Codility编程课一 PermMissingElem（Find the missing element in a given permutation.）

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#Codility编程 #PermMissingElem #Find missing in permutation.

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本文介绍了一个寻找指定范围内缺失整数的算法。该算法通过对比数组的实际累加值与理想累加值来找出缺失的数字，适用于包含不同整数的数组，并确保了线性时间和常数空间复杂度。

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PermMissingElem

Task description

An 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:

def solution(A)

that, given an 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) (not counting the storage required for input arguments).

def solution(A):
  ll = len(A)
  if ll == 0:
    return 1
  m = max(A)
  if m==ll:
    return m+1
  result = sum(A)
  assume = sum(range(1, m + 1))
  ret = assume - result
  return ret