Solution to Min-Max-Division by codility

6 Apr


Question Name: Min-Max-Division or MinMaxDivision

Logically, it seems to be similar with the boron2013 (Flags) challenge by Codility. And the following is my Python solution.

UPDATE – 2014/09/19: thanks to Martin Kysel. The function signature is changed to:
def solution(K, M, A):
Don’t be confused by the new parameter M. Ignore the M, use the original solution, and you will pass all the test.

In addition, thanks to @Guillermo (StackOverflow Profile), here is the C++ solution from @Guillermo, which inspired me. Thanks again for his sharing!

21 Replies to “Solution to Min-Max-Division by codility

  1. Java solution, greedy checking :

  2. I’m confused regarding the time complexity. Why is the time complexity O(N*log(N+M)) instead of O(N*log(N*M))? The upper bound of the binary search is equal to the sum of the elements in A, which is at most N*M.

    • Yes, you are right. The complexity is not exactly O(N*log(N+M)). O(N*log(N*M)) = O(N*(log(N) + log(M))). Therefore, when N is close to M, O(N*log(N*M)) is the same as O(N*log(N+M)). In generaly case, I do not know the answer.

  3. Thank you very much for your solution. Really enlightening 🙂
    Here’s the Java version of your Python solution:

  4. What is throwing me off is that the exercise is asking for “expected worst-case time complexity is O(N*log(N+M))”
    If I’m reading your solution correctly you’re first looping through all the elements followed by the binary search section. Isn’t that O(n) + log(n+m) ?

    • You are partly right. The binary search at #37 is inside the while loop around #35: so the complexity is O(N) * O(log(N+M)) = O(N*log(N+M)).

  5. I was tricked by M…”no greater than M” made me made the assumption that the largest element in the array must be M, which is not true, well, at least in Codility test cases. I got 43% just because of failing to recognize this “fact”…
    If we consider the smallest max as a monotonic sequence, the lower bound of the sequence is the largest element in the array, and the higher bound is the sum of all elements. Then we choose the possible “smallest max” at the middle of the sequence and always greedily drops half of of the sequence by comparing the number of partitions based upon current “smallest max” with the proposed K. If our partition L is less than K, we probably can find a even smaller “smallest max” by dropping the lager half of the sequence, otherwise, drop the smaller half…

  6. M is not misleading. In fact it can be proved that the result is between (mean,mean+M).
    Updated by Sailingfish on Aug 19, 2017.

  7. In the sample given in the question; K=3, A=[2, 1, 5, 1, 2, 2, 2] should the answer not be 5 instead of the given answer 6? You can group the elements as [2,2,1].[2,2,1],[5]

  8. Sheng, thank you for great work!
    I have one question, how can you prove that resultMaxMid is the minimal large sum?

  9. Great work. I am always inspired by your ideas and skills.
    For those who are still studying in 2021, you need to get the ceiling value of the average like this (using the ceil from math)

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