Find X Value of Array I

Find X Value of Array I

1. What is this problem about?

The Find X Value of Array I interview question asks you to find a specific value $X$ that satisfies a mathematical property across an array of numbers. Usually, this property involves finding a value $X$ such that if you perform an operation (like subtraction or absolute difference) on every element with $X$, the resulting sum or count meets a target.

2. Why is this asked in interviews?

Companies like Rubrik ask the Find X Value coding problem to test a candidate's ability to use Binary Search on the answer. It evaluates whether you can recognize a monotonic relationship: if increasing $X$ increases the result, then binary search is applicable. It's a test of efficient search in a continuous or discrete value space.

3. Algorithmic pattern used

This problem typically uses Binary Search on Value.

1. Define Range: Determine the minimum and maximum possible values for $X$ (e.g., the range of elements in the array).
2. Feasibility Function: Write a helper function check(X) that calculates the sum/count based on the problem's rules.
3. Binary Search:
   • If check(mid) is too small, move the search to the side that increases the result.
   • If check(mid) is too large, move the other way.
4. Dynamic Programming (Alternative): In some variations, the result for $X$ can be derived from the result for $X-1$ using DP.

4. Example explanation

Find $X$ such that $\sum \max(0, nums[i] - X) = Target$. Array: [10, 20, 30], Target: 15.

• Try $X=15$: $(0) + (5) + (15) = 20$. (Too high, need larger X).
• Try $X=20$: $(0) + (0) + (10) = 10$. (Too low, need smaller X).
• Try $X=17$: $(0) + (3) + (13) = 16$.
• Try $X=18$: $(0) + (2) + (12) = 14$. Result is between 17 and 18.

5. Common mistakes candidates make

• Linear Search: Checking every integer value for $X$, which is too slow if the range is large.
• Precision Errors: If $X$ can be a non-integer, failing to handle the binary search termination condition correctly (e.g., while(right - left > 1e-7)).
• Inefficient check: Not optimizing the check(X) function, especially if it can be done in $O(1)$ after sorting.

6. Interview preparation tip

Practice "Binary Search on Answer" problems. They are distinct from searching in an array. The key is to identify if the "result" of the operation changes predictably as your guess $X$ changes.