Find Missing

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Unit 7 Session 1 (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Medium
• ⏰ Time to complete: 15 mins
• 🛠️ Topics: Binary Search, Arrays

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• Established a set (2-3) of test cases to verify their own solution later.
• Established a set (1-2) of edge cases to verify their solution handles complexities.
• Have fully understood the problem and have no clarifying questions.
• Have you verified any Time/Space Constraints for this problem?

• Q: What happens if there are no missing numbers?
  • A: If no numbers are missing, the missing number would logically be ( n ), since the numbers are from 0 to ( n-1 ).

HAPPY CASE
Input: nums = [0, 1, 3, 4, 5]
Output: 2
Explanation: The number 2 is missing in the sequence.

EDGE CASE
Input: nums = [0, 1, 2, 3, 4]
Output: 5
Explanation: Since no numbers are missing from 0 to 4, the missing number is 5.

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

This problem is a variant of the classic binary search:

• Adapting binary search to detect an inconsistency in an otherwise complete series of sequential numbers.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Use binary search to efficiently find the missing number in a series that is nearly complete.

1) Establish binary search bounds with `left` at 0 and `right` at the last index of the array.
2) While `left` is less than `right`:
   - Compute the middle index.
   - If the element at the middle index matches the index, adjust `left` to `mid + 1`.
   - Otherwise, adjust `right` to `mid`.
3) The missing number will be at the position indicated by `left` after the loop completes.

⚠️ Common Mistakes

• Not considering the possibility that the missing number could be at the very end of the sequence (i.e., ( n )).

4: I-mplement

Implement the code to solve the algorithm.

def find_missing(nums):
    left, right = 0, len(nums)
    while left < right:
        mid = (left + right) // 2
        if nums[mid] > mid:
            right = mid
        else:
            left = mid + 1

    return left

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

• Test with input [0, 1, 3, 4, 5] to confirm it finds the missing number 2.
• Check with input [0, 1, 2, 3, 4] to ensure it returns 5, demonstrating that it correctly identifies the next logical missing number.

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

• Time Complexity: O(log n) because each iteration of the loop narrows the search space by half.
• Space Complexity: O(1) as the space used does not scale with the size of the input.