Question

An array A contains n−1 unique integers in the range [0,n−1], that is, there is one number from this range that is not in A. Design an O(n)-time algorithm for finding that number. You are only allowed to use O(1) additional space besides the array A itself.

Answer 1

The question is about using an algorithm to find a missing number in an array with unique integers. The solution involves using a XOR operation, which ensures a O(n)-time complexity with O(1) space complexity.

Step-by-step explanation:

The subject of this question is an algorithm design problem that falls under the category of Computers and Technology. We are tasked with finding the missing integer in an array that contains unique integers within a specific range, using a O(n)-time algorithm and only O(1) additional space.

One efficient way to solve this problem is to use the XOR operation. The XOR of two identical numbers is 0 and the XOR of a number with 0 is the number itself. We can XOR all the numbers from 0 to n-1 with all the numbers in the array. The resulting value will be the number that is missing as it will not have been cancelled out by XORing with itself.

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3. Initialize a variable to hold the result, starting at 0.
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6. XOR this variable with each index from 0 to n-1.
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9. XOR the result with each number in the array A.
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12. The result is now the missing number.