' 'Alice']
# ['Alice' 'Bob' 'Charlie']
Note that I used strings for the elements of b ton avoid confusing them with indices. Of course, I could have used numbers from range(n):
a = [2,0,1]
b = np.array([0,1,2])
c = b
for i in range(3):
c = c[a]
print(c)
# [2 0 1]
# [1 2 0]
# [0 1 2]
You might see an interesting, but unsurprising fact: The first line is equal to a; in other words, the first result of applying a to b is equal to a itself. This is because b was initialised to [0 1 2], which represent the identity permutation id; thus, the permutations that we find by repeatedly applying a to b are:
id == a^0
a
a^2
a^3 == id
Can we always go back where we started? or The rank of a permutation
It is a well-known result of algebra that if you apply the same permutation again and again, you will eventually end up on the identity permutation. In algebraic notations: for every permutation a, there exists an integer k such that a^k == id.
Can we guess the value of k?
The minimum value of k is called the rank of a permutation.
If a is a cycle, then the minimum possible k is the length of the cycle. In our previous example, a was a cycle of length 3, so it took three applications of a before we found the identity permutation again.
How about a cycle of length 2? A cycle of length 2 is just "swapping two elements". For instance, swapping elements 0 and 1:
a = [1,0,2]
b = np.array([0,1,2])
c = b
for i in range(2):
c = c[a]
print(c)
# [1 0 2]
# [0 1 2]
We swap 0 and 1, then we swap them back.
How about two disjoint cycles? Let's try a cycle of length 3 on the first three elements, simultaneously with swapping the last two elements:
a = [2,0,1,3,4,5,7,6]
b = np.array([0,1,2,3,4,5,6,7])
c = b
for i in range(6):
c = c[a]
print(c)
# [2 0 1 3 4 5 7 6]
# [1 2 0 3 4 5 6 7]
# [0 1 2 3 4 5 7 6]
# [2 0 1 3 4 5 6 7]
# [1 2 0 3 4 5 7 6]
# [0 1 2 3 4 5 6 7]
As you can see by carefully examining the intermediary results, there is a period of length 3 on the first three elements, and a period of length 2 on the last two elements. The overall period is the least common multiple of the two periods, which is 6.
What is k in general? A well-known theorem of algebra states: every permutation can be written as a product of disjoint cycles. The rank of a cycle is the length of the cycle. The rank of a product of disjoint cycles is the least common multiple of the ranks of cycles.
A coincidence in your code: sorting [2,1,4,7,6,5,0,3,8,9]
Let us go back to your python code.
a = np.array([2,1,4,7,6,5,0,3,8,9])
a = a[a]
a = a[a]
print(a)
# [0 1 2 3 4 5 6 7 8 9]
How many times did you apply permutation a? Note that because of the assignment a =, array a changed between the first and the second lines a = a[a]. Let us dissipate some confusion by using a different variable name for every different value. Your code is equivalent to:
a = np.array([2,1,4,7,6,5,0,3,8,9])
a2 = a[a]
a4 = a2[a2]
print(a4)
Or equivalently:
a = np.array([2,1,4,7,6,5,0,3,8,9])
a4 = (a[a])[a[a]]
This last line looks a little bit complicated. However, a cool result of algebra is that composition of permutations is associative. You already knew that addition and multiplication were associative: x+(y+z) == (x+y)+z and x(yz) == (xy)z. Well, it turns out that composition of permutations is associative as well! Using numpy's masks, this means that:
a[b[c]] == (a[b])[c]
Thus your python code is equivalent to:
a = np.array([2,1,4,7,6,5,0,3,8,9])
a4 = ((a[a])[a])[a]
print(a4)
Or without the unneeded parentheses:
a = np.array([2,1,4,7,6,5,0,3,8,9])
a4 = a[a][a][a]
print(a4)
Since a4 is the identity permutation, this tells us that the rank of a divides 4. Thus the rank of a is 1, 2 or 4. This tells us that a can be written as a product of swaps and length-4 cycles. The only permutation of rank 1 is the identity itself. Permutations of rank 2 are products of disjoint swaps, and we can see that this is not the case of a. Thus the rank of a must be exactly 4.
You can find the cycles by choosing an element, and following its orbit: what values is that element successively transformed into? Here we see that:
0 is transformed into 2; 2 is transformed into 4; 4 is transformed into 6; 6 is transformed into 0;
1 remains untouched;
3 becomes 7; 7 becomes 3;
5 is untouched; 8 and 9 are untouched.
Conclusion: Your numpy array represents the permutation (0 -> 2 -> 4 -> 6 -> 0)(3 <-> 7), and its rank is the least common multiple of 4 and 2, lcm(4,2) == 4.
it's took some time but I figure a way to do it.
numpy doesn't have this fiture but panda does have.
by using df.reindex I can sort a data frame by it indexes
import pandas as pd
import numpy as np
train_df = pd.DataFrame(range(10))
train_df = train_df.reindex(np.random.permutation(train_df.index))
print(train_df) # random dataframe contaning all values up to 9
train_df = train_df.reindex(range(10))
print(train_df) # sort data frame
This question already has answers here:
Sliding window maximum in O(n) time
(3 answers)
Closed 2 years ago.
Given an array of integers A. There is a sliding window of size B which
is moving from the very left of the array to the very right.
You can only see the w numbers in the window. Each time the sliding window moves
rightwards by one position. You have to find the maximum for each window.
The following example will give you more clarity.
The array A is [1 3 -1 -3 5 3 6 7], and B is 3.
Example:
Window position Max
[1 3 -1] -3 5 3 6 7 3
1 [3 -1 -3] 5 3 6 7 3
1 3 [-1 -3 5] 3 6 7 5
1 3 -1 [-3 5 3] 6 7 5
1 3 -1 -3 [5 3 6] 7 6
1 3 -1 -3 5 [3 6 7] 7
Input 1:
A = [1, 3, -1, -3, 5, 3, 6, 7]
B = 3
Output 1:
C = [3, 3, 5, 5, 6, 7]
NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified.
My Code:
class Solution:
# #param A : tuple of integers
# #param B : integer
# #return a list of integers
def slidingMaximum(self, A, B):
stack = []
if B>=len(A):
return [max(A)]
else:
for i in range((len(A))+1-B):
stack.append(A[i:i+B])
stack[i]=max(stack[i])
return stack
It's showing me time limit exceeded. Can anyone tell me why?
Time Limit Exceeded. Your submission didn't complete in the allocated time limit
It's because in the branch if B>=len(A): you are returning single value. There should be return [max(A)]
This question already has answers here:
How to remove items from a list while iterating?
(25 answers)
Closed 6 years ago.
My code should recieve a list of numbers and then output on the screen the only numbers which repeat more then once. I don't know why but it don't work with the numbers in the middle of list. My code:
a = [int(i) for i in (input().split())]
a.sort()
for number in a:
if a.count(number)==1:
a.remove(number)
else:
a.remove(a.count(number)-a.count(number)+number)
for number in a:
print(number, end=' ')
I tried changing if on while on 4th string, but then the last number is left in the list.
It should work like:
Sample Input 1: 4 8 0 3 4 2 0 3 Sample Output 1: 0 3 4
Sample Input 2: 10 Sample Output 2:
Sample Input 3: 1 1 2 2 3 3 Sample Output 3: 1 2 3
Sample Input 4: 1 1 1 1 1 2 2 2 Sample Output 4: 1 2
You could approach this problem using set instead:
a = list(map(int, input().split()))
print(" ".join(map(str, set(i for i in a if a.count(i) > 1))))
Explanation:
Firstly, it looks like you should read up on the map function. Instead of a = [int(i) for i in (input().split())], you can just use list(map(int, input().split())), which is much more Pythonic.
Secondly, the important part of the second line is set(i for i in a if a.count(i) > 1), which just creates a new list containing only the duplicates from a (i.e. [1, 2, 3, 2, 3] becomes [2, 3, 2, 3] and then applies set to it, which converts [2, 3, 2, 3] into {2, 3} (which is a set object).
In case you're wondering what map(str, ...) is for, it's so that you can print each of the elements inside your new set (e.g. {2, 3}).
You can use built-in lib collections to count list items and filter it by a required condition.
import collections
ints = map(int, input().split())
count = collections.Counter(ints)
print filter(lambda x: count[x] > 1, count)