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Minimum Numbers of Function Calls to Make Target Array

Difficulty: Medium

Problem Description

You are given an integer array nums. You have an integer array arr of the same length with all values set to 0 initially. You also have the following modify function: You want to use the modify function to convert arr to nums using the minimum number of calls. Return the minimum number of function calls to make nums from arr.

Key Insights

  • The modify function allows you to increment each element or to double all elements in arr.
  • To reach the desired nums, we can focus on the highest number in nums and work backwards.
  • Doubling operations should be prioritized when possible to minimize the number of increments needed.
  • The number of increments required for each element can be computed by evaluating the operations from the highest value down to zero.

Space and Time Complexity

Time Complexity: O(n) - where n is the length of the array nums, as we may need to traverse the array to determine the maximum and calculate the number of operations.
Space Complexity: O(1) - we use a constant amount of space for tracking the number of operations.

Solution

The solution involves iterating over the nums array to determine the maximum value. From there, we calculate how many times we can apply the double operation until we reach the desired values in nums. After maximizing the use of the double operation, we apply the necessary increments to reach each target value.

Code Solutions

def minOperations(nums):
    max_num = max(nums)
    operations = 0
    
    while max_num > 0:
        for i in range(len(nums)):
            if nums[i] >= max_num:
                continue
            # Count the number of increments needed
            operations += (max_num - nums[i]) % 2  # Increment if odd
            nums[i] = (nums[i] + (max_num - nums[i]) // 2)  # Halve the difference
            
        # Halve max_num for the next round of operations
        max_num //= 2
        operations += 1  # account for the doubling operation

    return operations
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