2501. Longest Square Streak in an Array

Difficulty: Medium

Topics: Array, Hash Table, Binary Search, Dynamic Programming, Sorting

You are given an integer array nums. A subsequence of nums is called a square streak if:

• The length of the subsequence is at least 2, and
• after sorting the subsequence, each element (except the first element) is the square of the previous number.

Return the length of the longest square streak in nums, or return -1 if there is no square streak.

A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

Example 1:

• Input: nums = [4,3,6,16,8,2]
• Output: 3
• Explanation: Choose the subsequence [4,16,2]. After sorting it, it becomes [2,4,16].
  • 4 = 2 * 2.
  • 16 = 4 * 4.
  • Therefore, [4,16,2] is a square streak.
  • It can be shown that every subsequence of length 4 is not a square streak.

Example 2:

• Input: nums = [2,3,5,6,7]
• Output: -1
• Explanation: There is no square streak in nums so return -1.

Constraints:

• 2 <= nums.length <= 105
• 2 <= nums[i] <= 105

Hint:

1. With the constraints, the length of the longest square streak possible is 5.
2. Store the elements of nums in a set to quickly check if it exists.

Solution:

We need to identify the longest square streak in the nums array. A square streak is a subsequence where each subsequent element is the square of the previous element, and it must be at least two elements long.

Here's the solution approach:

1. Use a Set for Quick Lookup:

   • Store the numbers in a set to quickly verify if an element's square is also in the array.

2. Iterate Through the Array:

   • For each number in the array, try to build a square streak starting from that number.
   • Check if the square of the current number exists in the set and keep extending the streak until there’s no further square match.

3. Track Maximum Length:

   • Track the maximum length of all possible square streaks encountered. If no square streak is found, return -1.

4. Optimization:

   • Sort the array before checking each element to ensure the subsequence is checked in ascending order. This will help avoid redundant checks.

Let's implement this solution in PHP: 2501. Longest Square Streak in an Array

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

// Test cases
$nums1 = [4, 3, 6, 16, 8, 2];
echo longestSquareStreak($nums1) . "\n";  // Output: 3

$nums2 = [2, 3, 5, 6, 7];
echo longestSquareStreak($nums2) . "\n";  // Output: -1
?>

Explanation:

• Sorting: Sorting nums ensures we can check sequences in ascending order.
• Set Lookup: Using array_flip creates a set-like structure for $numSet with $nums as keys, allowing fast existence checks.
• Loop through each number: For each num in nums, check if the square of the current number is in the set. If it is, continue the streak. Otherwise, break the streak and check if it’s the longest found.

Complexity Analysis

• Time Complexity: O(n log n) due to sorting, where n is the number of elements in nums. The subsequent lookups and square streak checks are O(n).
• Space Complexity: O(n), mainly for storing nums in the set.

This solution efficiently finds the longest square streak or returns -1 if no valid streak exists.

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