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