Given an integer N, below operations can be performed any number of times on N:
- Multiply N by any positive integer X i.e. N = N * X.
- Replace N with square root of N (N must be an integer) i.e. N = sqrt(N).
The task is to find the minimum integer to which N can be reduced with the above operations.
Input: N = 20
We can multiply 20 by 5, then take sqrt(20*5) = 10, this is the minimum number that 20 can be reduced to with the given operations.
Input: N = 36
Take sqrt(36). Number 6 can’t be reduced further.
- First factorize the number N.
- Say, 12 has factors 2, 2 and 5. Only the factors that are repeating can be reduced with sqrt(n) i.e. sqrt(2*2) = 2.
- The numbers appearing only once in the factors cannot be further reduced.
- So, the final answer will be the product of all the distinct prime factors of number N
Below is the implementation of the above approach:
- Print matrix after applying increment operations in M ranges
- Sort an array after applying the given equation
- Minimize the sum of digits of A and B such that A + B = N
- Minimize the sum of the array according the given condition
- Minimize the cost to split a number
- Minimize the cost of buying the Objects
- Minimize the absolute difference of sum of two subsets
- Minimize the number by changing at most K digits
- Minimize sum by dividing all elements of a subarray by K
- Remove an element to minimize the LCM of the given array
- Minimize the cost of partitioning an array into K groups
- Minimize the maximum minimum difference after one removal from array
- Minimize the number of steps required to reach the end of the array | Set 2
- Minimize sum of adjacent difference with removal of one element from array
- Minimize the sum of the squares of the sum of elements of each group the array is divided into
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