What is Order Statistics?
The ith order statistics is defined as the value that comes in the ith position of the N element sequence when the sequence is sorted in increasing order.
In simple terms, the order statistics is the ith 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
Easy Practice Problems in Array Order Statistics:
- Program to find largest element in an array
- Find the largest three elements in an array
- Program for Mean and median of an unsorted array
- Find Second largest element in an array
- Find the smallest and second smallest elements in an array
- Maximum and minimum of an array using minimum number of comparisons
- Find the largest pair sum in an unsorted array
- Find all elements in array which have at-least two greater elements
- Count Strictly Increasing Subarrays
- Minimum product of k integers in an array of positive Integers
- K’th Smallest/Largest Element using STL
Medium Practice Problems in Array Order Statistics:
- K’th Smallest/Largest Element in Unsorted Array
- K’th Smallest/Largest Element in Unsorted Array | Expected Linear Time
- K’th Smallest/Largest Element in Unsorted Array | Worst case Linear Time
- Find the smallest missing number
- K’th largest element in a stream
- Next Greater Element
- Maximum sum such that no two elements are adjacent
- K-th Largest Sum Contiguous Subarray
- K maximum sums of non-overlapping contiguous sub-arrays
- Find k pairs with smallest sums in two arrays
- Find k numbers with most occurrences in the given array
- Longest Monotonically Increasing Subsequence Size (N log N)
Hard Practice Problems in Array Order Statistics:
- Kth smallest element in a row-wise and column-wise sorted 2D array
- Median of Stream of Running Integers using STL
- k smallest elements in same order using O(1) extra space
- Maximum of all subarrays of size k
- Find the smallest positive number missing from an unsorted array | Set 1
- Find the maximum repeating number in O(n) time and O(1) extra space
- Minimum number of elements to add to make median equals x
- k-th smallest absolute difference of two elements in an array
- Smallest greater elements in whole array
- K maximum sums of overlapping contiguous sub-arrays
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