2154. Keep Multiplying Found Values by Two

2154. Keep Multiplying Found Values by Two

Difficulty: Easy

Topics: Array, Hash Table, Sorting, Simulation, Weekly Contest 278

You are given an array of integers nums. You are also given an integer original which is the first number that needs to be searched for in nums.

You then do the following steps:

• If original is found in nums, multiply it by two (i.e., set original = 2 * original).
• Otherwise, stop the process.
• Repeat this process with the new number as long as you keep finding the number.

Return the final value of original.

Example 1:

• Input: nums = [5,3,6,1,12], original = 3
• Output: 24
• Explanation:
  • 3 is found in nums. 3 is multiplied by 2 to obtain 6.
  • 6 is found in nums. 6 is multiplied by 2 to obtain 12.
  • 12 is found in nums. 12 is multiplied by 2 to obtain 24.
  • 24 is not found in nums. Thus, 24 is returned.

Example 2:

• Input: nums = [2,7,9], original = 4
• Output: 4
• Explanation:
  • 4 is not found in nums. Thus, 4 is returned.

Constraints:

• 1 <= nums.length <= 1000
• 1 <= nums[i], original <= 1000

Hint:

1. Repeatedly iterate through the array and check if the current value of original is in the array.
2. If original is not found, stop and return its current value.
3. Otherwise, multiply original by 2 and repeat the process.
4. Use set data structure to check the existence faster.

Solution:

We need to repeatedly check if the current value of original exists in the given array nums. If it does, we double original and continue checking. This process stops when original is no longer found in nums.

Approach:

1. Efficient Lookup: Convert the array nums into a set for O(1) average time complexity lookups.
2. Iterative Checking: Continuously check if the current value of original exists in the set. If it does, double original and repeat the process. If not, return the current value of original.

Let's implement this solution in PHP: 2154. Keep Multiplying Found Values by Two

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

// Test cases
echo findFinalValue([5,3,6,1,12], 3) . "\n";    // Output: 24
echo findFinalValue([2,7,9], 4) . "\n";         // Output: 4
echo findFinalValue([1,2,3], 10) . "\n";        // Output: 10
?>

Explanation:

1. Convert to Set: Using array_flip converts the array into a set-like structure where the values from nums become keys. This allows O(1) average time complexity for membership checks.
2. Loop Until Not Found: The while loop checks if the current original exists in the set. If it does, original is doubled. This continues until original is not found in the set, at which point the loop exits and the current value of original is returned.

This approach efficiently checks for the existence of original and its subsequent doubled values, ensuring optimal performance even for the upper constraint limits. The use of a set ensures that each check is done in constant time, making the overall time complexity O(n) in the worst case, where n is the number of elements in nums.

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