Find duplicates in an array

Given an array of size 'n', containing elements from 1 to 'n', find out if there are any duplicates in the array. Solve this, if

• a single duplicate number exists
• multiple duplicate numbers exist

 Source : CLRS & this blog question (that I did not get)

Find subarray with maximum sum

Given an array of size n, containing positive and negative integers, find the longest sub-array such that the sum of the elements in the sub-array is the maximum.

For example,
Given array :
10, 8, -5, 1, -27, 5, 7, -5, 11
the sub array should be : 10, 8

Source : CLRS & this sample interview question