Limit input data to achieve a better Big O complexity

Question

You are given an unsorted array of n integers, and you would like to find if there are any duplicates in the array (i.e. any integer appearing more than once). D

Answer 1

nested loops get you O(N*M) or O(N*log(M)) for O(N) you can not use nested loops !!!

I would do it by use of histogram instead:

DWORD in[N]={ ... }; // input data ... values are from < 0 , M )
DWORD his[M]={ ... }; // histogram of in[]
int i,j;

// compute histogram O(N)
for (i=0;i

[Notes]

• if value range is too big with sparse areas then you need to convert his[]
• to dynamic list with two values per item
• one is the value from in[] and the second is its occurrence count
• but then you need nested loop -> O(N*M)
• or with binary search -> O(N*log(M))