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
- Minimize operations required to make each element of Array equal to it's index value
- Sort an array after applying the given equation
- Minimize cost to convert given two integers to zero using given operations
- Minimize operations required to obtain N
- Minimize prize count required such that smaller value gets less prize in an adjacent pair
- Minimum value of X that can be added to N to minimize sum of the digits to ≤ K
- Find maximum value of the last element after reducing the array with given operations
- Minimize the sum of the array according the given condition
- Remove an element to minimize the LCM of the given array
- Minimize the non-zero elements in the Array by given operation
- Minimize steps required to move all 1's in a matrix to a given index
- Minimize K whose XOR with given array elements leaves array unchanged
- Reverse a subarray of the given array to minimize the sum of elements at even position
- Minimize cost to Swap two given Arrays
- Minimize cost to empty a given string by removing characters alphabetically
- Minimize cost to convert a given matrix to another by flipping columns and reordering rows
- Minimize count of unequal elements at corresponding indices between given arrays
- Maximum value in an array after m range increment operations
- Minimum Operations to make value of all vertices of the tree Zero
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