Formatted question description: https://leetcode.ca/all/2154.html

# 2154. Keep Multiplying Found Values by Two (Easy)

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 = 3Output:24Explanation:- 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 = 4Output:4Explanation:- 4 is not found in nums. Thus, 4 is returned.

**Constraints:**

`1 <= nums.length <= 1000`

`1 <= nums[i], original <= 1000`

**Similar Questions**:

## Solution 1. Set + Simulation

```
// OJ: https://leetcode.com/problems/keep-multiplying-found-values-by-two/
// Time: O(NlogN)
// Space: O(N)
class Solution {
public:
int findFinalValue(vector<int>& A, int n) {
set<int> s(begin(A), end(A));
while (s.count(n)) n *= 2;
return n;
}
};
```

## Solution 2. Bucket Count + Simulation

```
// OJ: https://leetcode.com/problems/keep-multiplying-found-values-by-two/
// Time: O(N)
// Space: O(R) where `R` is the range of numbers in `A`
class Solution {
public:
int findFinalValue(vector<int>& A, int n) {
int seen[1001] = {};
for (int x : A) seen[x] = 1;
while (n < 1001 && seen[n]) n *= 2;
return n;
}
};
```

## Solution 3. Sorting + One Pass

```
// OJ: https://leetcode.com/problems/keep-multiplying-found-values-by-two/
// Time: O(NlogN)
// Space: O(1)
class Solution {
public:
int findFinalValue(vector<int>& A, int n) {
sort(begin(A), end(A));
for (int i = 0, N = A.size(); i < N;) {
while (i < N && A[i] < n) ++i;
if (i == N || A[i] != n) break;
n *= 2;
}
return n;
}
};
```

## Discuss

https://leetcode.com/problems/keep-multiplying-found-values-by-two/discuss/1730124