This approach uses the formula for the sum of the first n natural numbers: Sum = n * (n + 1) / 2. By calculating the sum of the numbers from the array and subtracting it from the expected sum, we can find the missing number.
Time Complexity: O(n), where n is the length of the array.
Space Complexity: O(1), as no additional space is used beyond variables.
1class Solution:
2 def missingNumber(self, nums):
3 n = len(nums)
4 total = n * (n + 1) // 2
5 return total - sum(nums)
6
7# Usage
8nums = [3, 0, 1]
9sol = Solution()
10print(f"Missing number: {sol.missingNumber(nums)}")This Python solution calculates the expected total using n * (n + 1) // 2 and uses the built-in sum() function to find the sum of the array. The missing number is found by subtracting these sums.
An efficient approach is using XOR. XORing a number with itself results in zero (n ^ n = 0), and XOR of any number with zero keeps the number unchanged (n ^ 0 = n). By XORing all indices and array elements together, each number present in both will cancel out, leaving the missing number.
Time Complexity: O(n), iterating through the array.
Space Complexity: O(1), using constant space.
1function missingNumber(nums) {
2 let xorResult = 0;
3 for (let i = 0; i < nums.length; i++) {
4 xorResult ^= i ^ nums[i];
5 }
6 return xorResult ^ nums.length;
7}
8
9// Usage
10const nums = [3, 0, 1];
11console.log("Missing number:", missingNumber(nums));This JavaScript solution applies XOR logic to efficiently compute the missing number from the sequence by exploiting cancellation properties.