Codility ‘PermMissingElem’ Solution

Short Problem Definition:

Find the missing element in a given permutation.

Link

PermMissingElem

Complexity:

expected worst-case time complexity is O(N);

expected worst-case space complexity is O(1)

Execution:

Sum all elements that should be in the list and sum all elements that actually are in the list. The sum is 0 based, so +1 is required. The first solution using the + operator can cause int overflow in not-python languages. Therefore the use of a binary XOR is adequate.

Solution:
def solution(A):
    should_be = len(A) # you never see N+1 in the iteration
    sum_is = 0

    for idx in xrange(len(A)):
        sum_is += A[idx]
        should_be += idx+1

    return should_be - sum_is +1

def solution(A):
    missing_element = len(A)+1
    
    for idx,value in enumerate(A):
        missing_element = missing_element ^ value ^ (idx+1)
        
    return missing_element

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