algoadvance

We are given an array of integers nums, and we need to find the smallest index i such that i % 10 == nums[i]. If there is no such index, we should return -1.

Clarifying Questions

  1. Is the array guaranteed to have positive integers, or can it include negative numbers?
    • Typically, such problems deal with non-negative indices, so the elements are expected to be non-negative integers.
  2. What should be the value range for numbers in the array?
    • It’s not explicitly given, but it’s reasonable to consider typical constraints such as 0 <= nums[i] <= 10^3.
  3. What should be the length of the array?
    • Again, while not explicitly stated, typical lengths might be 1 <= nums.length <= 10^5.

Given these typical constraints, we can proceed with our solution.

Strategy

  1. Iterate through the array nums:
    • For each index i, check if i % 10 is equal to nums[i].
    • As soon as you find such an index, return it.
    • If you finish the iteration without finding such an index, return -1.

Code

def smallest_equal(nums):
    for i in range(len(nums)):
        if i % 10 == nums[i]:
            return i
    return -1

Time Complexity

The time complexity of this solution is O(n), where n is the length of the array nums. This is because we might have to look at each element once in the worst case.

The space complexity is O(1) as we are not using any extra space that’s dependent on the size of the input array, merely a few variables for iteration.

Let’s now run through an example to confirm understanding:

Example:

nums = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
smallest_equal(nums)  # This should return 0 because 0 % 10 == 0

In this case, the function will return 0 as expected.

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