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By back_slash, history, 7 months ago, ,

You are given two natural numbers N and K. You need to represent the number N as a product of K numbers such that all the K numbers are >= 2 and the sum of the K numbers is minimum. The constraints on the value of N <= 10^12. Given such values of K for which the answer always exist.

My Solution:- After finding the prime factorization of the number N. Insert the factors in a multiset and then solve the problem greedily. Take the first 2 elements of the multiset, remove them and then insert their product in the multiset. Keep on repeating this process until the size of multiset becomes equal to K.

I don't know whether the above approach is correct or not and also I am not sure whether the answer will be unique or not.

Any suggestions for the given approach or some new approach are welcomed.

UPD:- I know my approach is incorrect but still I am unable to figure out anything about uniqueness. Whether the answer will be unique or not.

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 » 7 months ago, # | ← Rev. 4 →   +31 Your solution is wrong; take N = 36, K = 2. You can solve the problem in with DP.EDIT: This might be too slow, depending on the test data.
•  » » 7 months ago, # ^ |   +5 Thanks for the reply!!! Can we say anything about the uniqueness of the K numbers?? If we take the numbers in sorted order will the answer be unique?
•  » » » 7 months ago, # ^ |   +5 Any Updates???
 » 7 months ago, # |   0 Auto comment: topic has been updated by back_slash (previous revision, new revision, compare).