3254. Find the Power of K-Size Subarrays I

#php #leetcode #algorithms #programming

Difficulty: Medium

Topics: Array, Sliding Window

You are given an array of integers nums of length n and a positive integer k.

The power of an array is defined as:

Its maximum element if all of its elements are consecutive and sorted in ascending order.
-1 otherwise.

You need to find the power of all subarrays¹ of nums of size k.

Return an integer array results of size n - k + 1, where results[i] is the power of nums[i..(i + k - 1)].

Example 1:

Input: nums = [1,2,3,4,3,2,5], k = 3
Output: [3,4,-1,-1,-1]
Explanation: There are 5 subarrays of nums of size 3:
- [1, 2, 3] with the maximum element 3.
- [2, 3, 4] with the maximum element 4.
- [3, 4, 3] whose elements are not consecutive.
- [4, 3, 2] whose elements are not sorted.
- [3, 2, 5] whose elements are not consecutive.

Example 2:

Input: nums = [2,2,2,2,2], k = 4
Output: [-1,-1]

Example 3:

Input: nums = [3,2,3,2,3,2], k = 2
Output: [-1,3,-1,3,-1]

Constraints:

1 <= n == nums.length <= 500
1 <= nums[i] <= 10⁵
1 <= k <= n

Hint:

Can we use a brute force solution with nested loops and HashSet?

Solution:

We can break down the task as follows:

Problem Breakdown:

We are given an array nums of length n, and a positive integer k. We need to consider all subarrays of size k and compute their power.
The power of a subarray is:
- The maximum element of the subarray if all the elements are consecutive and sorted in ascending order.
- -1 otherwise.
We need to return an array of size n - k + 1, where each element corresponds to the power of the respective subarray.

Plan:

Sliding Window Approach: We will slide over the array and check each subarray of length k.
Check if the Subarray is Sorted: We need to check if the subarray has elements that are consecutive and sorted in ascending order.
Return Maximum or -1: If the subarray is valid, we return the maximum element. Otherwise, return -1.

Steps:

Check if the subarray is sorted:
- A sorted subarray with consecutive elements should have the property: nums[i+1] - nums[i] == 1 for every i in the subarray.
Sliding Window:
- For each subarray of length k, check if it is sorted and return the maximum element if valid, otherwise return -1.

Let's implement this solution in PHP: 3254. Find the Power of K-Size Subarrays I

<?php
/**
 * @param Integer[] $nums
 * @param Integer $k
 * @return Integer[]
 */
function resultsArray($nums, $k) {
    ...
    ...
    ...
    /**
     * go to ./solution.php
     */
}

// Test cases
print_r(resultsArray([1, 2, 3, 4, 3, 2, 5], 3));  // Output: [3, 4, -1, -1, -1]
print_r(resultsArray([2, 2, 2, 2, 2], 4));  // Output: [-1, -1]
print_r(resultsArray([3, 2, 3, 2, 3, 2], 2));  // Output: [-1, 3, -1, 3, -1]
?>

Explanation:

Sliding Window: We use a for loop from i = 0 to i = n - k to consider all subarrays of size k. For each subarray, we use array_slice() to extract the subarray.
Sorting Check: For each subarray, we check if it is sorted with consecutive elements by iterating through the subarray and checking if each pair of consecutive elements has a difference of 1.
Result: If the subarray is valid, we append the maximum value of the subarray to the result. Otherwise, we append -1.

Time Complexity:

We are iterating over n - k + 1 subarrays.
For each subarray, we check if the elements are consecutive, which takes O(k) time.
Thus, the overall time complexity is O((n - k + 1) * k) which simplifies to O(n * k).

Edge Case Considerations:

If k = 1, every subarray is trivially sorted (it only contains one element), and the power of each subarray will be the element itself.
If the subarray is not consecutive, it will immediately return -1.

Example Outputs:

For nums = [1, 2, 3, 4, 3, 2, 5], k = 3, the output is [3, 4, -1, -1, -1].
For nums = [2, 2, 2, 2, 2], k = 4, the output is [-1, -1].
For nums = [3, 2, 3, 2, 3, 2], k = 2, the output is [-1, 3, -1, 3, -1].

This solution should efficiently work for the problem constraints.

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