Missing Number

ID: 268; easy

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Solution 1

func missingNumber(nums []int) int {
    numsSum, n := 0, len(nums)
    for _,v := range nums {
        numsSum += v
    }
    rangeSum := n*(n+1) / 2
    return rangeSum - numsSum
}

The thought process here is easy, compared to solution 2. We are given the nums array with one element missing from the range [0, n]. Since the numbers are distinct, the difference between the sum of the nums array and the sum of all numbers in the range [0, n] is actually the missing number.

The rangeSum uses the formula for summing arithmetic sequences:

$$1+2+\cdots+n = \frac{(1+n)\times n}{2}$$

Solution 2

func missingNumber(nums []int) int {
    xor, i := 0, 0
    for ; i < len(nums); i++ {
        xor = xor ^ i ^ nums[i]
    }
    return xor ^ i
}

Bit manipulation. Note that XOR returns 1 if and only if the bits differ.

We use the properties that X ^ X = 0 and X ^ 0 = X. Consider the following example, we have the array [3, 0, 1], n = 3 in this case, and we are missing 2.

The important thing to notice here is that if we have every number in [0, n], then taking the XOR results of all the numbers should give us a 0. For this example,

The array [3, 0, 1, 2] contains every number in [0, 3], and

0 ^ 0 ^ 3 ^ 1 ^ 0 ^ 2 ^ 1 ^ 3 ^ 2 = 0    // order doesn't matter

For the array with a missing element 2: [3, 0, 1], we have

0 ^ 0 ^ 3 ^ 1 ^ 0 ^ 2 ^ 1 = 0 ^ 3 ^ 2 = 3 ^ 2

The result here is actually 3 (i.e., n) and 2 (the missing element) because the difference between [0, n-1] and [0, n] is n and 2 has nothing to cancel itself with. Therefore, taking this result and XOR it with n gives us the final result:

3 ^ 2 ^ 3 = 2