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Apply Operations to Make All Array Elements Equal to Zero

Difficulty: Medium

Problem Description

You are given a 0-indexed integer array nums and a positive integer k. You can apply the following operation on the array any number of times: Choose any subarray of size k from the array and decrease all its elements by 1. Return true if you can make all the array elements equal to 0, or false otherwise.

Key Insights

  • The operation can only affect contiguous subarrays of length k.
  • The goal is to ensure that every element in the array can be reduced to zero using the allowed operations.
  • If at any point there exists an element that cannot be reduced to zero due to the constraints of k, the answer is false.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve this problem, we can leverage a greedy approach. We iterate through the array while maintaining the cumulative effect of the operations applied to each element. We track how many operations we have effectively "activated" at each position using a variable. When we encounter an element that is greater than zero, we determine how many operations are required to bring it to zero. We can only apply operations starting from the current index until k elements have been affected. If we ever find an element that cannot be zeroed out due to the constraints of k, we return false.

Code Solutions

def canMakeAllZero(nums, k):
    n = len(nums)
    operations = 0  # This will track the cumulative operations applied
    for i in range(n):
        # Reduce the current number by the number of operations applied so far
        nums[i] -= operations
        # If the current number is greater than 0, we need to apply operations
        if nums[i] > 0:
            # Calculate how many operations we need to apply
            operations_needed = nums[i]
            operations += operations_needed
            # We can only affect the next k elements
            if i + k <= n:
                # We apply this operation until the end of the subarray
                if i + k < n:
                    nums[i + k] += operations_needed
            else:
                return False  # If we can't apply enough operations, return False
    return True
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