First, I want to find the highest number in the list which is the second number in the list, then split it in two parts. The first part contains the 2nd highest number, while the second part contains the number from the list that sums to the highest number. Then, return the list
eg: input: [4,9,6,3,2], expected output:[4,6,3,6,3,2] 6+3 sums to 9 which is the highest number in the list
Please code it without itertools.
python
def length(s):
val=max(s)
s.remove(val)
for j in s:
if j + j == val:
s.append(j)
s.append(j)
return s
Here's what I have but it doesn't return what the description states.
Any help would be appreciated as I spent DAYS on this.
Thanks,
The main issue in your code seems to be that you are editing the list s whilst iterating through it, which can cause issues with the compiler and is generally just something you want to avoid doing in programming. A solution to this could be iterating through a copy of the original list.
The second problem is that your program doesn't actually find the second biggest value in the list, just a value which doubles to give you the biggest value.
The final problem (which I unfortunately only noticed after uploading what I thought was a solution) is that the split values are appended to the end of the list rather than to the position where originally the largest value was.
Hopefully this helps:
def length(array):
val = max(array)
idx = array.index(val) # gets the position of the highest value in the array (val)
array.remove(val)
for i in array.copy(): # creates a copy of the original list which we can iterate through without causing buggy behaviour
if max(array) + i == val:
array = array[:idx] + [max(array), i] + array[idx:]
# Redefines the list by placing inside of it: all values in the list upto the previous highest values, the 2 values we got from splitting the highest value, and all values which previously went after the highest value.
return array
This will return None if there is no value which can be added to the second highest value to get the highest value in the given array.
Input:
print(length([1,2,3,4,5]))
print(length([4,8,4,3,2]))
print(length([11,17,3,2,20]))
print(length([11,17,3,2,21]))
Output:
[1, 2, 3, 4, 4, 1]
[4, 4, 4, 4, 3, 2]
[11, 17, 3, 2, 17, 3]
None
Here are the docs on list slicing (which are impossible to understand) and a handy tutorial.
when you say "The first part contains the 2nd highest number" does that mean second highest number from the list or the larger of the two numbers that add up the largest number from list?
Here I assume you just wanted the larger of the two numbers that add up to the largest number to come first.
def length(s:list):
#start by finding the largest value and it's position in the list:
largest_pos = 0
for i in range(len(s)):
if s[i] > s[largest_pos]:
largest_pos = i
# find two numbers that add up to the largest number in the s
for trail in range(len(s)):
for lead in range(trail, len(s)):
if (s[trail] + s[lead]) == s[largest_pos]:
if s[trail] > s[lead]:
s[largest_pos] = s[trail]
s.insert(largest_pos +1, s[lead])
else:
s[largest_pos] = s[lead]
s.insert(largest_pos + 1, s[trail])
return s
# if no two numbers add up to the largest number. return s
return s
Since you are limited to 2 numbers, a simple nested loop works.
def length(s):
val = max(s)
idx = s.index(val)
s.remove(val)
for i in range(len(s) - 1):
for j in range(i + 1, len(s)):
if s[i] + s[j] == val:
s = s[:idx] + [s[i], s[j]] + s[idx:]
return s
print(length([4,9,6,3,2]))
Output:
[4, 6, 3, 6, 3, 2]
I used deque library
first to find the highest element or elements then remove all of them and replace them with second high value and rest like : 9 replace with 6 and 3 in example:
from collections import deque
l = [4, 9, 6, 3, 2]
a = deque(l)
e = a.copy()
s = max(a)
while s in a:
a.remove(s) # remove all highest elements
s2 = max(a) # find second high value
c = s - s2
for i in l:
if i == s:
w = e.index(i) # find index of high values
e.remove(max(e))
e.insert(w, s2)
e.insert(w+1, c)
print(list(e))
I have a list of numbers. I also have a certain sum. The sum is made from a few numbers from my list (I may/may not know how many numbers it's made from). Is there a fast algorithm to get a list of possible numbers? Written in Python would be great, but pseudo-code's good too. (I can't yet read anything other than Python :P )
Example
list = [1,2,3,10]
sum = 12
result = [2,10]
NOTE: I do know of Algorithm to find which numbers from a list of size n sum to another number (but I cannot read C# and I'm unable to check if it works for my needs. I'm on Linux and I tried using Mono but I get errors and I can't figure out how to work C# :(
AND I do know of algorithm to sum up a list of numbers for all combinations (but it seems to be fairly inefficient. I don't need all combinations.)
This problem reduces to the 0-1 Knapsack Problem, where you are trying to find a set with an exact sum. The solution depends on the constraints, in the general case this problem is NP-Complete.
However, if the maximum search sum (let's call it S) is not too high, then you can solve the problem using dynamic programming. I will explain it using a recursive function and memoization, which is easier to understand than a bottom-up approach.
Let's code a function f(v, i, S), such that it returns the number of subsets in v[i:] that sums exactly to S. To solve it recursively, first we have to analyze the base (i.e.: v[i:] is empty):
S == 0: The only subset of [] has sum 0, so it is a valid subset. Because of this, the function should return 1.
S != 0: As the only subset of [] has sum 0, there is not a valid subset. Because of this, the function should return 0.
Then, let's analyze the recursive case (i.e.: v[i:] is not empty). There are two choices: include the number v[i] in the current subset, or not include it. If we include v[i], then we are looking subsets that have sum S - v[i], otherwise, we are still looking for subsets with sum S. The function f might be implemented in the following way:
def f(v, i, S):
if i >= len(v): return 1 if S == 0 else 0
count = f(v, i + 1, S)
count += f(v, i + 1, S - v[i])
return count
v = [1, 2, 3, 10]
sum = 12
print(f(v, 0, sum))
By checking f(v, 0, S) > 0, you can know if there is a solution to your problem. However, this code is too slow, each recursive call spawns two new calls, which leads to an O(2^n) algorithm. Now, we can apply memoization to make it run in time O(n*S), which is faster if S is not too big:
def f(v, i, S, memo):
if i >= len(v): return 1 if S == 0 else 0
if (i, S) not in memo: # <-- Check if value has not been calculated.
count = f(v, i + 1, S, memo)
count += f(v, i + 1, S - v[i], memo)
memo[(i, S)] = count # <-- Memoize calculated result.
return memo[(i, S)] # <-- Return memoized value.
v = [1, 2, 3, 10]
sum = 12
memo = dict()
print(f(v, 0, sum, memo))
Now, it is possible to code a function g that returns one subset that sums S. To do this, it is enough to add elements only if there is at least one solution including them:
def f(v, i, S, memo):
# ... same as before ...
def g(v, S, memo):
subset = []
for i, x in enumerate(v):
# Check if there is still a solution if we include v[i]
if f(v, i + 1, S - x, memo) > 0:
subset.append(x)
S -= x
return subset
v = [1, 2, 3, 10]
sum = 12
memo = dict()
if f(v, 0, sum, memo) == 0: print("There are no valid subsets.")
else: print(g(v, sum, memo))
Disclaimer: This solution says there are two subsets of [10, 10] that sums 10. This is because it assumes that the first ten is different to the second ten. The algorithm can be fixed to assume that both tens are equal (and thus answer one), but that is a bit more complicated.
I know I'm giving an answer 10 years later since you asked this, but i really needed to know how to do this an the way jbernadas did it was too hard for me, so i googled it for an hour and I found a python library itertools that gets the job done!
I hope this help to future newbie programmers.
You just have to import the library and use the .combinations() method, it is that simple, it returns all the subsets in a set with order, I mean:
For the set [1, 2, 3, 4] and a subset with length 3 it will not return [1, 2, 3][1, 3, 2][2, 3, 1] it will return just [1, 2, 3]
As you want ALL the subsets of a set you can iterate it:
import itertools
sequence = [1, 2, 3, 4]
for i in range(len(sequence)):
for j in itertools.combinations(sequence, i):
print(j)
The output will be
()
(1,)
(2,)
(3,)
(4,)
(1, 2)
(1, 3)
(1, 4)
(2, 3)
(2, 4)
(3, 4)
(1, 2, 3)
(1, 2, 4)
(1, 3, 4)
(2, 3, 4)
Hope this help!
So, the logic is to reverse sort the numbers,and suppose the list of numbers is l and sum to be formed is s.
for i in b:
if(a(round(n-i,2),b[b.index(i)+1:])):
r.append(i)
return True
return False
then, we go through this loop and a number is selected from l in order and let say it is i .
there are 2 possible cases either i is the part of sum or not.
So, we assume that i is part of solution and then the problem reduces to l being l[l.index(i+1):] and s being s-i so, if our function is a(l,s) then we call a(l[l.index(i+1):] ,s-i). and if i is not a part of s then we have to form s from l[l.index(i+1):] list.
So it is similar in both the cases , only change is if i is part of s, then s=s-i and otherwise s=s only.
now to reduce the problem such that in case numbers in l are greater than s we remove them to reduce the complexity until l is empty and in that case the numbers which are selected are not a part of our solution and we return false.
if(len(b)==0):
return False
while(b[0]>n):
b.remove(b[0])
if(len(b)==0):
return False
and in case l has only 1 element left then either it can be part of s then we return true or it is not then we return false and loop will go through other number.
if(b[0]==n):
r.append(b[0])
return True
if(len(b)==1):
return False
note in the loop if have used b..but b is our list only.and i have rounded wherever it is possible, so that we should not get wrong answer due to floating point calculations in python.
r=[]
list_of_numbers=[61.12,13.11,100.12,12.32,200,60.00,145.34,14.22,100.21,14.77,214.35,200.32,65.43,0.49,132.13,143.21,156.34,11.32,12.34,15.67,17.89,21.23,14.21,12,122,134]
list_of_numbers=sorted(list_of_numbers)
list_of_numbers.reverse()
sum_to_be_formed=401.54
def a(n,b):
global r
if(len(b)==0):
return False
while(b[0]>n):
b.remove(b[0])
if(len(b)==0):
return False
if(b[0]==n):
r.append(b[0])
return True
if(len(b)==1):
return False
for i in b:
if(a(round(n-i,2),b[b.index(i)+1:])):
r.append(i)
return True
return False
if(a(sum_to_be_formed,list_of_numbers)):
print(r)
this solution works fast.more fast than one explained above.
However this works for positive numbers only.
However also it works good if there is a solution only otherwise it takes to much time to get out of loops.
an example run is like this lets say
l=[1,6,7,8,10]
and s=22 i.e. s=1+6+7+8
so it goes through like this
1.) [10, 8, 7, 6, 1] 22
i.e. 10 is selected to be part of 22..so s=22-10=12 and l=l.remove(10)
2.) [8, 7, 6, 1] 12
i.e. 8 is selected to be part of 12..so s=12-8=4 and l=l.remove(8)
3.) [7, 6, 1] 4
now 7,6 are removed and 1!=4 so it will return false for this execution where 8 is selected.
4.)[6, 1] 5
i.e. 7 is selected to be part of 12..so s=12-7=5 and l=l.remove(7)
now 6 are removed and 1!=5 so it will return false for this execution where 7 is selected.
5.)[1] 6
i.e. 6 is selected to be part of 12..so s=12-6=6 and l=l.remove(6)
now 1!=6 so it will return false for this execution where 6 is selected.
6.)[] 11
i.e. 1 is selected to be part of 12..so s=12-1=1 and l=l.remove(1)
now l is empty so all the cases for which 10 was a part of s are false and so 10 is not a part of s and we now start with 8 and same cases follow.
7.)[7, 6, 1] 14
8.)[6, 1] 7
9.)[1] 1
just to give a comparison which i ran on my computer which is not so good.
using
l=[61.12,13.11,100.12,12.32,200,60.00,145.34,14.22,100.21,14.77,214.35,145.21,123.56,11.90,200.32,65.43,0.49,132.13,143.21,156.34,11.32,12.34,15.67,17.89,21.23,14.21,12,122,134]
and
s=2000
my loop ran 1018 times and 31 ms.
and previous code loop ran 3415587 times and took somewhere near 16 seconds.
however in case a solution does not exist my code ran more than few minutes so i stopped it and previous code ran near around 17 ms only and previous code works with negative numbers also.
so i thing some improvements can be done.
#!/usr/bin/python2
ylist = [1, 2, 3, 4, 5, 6, 7, 9, 2, 5, 3, -1]
print ylist
target = int(raw_input("enter the target number"))
for i in xrange(len(ylist)):
sno = target-ylist[i]
for j in xrange(i+1, len(ylist)):
if ylist[j] == sno:
print ylist[i], ylist[j]
This python code do what you asked, it will print the unique pair of numbers whose sum is equal to the target variable.
if target number is 8, it will print:
1 7
2 6
3 5
3 5
5 3
6 2
9 -1
5 3
I have found an answer which has run-time complexity O(n) and space complexity about O(2n), where n is the length of the list.
The answer satisfies the following constraints:
List can contain duplicates, e.g. [1,1,1,2,3] and you want to find pairs sum to 2
List can contain both positive and negative integers
The code is as below, and followed by the explanation:
def countPairs(k, a):
# List a, sum is k
temp = dict()
count = 0
for iter1 in a:
temp[iter1] = 0
temp[k-iter1] = 0
for iter2 in a:
temp[iter2] += 1
for iter3 in list(temp.keys()):
if iter3 == k / 2 and temp[iter3] > 1:
count += temp[iter3] * (temp[k-iter3] - 1) / 2
elif iter3 == k / 2 and temp[iter3] <= 1:
continue
else:
count += temp[iter3] * temp[k-iter3] / 2
return int(count)
Create an empty dictionary, iterate through the list and put all the possible keys in the dict with initial value 0.
Note that the key (k-iter1) is necessary to specify, e.g. if the list contains 1 but not contains 4, and the sum is 5. Then when we look at 1, we would like to find how many 4 do we have, but if 4 is not in the dict, then it will raise an error.
Iterate through the list again, and count how many times that each integer occurs and store the results to the dict.
Iterate through through the dict, this time is to find how many pairs do we have. We need to consider 3 conditions:
3.1 The key is just half of the sum and this key occurs more than once in the list, e.g. list is [1,1,1], sum is 2. We treat this special condition as what the code does.
3.2 The key is just half of the sum and this key occurs only once in the list, we skip this condition.
3.3 For other cases that key is not half of the sum, just multiply the its value with another key's value where these two keys sum to the given value. E.g. If sum is 6, we multiply temp[1] and temp[5], temp[2] and temp[4], etc... (I didn't list cases where numbers are negative, but idea is the same.)
The most complex step is step 3, which involves searching the dictionary, but as searching the dictionary is usually fast, nearly constant complexity. (Although worst case is O(n), but should not happen for integer keys.) Thus, with assuming the searching is constant complexity, the total complexity is O(n) as we only iterate the list many times separately.
Advice for a better solution is welcomed :)
I am trying to find the total possibilities of how to place 90 apples in 90 boxes. Any amount of apples can be placed in one box (0 to 90 apples), but all apples have to be placed into boxes. I used recursion but it took way too much time to complete the calculation. I was only able to test my code with small amounts of apples and boxes. Could anyone help me on reduce the time complexity of my code? Thanks in advance.
import math
boxes = 3
apples = 3
def possibilities(apples, boxes):
if apples == 0:
return 1
if boxes == 0:
return 0
start_point = 0 if boxes > 1 else math.floor(apples/boxes)
p = 0
for n in range(start_point, apples+1):
p += possibilities(apples-n, boxes-1)
return p
t = possibilities(apples,boxes)
print(t)
The way I see it, the problem consists in finding the number of sorted list of max 90 elements which have a sum equal to 90.
There is a concept which is quite close to this and we call it the partitions of a number.
For example, the partitions of 4 are [4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1].
After a bit of research I found this article which is relevant to your problem.
As explained in there, the recursion method results in a very long calculation for large numbers, but...
A much more efficient approach is via an approach called dynamic programming. Here we compute a function psum(n,k), which is the total number of n-partitions with largest component of k or smaller. At any given stage we will have computed the values of psum(1,k), psum(2,k), psum(3,k), ..., psum(n,k) for some fixed k. Given this vector of n values we compute the values for k+1 as follows:
psum(i,k+1) = psum(i,k) + p(i,k) for any value i
But recall that p(i,k) = Σj p(i-k,j) = psum(i-k,k)
So psum(i,k+1) = psum(i,k) + psum(i-k,k)
So with a little care we can reuse the vector of values and compute the values of psum(i,k) in a rolling value for successively greater values of k. Finally, we have a vector whose values are psum(i,n). The value psum(n,n) is the desired value p(n). As an additional benefit we see that we have simultaneously computed the values of p(1), p(2), ..., p(n).
Basically, if you keep the intermediate values in a list and use the recurrence presented in the article,
psum(i,k+1) = psum(i,k) + psum(i-k,k)
you can use the following function:
def partitionp(n):
partpsum = [1] * (n + 1)
for i in range(2, n + 1):
for j in range(i, n + 1):
partpsum[j] += partpsum[j - i]
return partpsum[n]
At each iteration of the outer for loop, the list partpsum contains all the value psum(1,k), psum(2,k), psum(3,k), ..., psum(n,k). At the end of the iteration, you only need to return psum(n,n).
This question comes from Google Foobar, and my code passes all but the last test, with the input/output hidden.
The prompt
In other words, choose two elements of the array, x[i] and x[j]
(i distinct from j) and simultaneously increment x[i] by 1 and decrement
x[j] by 1. Your goal is to get as many elements of the array to have
equal value as you can.
For example, if the array was [1,4,1] you could perform the operations
as follows:
Send a rabbit from the 1st car to the 0th: increment x[0], decrement
x[1], resulting in [2,3,1] Send a rabbit from the 1st car to the 2nd:
increment x[2], decrement x[1], resulting in [2,2,2].
All the elements are of the array are equal now, and you've got a
strategy to report back to Beta Rabbit!
Note that if the array was [1,2], the maximum possible number of equal
elements we could get is 1, as the cars could never have the same
number of rabbits in them.
Write a function answer(x), which takes the array of integers x and
returns the maximum number of equal array elements that we can get, by
doing the above described command as many times as needed.
The number of cars in the train (elements in x) will be at least 2,
and no more than 100. The number of rabbits that want to share a car
(each element of x) will be an integer in the range [0, 1000000].
My code
from collections import Counter
def most_common(lst):
data = Counter(lst)
return data.most_common(1)[0][1]
def answer(x):
"""The goal is to take all of the rabbits in list x and distribute
them equally across the original list elements."""
total = sum(x)
length = len(x)
# Find out how many are left over when distributing niavely.
div, mod = divmod(total, length)
# Because of the variable size of the list, the remainder
# might be greater than the length of the list.
# I just realized this is unnecessary.
while mod > length:
div += length
mod -= length
# Create a new list the size of x with the base number of rabbits.
result = [div] * length
# Distribute the leftovers from earlier across the list.
for i in xrange(mod):
result[i] += 1
# Return the most common element.
return most_common(result)
It runs well under my own testing purposes, handling one million tries in ten or so seconds. But it fails under an unknown input.
Have I missed something obvious, or did I make an assumption I shouldn't have?
Sorry, but your code doesn't work in my testing. I fed it [0, 0, 0, 0, 22] and got back a list of [5, 5, 4, 4, 4] for an answer of 3; the maximum would be 4 identical cars, with the original input being one such example. [4, 4, 4, 4, 6] would be another. I suspect that's your problem, and that there are quite a few other such examples in the data base.
For N cars, the maximum would be either N (if the rabbit population is divisible by the number of cars) or N-1. This seems so simple that I fear I'm missing a restriction in the problem. It didn't ask for a balanced population, just as many car populations as possible should be equal. In short:
def answer(census):
size = len(census)
return size if sum(census) % size == 0 else (size-1)
I have been looking for how to find the middle number in the list so that I do not use the median function, but cannot find the information how to do that.
I need to write a code which takes middle(L) function (have to define it), makes a list L as its argument, and returns the item in the middle position of L. (In order that the middle is well-defined, i should assume that L has odd length.)
It is all i have right now and actually have no idea how to do that.
def middle (L):
i= len((L)[0:-1])/2
return i
print (middle)
To find the median, just sort the list and return the number in the middle position or (if the list has even number of elements), return the average of the 2 elements in middle:
def middle(L):
L = sorted(L)
n = len(L)
m = n - 1
return (L[n/2] + L[m/2]) / 2.0
Example:
>>> print middle([1, 2, 3, 4, 5])
3.0
>>> print middle([1, 2, 3, 4, 5, 6])
3.5
As NPE's answer suggests you just have to get the middle element of a sorted list when the list has an uneven number of elements, if it has an even number of elements you take the average of the middle two elements:
def median(l):
srt = sorted(l)
mid = len(l)//2
if len(l) % 2: # f list length mod 2 has a remainder the list is an odd lenght
return srt[mid]
else:
med = (srt[mid] + srt[mid-1]) / 2 # in a list [1,2,3,4] srt[mid]-> 2, srt[mid-1] -> 3
return med
For optimization, we should use binary search to detect the median, rather than to sort all numbers.
For details, please check:
https://www.quora.com/Given-a-list-of-unsorted-numbers-how-would-you-find-the-median-without-sorting-the-original-array
For the code, please check:
https://medium.com/#nxtchg/calculating-median-without-sorting-eaa639cedb9f
There are two well-known ways to calculate median:
naive way (sort, pick the middle)
using quickselect (or similar algorithm for weighted median)
Hope it helps.