Missing Number
Given an array containing n distinct numbers from 0, 1, 2, ..., n, find the one that is missing.
Example:
3,0,1
2
- The input array is
[3, 0, 1], containingn = 3distinct numbers. - We notice that the array should contain numbers from
0ton, so the complete set should be[0, 1, 2, 3]. - Comparing the input array to the complete set, we find that the number 2 is missing.
- The final output is therefore
2.
Constraints:
- 1 <= n <= 10^4
- 0 <= nums[i] <= n
- All numbers are unique
Background Knowledge
The "Missing Number" problem is a classic example of a mathematical puzzle that can be solved using various approaches. To tackle this problem, it's essential to understand the concept of sequences and series. A sequence is a set of numbers in a specific order, and a series is the sum of the terms of a sequence. In this case, we're dealing with a sequence of distinct numbers from 0 to n.
The problem can be approached using arithmetic series formulas, which describe the sum of a sequence of numbers with a common difference. The formula for the sum of an arithmetic series is S=2n​(a+l), where S is the sum, n is the number of terms, a is the first term, and l is the last term. Understanding this concept can help you derive a solution to find the missing number.
Another crucial concept is bit manipulation, which involves using bitwise operations to solve problems. This approach can be useful when dealing with binary representations of numbers. However, it's not the only way to solve this problem, and other methods, such as mathematical formulas or iterative approaches, can also be employed.
Continue the full explanation
You're reading the free preview. Unlock the complete walkthrough, the code editor, test runner and reference solution with Premium.
Editor locked
The code editor is locked for Pro problems. It is only available for free problems. Please upgrade to gain access to the code editor for all problems.