How do you solve Find Missing Observations on LeetCode?

Find Missing Observations (LeetCode #2028) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: The average must be an integer, which means the total sum must be divisible by n + m.

What is the time complexity of Find Missing Observations?

The optimal solution for Find Missing Observations runs in O(n) time and uses O(n) space. This complexity comes from creating the output array of size n and performing constant time calculations.

What is the brute force solution for Find Missing Observations?

The brute force approach for Find Missing Observations is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach would involve generating all possible combinations of n missing rolls and checking if their sum can yield the required average. This is inefficient and impractical for larger values of n. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find Missing Observations?

Find Missing Observations uses the following concepts: Array, Math, Simulation. The recommended patterns to study are: Mathematical calculations for averages., Array manipulation for generating results..

What are the interview tips for Find Missing Observations?

Always validate the input constraints before proceeding with calculations. Think about edge cases, such as when the mean is too high or too low. Communicate your thought process clearly, especially when transitioning from brute force to optimal solutions.

What are common mistakes when solving Find Missing Observations?

Not checking if the missing sum is within the valid range (n to 6 * n). Failing to account for the case where the mean is not achievable with the given rolls.

#2028

Find Missing Observations

Medium

ArrayMathSimulationMathematical calculations for averages.Array manipulation for generating results.

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

Instead of generating combinations, we can directly calculate the required missing rolls based on the desired mean. This approach is efficient and straightforward.

⚙️

Algorithm

5 steps

1Step 1: Calculate the total sum required for n + m rolls: total_sum = mean * (n + m).
2Step 2: Calculate the current sum of the given rolls.
3Step 3: Determine the sum needed for the missing rolls: missing_sum = total_sum - current_sum.
4Step 4: Check if the missing_sum is within the valid range (n to 6 * n). If not, return an empty array.
5Step 5: If valid, create an array filled with the average value (missing_sum / n) and adjust the last element to ensure the sum matches missing_sum.

solution.py12 lines

1# Full working Python code
2
3def find_missing_observations(rolls, mean, n):
4    total_sum = mean * (len(rolls) + n)
5    current_sum = sum(rolls)
6    missing_sum = total_sum - current_sum
7    if missing_sum < n or missing_sum > 6 * n:
8        return []
9    missing_obs = [missing_sum // n] * n
10    for i in range(missing_sum % n):
11        missing_obs[i] += 1
12    return missing_obs

ℹ

Complexity note: This complexity comes from creating the output array of size n and performing constant time calculations.

1The average must be an integer, which means the total sum must be divisible by n + m.
2The missing observations must be within the range of 1 to 6, as they represent dice rolls.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.