Introduction to Algorithms 2.3-7

problem: Given the set S of N integers and another integer x, describes an algorithm that runs at O (log N), which determines if there are two elements in s that are exactly X

Algorithm Description:

1. Sort the elements of the set in array a first

2, for each element in the set A[i], in a sorted array a binary find X-a[i]

3, the search success exists, the end of the loop after the search is not successful does not exist

Pseudo code:

1 Sort (A) 2 n = a.length3for1 to n4     1, N) /c12>5     if ans! = NotFound6         returntrue 7 return false

Algorithm Complexity Analysis:

T (n) = log 1 + log 2 + log3 +....+logn = log (n!) = log (sqrt (2*pi*n) * (n/e) ^n) = O (n log n)

Complexity of O (LOGN)

Introduction to Algorithms 2.3-7