Keep Multiplying Found Values by Two

Problem Description

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:

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

Return the final value of original.

Key Insights

• The problem involves repeatedly searching for a number in an array and modifying it until it is no longer found.
• We can utilize a set for efficient lookup to check if the current value of original exists in nums.
• The process continues doubling the value of original until it is no longer present in the array.

Space and Time Complexity

Time Complexity: O(n) - where n is the length of nums, in the worst case, we may need to check all elements. Space Complexity: O(n) - if we use a set to store the elements of nums for fast lookup.

Solution

To solve the problem, we can use a set to store the values from the nums array. This allows for O(1) average-time complexity during lookups. The algorithm proceeds by checking if original exists in the set, multiplying it by two if it does, and repeating this process until original is no longer found in the set.

Code Solutions