Array Homework Question

Question

You are given an array with integers between 1 and 1,000,000. One integer is in the array twice. How can you determine which one? Can you think of a way to do it using littl

Answer 1

As a variant of your solution (2), you can use radix sort. No extra memory, and will run in linear time. You can argue that time is also affected by the size of numbers representation, but you have already given bounds for that: radix sort runs in time O(k n), where k is the number of digits you can sort ar each pass. That makes the whole algorithm O(7n)for sorting plus O(n) for checking the duplicated number -- which is O(8n)=O(n).

Pros:

• No extra memory
• O(n)

Cons:

• Need eight O(n) passes.