一个简单例子的空间复杂性

Question

So I was checking the codibility website for online code evaluation. I tried the demo example http://codility.com/c/intro/demoRVC9C9-W8X to familiarize myself with the system.

A zero-indexed array A consisting of N different integers is given. The array contains integers in the range [1..(N + 1)], which means that exactly one element is missing. Your goal is to find that missing element. Write a function:

class Solution { public int solution(int[] A); }

that, given a zero-indexed array A, returns the value of the missing element. For example, given array A such that:

A[0] = 2
A[1] = 3
A[2] = 1
A[3] = 5

the function should return 4, as it is the missing element. Assume that: N is an integer within the range [0..100,000]; the elements of A are all distinct; each element of array A is an integer within the range [1..(N + 1)].

Complexity:

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

expected worst-case space complexity is O(1), beyond input storage (not counting the storage required for input arguments).

Elements of input arrays can be modified.

Here is my solution in Python:

def solution(A):
  tmp = [ 0 for x in xrange( len(A) + 1 ) ]
  for i,x in enumerate( A ):
    tmp[ x - 1 ] = 1
  return 1 + tmp.index( 0 )

I was pretty sure that my solution would NOT be accepted because the space complexity is O(n) where n is the size of A. However the system accepted my answer with a perfect score. Am I missing something here?

Answer 1

My solution takes it's base from a ruby perspective.

in ruby

def solution(a)
  (1..(a.count+1)).select{|x| !a.include?(x)}.first
end 

in python

def solution(A):
    # write your code in Python 2.7
    return filter(lambda x: (x not in A), range(1, (len(A)+2)))[0] 

Answer 2

This solution resulted 100/100

def solution(A):

if not A:
    return 1
sumz=sum(xrange(1,(max(A)+1)))
if ((len(A)+1)) not in A:
    return len(A)+1

a_sum=sum(A)

return sumz-a_sum

Answer 3

My solution in Ruby.

def solution(a)    
  return 1 if a.empty?
  ac = a.count
  ((ac+1)*(ac+2))/2 - a.inject(0, :+)
end

.inject(0, :+) sums up elements in array.

Answer 4

Just start lernig Python and this is my 100 score solution:

def solution(A):
    a=[]
    a=A
    a.sort()
    b=0
    if len(a)<1:
        return 1
    if a[0] != 1:
        return 1
    else:
        for x in xrange(0,len(a)):
            b=b+int(a[x])
    if a[len(a)-1]==len(a)+1:        
        c=(1+len(a))*len(a)/2
        d=b-a[len(a)-1]
        e=c-d
        return e
    else:
        return len(a)+1

i know its not great im just start lerning Python

Answer 5

these are two complicated scenarios.

think simply.

step #1: order the array step #2: iterate trough the ordered array. if A[i] != i+1 you have fund the missing element. in case the loop iterates through the whole array than the last element is missing just return the last element + 1.

this is 100% solution.