Array | Order Statistics

What is Order Statistics?

The i^th order statistics is defined as the value that comes in the i^th position of the N element sequence when the sequence is sorted in increasing order.

In simple terms, the order statistics is the i^th smallest element in the given array. Below are a few examples to understand the order statistics:

• Minimum = Order statistics 1
• 2nd minimum = Order statistics 2
• Median = Order statistics floor((N+1)/2)
• 2nd Maximum = Order Statistics N-1
• Maximum = Order statistics N

Some practice problems in Order Statistics:

• Easy:
  1. Program to find largest element in an array
  2. Find the largest three elements in an array
  3. Program for Mean and median of an unsorted array
  4. Find Second largest element in an array
  5. Find the smallest and second smallest elements in an array
  6. Maximum and minimum of an array using minimum number of comparisons
  7. Find the largest pair sum in an unsorted array
  8. Find all elements in array which have at-least two greater elements
  9. Count Strictly Increasing Subarrays
  10. Minimum product of k integers in an array of positive Integers
  11. K’th Smallest/Largest Element using STL
• Intermediate:
  1. K’th Smallest/Largest Element in Unsorted Array
  2. K’th Smallest/Largest Element in Unsorted Array | Expected Linear Time
  3. K’th Smallest/Largest Element in Unsorted Array | Worst case Linear Time
  4. Find the smallest missing number
  5. K’th largest element in a stream
  6. Next Greater Element
  7. Maximum sum such that no two elements are adjacent
  8. K-th Largest Sum Contiguous Subarray
  9. K maximum sums of non-overlapping contiguous sub-arrays
  10. Find k pairs with smallest sums in two arrays
  11. Find k numbers with most occurrences in the given array
  12. Longest Monotonically Increasing Subsequence Size (N log N)
• Hard:
  1. Kth smallest element in a row-wise and column-wise sorted 2D array
  2. Median of Stream of Running Integers using STL
  3. k smallest elements in same order using O(1) extra space
  4. Maximum of all subarrays of size k
  5. Find the smallest positive number missing from an unsorted array | Set 1
  6. Find the maximum repeating number in O(n) time and O(1) extra space
  7. Minimum number of elements to add to make median equals x
  8. k-th smallest absolute difference of two elements in an array
  9. Smallest greater elements in whole array
  10. K maximum sums of overlapping contiguous sub-arrays

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